# strtab

key: ack-nhfb
filename: elefunt.bib
value:
Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, e-mail: path |beebe@math.utah.edu|, path |beebe@acm.org|, path |beebe@computer.org| (Internet), URL: path |https://www.math.utah.edu/~beebe/|

entry:
@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}


key: ack-mv
filename: elefunt.bib
value:
Matti Vuorinen, Department of Mathematics and Statistics, University of Turku, Vesilinnantie 5, 20014 Turku, Finland, e-mail: path |vuorinen@utu.fi|, URL: path |http://users.utu.fi/vuorinen/|

entry:
@String{ack-mv =  "Matti Vuorinen,
                   Department of Mathematics and Statistics,
                   University of Turku,
                   Vesilinnantie 5,
                   20014 Turku, Finland,
                   e-mail: \path|vuorinen@utu.fi|,
                   URL: \path|http://users.utu.fi/vuorinen/|"}


key: ack-nj
filename: elefunt.bib
value:
Norbert Juffa, 2445 Mission College Blvd., Santa Clara, CA 95054, USA, e-mail: path |norbert@@iit.com|

entry:
@String{ack-nj =  "Norbert Juffa,
                  2445 Mission College Blvd.,
                  Santa Clara, CA 95054,
                  USA,
                  e-mail: \path|norbert@@iit.com|"}


key: ack-rfb
filename: elefunt.bib
value:
Ronald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: path =boisvert@cam.nist.gov=

entry:
@String{ack-rfb = "Ronald F. Boisvert,
                  Applied and Computational Mathematics Division,
                  National Institute of Standards and Technology,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975 3812,
                  e-mail: \path=boisvert@cam.nist.gov="}


key: inst-ANL:adr
value: 9700 South Cass Avenue, Argonne, IL 60439-4801, USA
filename: elefunt.bib
entry:
@String{inst-ANL:adr            = "9700 South Cass Avenue, Argonne, IL
                                  60439-4801, USA"}


key: inst-BERKELEY-CS
value: Department of Computer Science, University of California
filename: elefunt.bib
entry:
@String{inst-BERKELEY-CS        = "Department of Computer Science, University
                                  of California"}


key: inst-CECM
value: Centre for Experimental and Constructive Mathematics (CECM) at Simon Fraser University (SFU)
filename: elefunt.bib
entry:
@String{inst-CECM               = "Centre for Experimental and Constructive
                                  Mathematics (CECM) at Simon Fraser
                                  University (SFU)"}


key: inst-CPAM-UCB
value: Center for Pure and Applied Mathematics, University of California, Berkeley
filename: elefunt.bib
entry:
@String{inst-CPAM-UCB           = "Center for Pure and Applied Mathematics,
                                  University of California, Berkeley"}


key: inst-CSC
value: Center for Scientific Computing, Department of Mathematics, University of Utah
filename: elefunt.bib
entry:
@String{inst-CSC                = "Center for Scientific Computing,
                                  Department of Mathematics, University of
                                  Utah"}


key: inst-IPTC
value: Institut fur Physikalische und Theoretische Chemie
filename: elefunt.bib
entry:
@String{inst-IPTC               = "{Institut f{\"u}r Physikalische und
                                  Theoretische Chemie}"}


key: inst-IPTC:adr
value: Universitat Regensburg, D-93040 Regensburg
filename: elefunt.bib
entry:
@String{inst-IPTC:adr           = "{Universit{\"a}t Regensburg, D-93040
                                  Regensburg}"}


key: inst-LORIA-INRIA-LORRAINE:adr
filename: elefunt.bib
value:
Batiment A, Technopole de Nancy-Brabois, 615 rue du jardin botanique, F-54602 Villers-les-Nancy Cedex, France

entry:
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
                                  Nancy-Brabois, 615 rue du jardin
                                  botanique, F-54602
                                  Villers-l{\`e}s-Nancy Cedex, France"}


key: inst-MATH-NPS
value: Department of Mathematics, Naval Postgraduate School
filename: elefunt.bib
entry:
@String{inst-MATH-NPS           = "Department of Mathematics, Naval Postgraduate
                                  School"}


key: inst-STAN-CS
value: Stanford University, Department of Computer Science
filename: elefunt.bib
entry:
@String{inst-STAN-CS            = "Stanford University, Department of
                                  Computer Science"}


key: j-ANN-INST-STAT-MATH-TOKYO
value: Annals of the Institute of Statistical Mathematics
filename: elefunt.bib
entry:
@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of
                                  Statistical Mathematics"}


key: j-ANN-MATH-ARTIF-INTELL
value: Annals of Mathematics and Artificial Intelligence
filename: elefunt.bib
entry:
@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
                                  Intelligence"}


key: j-APPL-COMPUT-HARMON-ANAL
filename: elefunt.bib
value:
Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications

entry:
@String{j-APPL-COMPUT-HARMON-ANAL = "Applied and Computational Harmonic
                                  Analysis. Time-Frequency and
                                  Time-Scale Analysis, Wavelets,
                                  Numerical Algorithms, and
                                  Applications"}


key: j-APPL-NUM-MATH
value: Applied Numerical Mathematics: Transactions of IMACS
filename: elefunt.bib
entry:
@String{j-APPL-NUM-MATH         = "Applied Numerical Mathematics: Transactions
                                  of IMACS"}


key: j-AUTOMATICA
value: Automatica: the journal of IFAC, the International Federation of Automatic Control
filename: elefunt.bib
entry:
@String{j-AUTOMATICA            = "Automatica: the journal of IFAC, the
                                  International Federation of Automatic
                                  Control"}


key: j-BIT
value: BIT (Nordisk tidskrift for informationsbehandling)
filename: elefunt.bib
entry:
@String{j-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}


key: j-BRITISH-J-HIST-MATH
value: British Journal for the History of Mathematics
filename: elefunt.bib
entry:
@String{j-BRITISH-J-HIST-MATH   = "British Journal for the History of
                                  Mathematics"}


key: j-BRITISH-J-PHILOS-SCI
value: British Journal for the Philosophy of Science
filename: elefunt.bib
entry:
@String{j-BRITISH-J-PHILOS-SCI  = "British Journal for the Philosophy of
                                  Science"}


key: j-BULL-AMS
value: Bulletin of the American Mathematical Society
filename: elefunt.bib
entry:
@String{j-BULL-AMS              = "Bulletin of the American Mathematical
                                  Society"}


key: j-C-R-ACAD-BULGARE-SCI
value: Comptes rendus de l'Academie bulgare des sciences
filename: elefunt.bib
entry:
@String{j-C-R-ACAD-BULGARE-SCI  = "Comptes rendus de l'Acad{\'e}mie bulgare
                                  des sciences"}


key: j-CAN-J-MATH
value: Canadian Journal of Mathematics = Journal canadien de mathematiques
filename: elefunt.bib
entry:
@String{j-CAN-J-MATH            = "Canadian Journal of Mathematics =
                                   Journal canadien de
                                   math{\'e}matiques"}


key: j-CAN-MATH-BULL
value: Bulletin canadien de mathematiques = Canadian Mathematical Bulletin
filename: elefunt.bib
entry:
@String{j-CAN-MATH-BULL         = "Bulletin canadien de
                                  math\-{\'e}\-mat\-iques = Canadian
                                  Mathematical Bulletin"}


key: j-CENTAURUS
value: Centaurus: An International Journal of the History of Science and its Cultural Aspects
filename: elefunt.bib
entry:
@String{j-CENTAURUS             = "Centaurus: An International Journal of the
                                  History of Science and its Cultural Aspects"}


key: j-COMM-PURE-APPL-MATH
value: Communications on Pure and Applied Mathematics (New York)
filename: elefunt.bib
entry:
@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}


key: j-COMMUN-STAT-SIMUL-COMPUT
value: Communications in Statistics: Simulation and Computation
filename: elefunt.bib
entry:
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}


key: j-COMMUN-STAT-THEORY-METH
value: Communications in Statistics: Theory and Methods
filename: elefunt.bib
entry:
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}


key: j-COMPUT-APPL-MATH
value: Journal of Computational and Applied Mathematics
filename: elefunt.bib
entry:
@String{j-COMPUT-APPL-MATH      = "Journal of Computational and Applied
                                  Mathematics"}


key: j-COMPUT-MATH-MATH-PHYS
value: Computational Mathematics and Mathematical Physics
filename: elefunt.bib
entry:
@String{j-COMPUT-MATH-MATH-PHYS = "Computational Mathematics and Mathematical
                                  Physics"}


key: j-COMPUTING
value: Computing: Archiv fur informatik und numerik
filename: elefunt.bib
entry:
@String{j-COMPUTING             = "Computing: Archiv fur informatik und
                                  numerik"}


key: j-ELECT-NOTES-THEOR-COMP-SCI
value: Electronic Notes in Theoretical Computer Science
filename: elefunt.bib
entry:
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
                                  Computer Science"}


key: j-ELECTRON-TRANS-NUMER-ANAL
value: Electronic Transactions on Numerical Analysis (ETNA)
filename: elefunt.bib
entry:
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
                                Analysis (ETNA)"}


key: j-HEWLETT-PACKARD-J
value: Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company
filename: elefunt.bib
entry:
@String{j-HEWLETT-PACKARD-J     = "Hew\-lett-Pack\-ard Journal: technical
                                  information from the laboratories of
                                  Hew\-lett-Pack\-ard Company"}


key: j-HIST-SCI-2
filename: elefunt.bib
value:
Historia Scientiarum. Second Series. International Journal of the History of Science Society of Japan

entry:
@String{j-HIST-SCI-2            = "Historia Scientiarum. Second Series.
                                  International Journal of the History
                                  of Science Society of Japan"}


key: j-IEEE-TRANS-CIRCUITS-SYST-2
value: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE Transactions on Circuits and
                                  Systems. 2, Analog and Digital Signal
                                  Processing"}


key: j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS
value: IEEE Transactions on Circuits and Systems II: Express Briefs
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
                                  Circuits and Systems II: Express Briefs"}


key: j-IEEE-TRANS-EMERG-TOP-COMPUT
value: IEEE Transactions on Emerging Topics in Computing
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
                                  Computing"}


key: j-IEEE-TRANS-MICROWAVE-THEORY-TECH
value: IEEE Transactions on Microwave Theory and Techniques
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-MICROWAVE-THEORY-TECH = "IEEE Transactions on Microwave
                                  Theory and Techniques"}


key: j-IEEE-TRANS-PAR-DIST-SYS
value: IEEE Transactions on Parallel and Distributed Systems
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                    Distributed Systems"}


key: j-IEEE-TRANS-VLSI-SYST
value: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-VLSI-SYST  = "IEEE Transactions on Very Large Scale
                                  Integration (VLSI) Systems"}


key: j-IEEE-TRANS-WIREL-COMMUN
value: IEEE Transactions on Wireless Communications
filename: elefunt.bib
entry:
@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless
                                  Communications"}


key: j-IJSAHPC
value: The International Journal of Supercomputer Applications and High Performance Computing
filename: elefunt.bib
entry:
@String{j-IJSAHPC               = "The International Journal of Supercomputer
                                  Applications and High Performance Computing"}


key: j-INT-J-COMPUT-INF-SCI
value: International Journal of Computer and Information Sciences
filename: elefunt.bib
entry:
@String{j-INT-J-COMPUT-INF-SCI  = "International Journal of Computer and
                                  Information Sciences"}


key: j-INT-J-COMPUT-MATH
value: International Journal of Computer Mathematics
filename: elefunt.bib
entry:
@String{j-INT-J-COMPUT-MATH     = "International Journal of Computer
                                  Mathematics"}


key: j-INT-J-HIGH-SPEED-COMPUTING
value: International Journal of High Speed Computing
filename: elefunt.bib
entry:
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
                                  Computing"}


key: j-INT-J-MATH-EDU-SCI-TECH
value: International journal of mathematical education in science and technology
filename: elefunt.bib
entry:
@String{j-INT-J-MATH-EDU-SCI-TECH = "International journal of mathematical
                                  education in science and technology"}


key: j-INT-J-MATH-MATH-SCI
value: International Journal of Mathematics and Mathematical Sciences
filename: elefunt.bib
entry:
@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}


key: j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER
value: International Journal on Software Tools for Technology Transfer (STTT)
filename: elefunt.bib
entry:
@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
                                 Software Tools for Technology Transfer (STTT)"}


key: j-INTERVAL-COMP
value: Interval Computations = Interval'nye vychisleniia
filename: elefunt.bib
entry:
@String{j-INTERVAL-COMP         = "Interval Computations = Interval'nye
                                  vychisleniia"}


key: j-J-ACM
value: Journal of the Association for Computing Machinery
filename: elefunt.bib
entry:
@String{j-J-ACM                 = "Journal of the Association for Computing
                                  Machinery"}


key: j-J-AM-STAT-ASSOC
value: Journal of the American Statistical Association
filename: elefunt.bib
entry:
@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}


key: j-J-AUSTRAL-MATH-SOC-SER-B
value: Journal of the Australian Mathematical Society: Series B, Applied Mathematics
filename: elefunt.bib
entry:
@String{j-J-AUSTRAL-MATH-SOC-SER-B = "Journal of the Australian Mathematical
                                  Society: Series B, Applied Mathematics"}


key: j-J-COMPUT-APPL-MATH
value: Journal of Computational and Applied Mathematics
filename: elefunt.bib
entry:
@String{j-J-COMPUT-APPL-MATH    = "Journal of Computational and Applied
                                  Mathematics"}


key: j-J-COMPUT-GRAPH-STAT
value: Journal of Computational and Graphical Statistics
filename: elefunt.bib
entry:
@String{j-J-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical
                                Statistics"}


key: j-J-INST-MATH-APPL
value: Journal of the Institute of Mathematics and its Applications
filename: elefunt.bib
entry:
@String{j-J-INST-MATH-APPL      = "Journal of the Institute of Mathematics and
                                  its Applications"}


key: j-J-KOREA-INFO-SCI-SOCIETY
value: Journal of the Korea Information Science Society = Chongbo Kwahakhoe nonmunji
filename: elefunt.bib
entry:
@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
                                  Society = Chongbo Kwahakhoe nonmunji"}


key: j-J-MATH-ANAL-APPL
value: Journal of Mathematical Analysis and Applications
filename: elefunt.bib
entry:
@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}


key: j-J-NUMER-METHODS-COMPUT-APPL
value: Journal on Numerical Methods and Computer Applications
filename: elefunt.bib
entry:
@String{j-J-NUMER-METHODS-COMPUT-APPL = "Journal on Numerical Methods and
                                  Computer Applications"}


key: j-J-OPT-THEORY-APPL
value: Journal of Optimization Theory and Applications
filename: elefunt.bib
entry:
@String{j-J-OPT-THEORY-APPL     = "Journal of Optimization Theory and
                                  Applications"}


key: j-J-PAR-DIST-COMP
value: Journal of Parallel and Distributed Computing
filename: elefunt.bib
entry:
@String{j-J-PAR-DIST-COMP       = "Journal of Parallel and Distributed
                                  Computing"}


key: j-J-R-STAT-SOC-SER-B-METHODOL
value: Journal of the Royal Statistical Society. Series B (Methodological)
filename: elefunt.bib
entry:
@String{j-J-R-STAT-SOC-SER-B-METHODOL = "Journal of the Royal Statistical
                                  Society. Series B (Methodological)"}


key: j-J-R-STAT-SOC-SER-D-STATISTICIAN
value: Journal of the Royal Statistical Society. Series D (The Statistician)
filename: elefunt.bib
entry:
@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
                                  Society. Series D (The Statistician)"}


key: j-J-RES-NATL-BUR-STAND-1934
value: Journal of Research of the National Bureau of Standards (1934)
filename: elefunt.bib
entry:
@String{j-J-RES-NATL-BUR-STAND-1934 = "Journal of Research of the National
                                  Bureau of Standards (1934)"}


key: j-J-RES-NATL-BUR-STAND-B
filename: elefunt.bib
value:
Journal of Research of the National Bureau of Standards. Section B, Mathematics and Mathematical Physics

entry:
@String{j-J-RES-NATL-BUR-STAND-B = "Journal of Research of the National Bureau
                                  of Standards. Section B, Mathematics
                                  and Mathematical Physics"}


key: j-J-STAT-COMPUT-SIMUL
value: Journal of Statistical Computation and Simulation
filename: elefunt.bib
entry:
@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                  Simulation"}


key: j-JETC
value: ACM Journal on Emerging Technologies in Computing Systems (JETC)
filename: elefunt.bib
entry:
@String{j-JETC                  = "ACM Journal on Emerging Technologies
                                  in Computing Systems (JETC)"}


key: j-MATH-MODEL-NUM-ANA
filename: elefunt.bib
value:
Mathematical modelling and numerical analysis = Modelisation mathematique et analyse numerique: $M^2AN$

entry:
@String{j-MATH-MODEL-NUM-ANA    = "Mathematical modelling and numerical
                                  analysis = Modelisation math{\'e}matique et
                                  analyse num{\'e}rique: $M^2AN$"}


key: j-MATH-TABLES-AIDS-COMPUT
value: Mathematical Tables and Aids to Computation
filename: elefunt.bib
entry:
@String{j-MATH-TABLES-AIDS-COMPUT = "Mathematical Tables and Aids to
                                  Computation"}


key: j-MATH-TABLES-OTHER-AIDS-COMPUT
value: Mathematical Tables and Other Aids to Computation
filename: elefunt.bib
entry:
@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
                                  to Computation"}


key: j-NAMS
value: Notices of the American Mathematical Society
filename: elefunt.bib
entry:
@String{j-NAMS                  = "Notices of the American Mathematical
                                  Society"}


key: j-NORDISK-TIDSKR-INFORM-BEHAND
value: Nordisk tidskrift for informationsbehandling
filename: elefunt.bib
entry:
@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
                                  informationsbehandling"}


key: j-PACMPL
value: Proceedings of the ACM on Programming Languages (PACMPL)
filename: elefunt.bib
entry:
@String{j-PACMPL                = "Proceedings of the ACM on Programming
                                   Languages (PACMPL)"}


key: j-PHILOS-TRANS-R-SOC-LOND
value: Philosophical Transactions of the Royal Society of London
filename: elefunt.bib
entry:
@String{j-PHILOS-TRANS-R-SOC-LOND = "Philosophical Transactions of the Royal
                                  Society of London"}


key: j-PHYS-REV-E
value: Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)
filename: elefunt.bib
entry:
@String{j-PHYS-REV-E            = "Physical Review E (Statistical physics,
                                  plasmas, fluids, and related
                                  interdisciplinary topics)"}


key: j-PROBAB-ENGRG-INFORM-SCI
value: Probability in the Engineering and Informational Sciences
filename: elefunt.bib
entry:
@String{j-PROBAB-ENGRG-INFORM-SCI = "Probability in the Engineering and
                                  Informational Sciences"}


key: j-PROC-AM-MATH-SOC
value: Proceedings of the American Mathematical Society
filename: elefunt.bib
entry:
@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}


key: j-PROC-CAMBRIDGE-PHIL-SOC
value: Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences
filename: elefunt.bib
entry:
@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge Philosophical
                                  Society. Mathematical and physical sciences"}


key: j-PROC-IEE
value: Proceedings of the Institution of Electrical Engineers
filename: elefunt.bib
entry:
@String{j-PROC-IEE              = "Proceedings of the Institution of Electrical
                                  Engineers"}


key: j-PROC-LONDON-MATH-SOC-1
value: Proceedings of the London Mathematical Society. First Series
filename: elefunt.bib
entry:
@String{j-PROC-LONDON-MATH-SOC-1 = "Proceedings of the London Mathematical
                                  Society. First Series"}


key: j-PROC-LONDON-MATH-SOC-2
value: Proceedings of the London Mathematical Society. Second Series
filename: elefunt.bib
entry:
@String{j-PROC-LONDON-MATH-SOC-2 = "Proceedings of the London Mathematical
                                  Society. Second Series"}


key: j-PROC-LONDON-MATH-SOC-3
value: Proceedings of the London Mathematical Society. Third Series
filename: elefunt.bib
entry:
@String{j-PROC-LONDON-MATH-SOC-3  = "Proceedings of the London Mathematical
                                  Society. Third Series"}


key: j-PROC-R-SOC-LOND-SER-A-MATH-PHYS
filename: elefunt.bib
value:
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

entry:
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS = "Proceedings of the Royal Society of
                                  London. Series A, Containing Papers of a
                                  Mathematical and Physical Character"}


key: j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI
value: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
filename: elefunt.bib
entry:
@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI = "Proceedings of the Royal
                                  Society of London. Series A, Mathematical
                                  and physical sciences"}


key: j-PROG-COMP-SOFT
value: Programming and Computer Software; translation of Programmirovaniye (Moscow, USSR) Plenum
filename: elefunt.bib
entry:
@String{j-PROG-COMP-SOFT        = "Programming and Computer Software;
                                  translation of Programmirovaniye (Moscow,
                                  USSR) Plenum"}


key: j-REND-CIRC-MAT
value: Rendiconti del Circolo matematico di Palermo
filename: elefunt.bib
entry:
@String{j-REND-CIRC-MAT         = "Rendiconti del Circolo matematico di
                                  Palermo"}


key: j-SIAM-J-MAT-ANA-APPL
value: SIAM Journal on Matrix Analysis and Applications
filename: elefunt.bib
entry:
@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}


key: j-SIAM-J-NUM-ANALYSIS-B
value: Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis
filename: elefunt.bib
entry:
@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
                                  Applied Mathematics: Series B, Numerical
                                  Analysis"}


key: j-SIAM-J-SCI-STAT-COMP
value: SIAM Journal on Scientific and Statistical Computing
filename: elefunt.bib
entry:
@String{j-SIAM-J-SCI-STAT-COMP  = "SIAM Journal on Scientific and Statistical
                                  Computing"}


key: j-SIGCSE
value: SIGCSE Bulletin (ACM Special Interest Group on Computer Science Education)
filename: elefunt.bib
entry:
@String{j-SIGCSE                = "SIGCSE Bulletin (ACM Special Interest Group
                                  on Computer Science Education)"}


key: j-SIGSAM
value: SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)
filename: elefunt.bib
entry:
@String{j-SIGSAM                = "SIGSAM Bulletin (ACM Special Interest Group
                                  on Symbolic and Algebraic Manipulation)"}


key: j-TECS
value: ACM Transactions on Embedded Computing Systems
filename: elefunt.bib
entry:
@String{j-TECS                  = "ACM Transactions on Embedded Computing
                                  Systems"}


key: j-TELO
value: ACM Transactions on Evolutionary Learning and Optimization (TELO)
filename: elefunt.bib
entry:
@String{j-TELO                  = "ACM Transactions on Evolutionary
                                  Learning and Optimization (TELO)"}


key: j-TRANS-AM-MATH-SOC
value: Transactions of the American Mathematical Society
filename: elefunt.bib
entry:
@String{j-TRANS-AM-MATH-SOC     = "Transactions of the American Mathematical
                                  Society"}


key: j-TRANS-INFO-PROCESSING-SOC-JAPAN
value: Transactions of the Information Processing Society of Japan
filename: elefunt.bib
entry:
@String{j-TRANS-INFO-PROCESSING-SOC-JAPAN = "Transactions of the Information
                                  Processing Society of Japan"}


key: j-TRANS-SOC-COMP-SIM
value: Transactions of the Society for Computer Simulation
filename: elefunt.bib
entry:
@String{j-TRANS-SOC-COMP-SIM    = "Transactions of the Society for Computer
                                  Simulation"}


key: j-TRETS
value: ACM Transactions on Reconfigurable Technology and Systems (TRETS)
filename: elefunt.bib
entry:
@String{j-TRETS                 = "ACM Transactions on Reconfigurable Technology
                                  and Systems (TRETS)"}


key: j-USSR-COMP-MATH-MATH-PHYS
value: U.S.S.R. Computational Mathematics and Mathematical Physics
filename: elefunt.bib
entry:
@String{j-USSR-COMP-MATH-MATH-PHYS = "U.S.S.R. Computational Mathematics and
                                  Mathematical Physics"}


key: j-Z-ANAL-ANWEND
value: Zeitschrift fur Analysis und ihre Anwendungen
filename: elefunt.bib
entry:
@String{j-Z-ANAL-ANWEND         = "Zeitschrift f{\"u}r Analysis und ihre
                                  Anwendungen"}


key: j-Z-ANGE-MATH-MECH
value: Zeitschrift fur Angewandte Mathematik und Mechanik
filename: elefunt.bib
entry:
@String{j-Z-ANGE-MATH-MECH      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik}"}


key: j-Z-ANGE-MATH-PHYS
value: Zeitschrift fur Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics
filename: elefunt.bib
entry:
@String{j-Z-ANGE-MATH-PHYS      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Physik = Journal of Applied Mathematics
                                  and Physics}"}


key: j-Z-MATH-LOGIK-GRUNDL-MATH
value: Zeitschrift fur mathematische Logik und Grundlagen der Mathematik
filename: elefunt.bib
entry:
@String{j-Z-MATH-LOGIK-GRUNDL-MATH = "Zeitschrift f{\"u}r mathematische
                                  Logik und Grundlagen der Mathematik"}


key: pub-BALTZER
value: J. C. Baltzer AG, Scientific Publishing Company
filename: elefunt.bib
entry:
@String{pub-BALTZER             = "J. C. Baltzer AG, Scientific
                                  Publishing Company"}


key: pub-BIRKHAUSER:adr
value: Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland
filename: elefunt.bib
entry:
@String{pub-BIRKHAUSER:adr      = "Cambridge, MA, USA; Berlin, Germany; Basel,
                                  Switzerland"}


key: pub-CRC:adr
value: 2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA
filename: elefunt.bib
entry:
@String{pub-CRC:adr             = "2000 N.W. Corporate Blvd., Boca Raton,
                                  FL 33431-9868, USA"}


key: pub-IEEE:adr
value: 1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA
filename: elefunt.bib
entry:
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300, Silver
                                   Spring, MD 20910, USA"}


key: pub-IOS:adr
value: Postal Drawer 10558, Burke, VA 2209-0558, USA
filename: elefunt.bib
entry:
@String{pub-IOS:adr             = "Postal Drawer 10558, Burke, VA
                                  2209-0558, USA"}


key: pub-ISO
value: International Organization for Standardization
filename: elefunt.bib
entry:
@String{pub-ISO                 = "International Organization for
                                  Standardization"}


key: pub-REIDEL:adr
value: Dordrecht, The Netherlands; Boston, MA, USA; Lancaster, UK; Tokyo, Japan
filename: elefunt.bib
entry:
@String{pub-REIDEL:adr          = "Dordrecht, The Netherlands; Boston, MA, USA;
                                   Lancaster, UK; Tokyo, Japan"}


key: pub-SIAM
value: Society for Industrial and Applied Mathematics
filename: elefunt.bib
entry:
@String{pub-SIAM                = "Society for Industrial and Applied
                                  Mathematics"}


key: pub-SPIE
value: Society of Photo-optical Instrumentation Engineers (SPIE)
filename: elefunt.bib
entry:
@String{pub-SPIE                = "Society of Photo-optical
                                  Instrumentation Engineers (SPIE)"}


key: pub-SV:adr
value: Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc.
filename: elefunt.bib
entry:
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}


key: pub-WORLD-SCI
value: World Scientific Publishing Co. Pte. Ltd.
filename: elefunt.bib
entry:
@String{pub-WORLD-SCI           = "World Scientific Publishing
                                  Co. Pte. Ltd."}


key: pub-WORLD-SCI:adr
value: P. O. Box 128, Farrer Road, Singapore 9128
filename: elefunt.bib
entry:
@String{pub-WORLD-SCI:adr       = "P. O. Box 128, Farrer Road,
                                  Singapore 9128"}


key: ser-APPL-MATH-SER-NBS
value: Applied Mathematics Series / National Bureau of Standards
filename: elefunt.bib
entry:
@String{ser-APPL-MATH-SER-NBS   = "Applied Mathematics Series / National Bureau
                                  of Standards"}


# bibtab

bibtype: article
filename: elefunt.bib
label: Horner:1819:XNM
author: William George Horner
title: XXI. A new method of solving numerical equations of all orders, by continuous approximation
journal: j-PHILOS-TRANS-R-SOC-LOND
volume: 109
pages: 308--335
year: 1819
CODEN: PTRSAV
DOI: https://doi.org/10.1098/rstl.1819.0023
ISSN: 0370-2316 (print), 2053-9207 (electronic) OR 03702316 (print), 20539207 (electronic)
bibdate: Sat Oct 21 12:27:25 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.21 12:27:25 ???
URL: https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1819.0023
fjournal: Philosophical Transactions of the Royal Society of London
keywords: Horner's nested form; number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
journalURL: http://rsta.royalsocietypublishing.org/
rawauthor: William George Horner
rawtitle: {XXI}. {A} new method of solving numerical equations of all orders, by continuous approximation
entry:
@Article{Horner:1819:XNM,
  author =       "William George Horner",
  title =        "{XXI}. {A} new method of solving numerical equations
                 of all orders, by continuous approximation",
  journal =      j-PHILOS-TRANS-R-SOC-LOND,
  volume =       "109",
  pages =        "308--335",
  year =         "1819",
  CODEN =        "PTRSAV",
  DOI =          "https://doi.org/10.1098/rstl.1819.0023",
  ISSN =         "0370-2316 (print), 2053-9207 (electronic)",
  bibdate =      "Sat Oct 21 12:27:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1819.0023",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Transactions of the Royal Society of
                 London",
  journal-URL =  "http://rsta.royalsocietypublishing.org/",
  keywords =     "Horner's nested form; number of multiplications to
                 evaluate a polynomial",
  read =         "1 July 1819",
  remark-1 =     "Communicated by Davies Gilbert, Esq. F.R.S.",
  remark-2 =     "On page 310 of this paper, Horner gives the steps of
                 the nested form as a chain of fused multiply-add
                 operations, and credits this idea to Joseph-Louis
                 Lagrange (1736--1813) in his 1813 book
                 \booktitle{Th{\'e}orie des fonctions analytiques}.",
  remark-3 =     "Knuth \cite[p. 486]{Knuth:1998:SA} gives this paper as
                 the reference for Horner's nested form, but also
                 reports that Isaac Newton used it in unpublished notes
                 150 years earlier, and that it was employed by the
                 Chinese in the 13th century CE.",
}


bibtype: article
filename: elefunt.bib
label: Lovelace:1843:SAE
author: Ada Augusta Lovelace
title: Sketch of the Analytical Engine
journal: Scientific Memoirs
volume: 3
pages: 666--731
year: 1843
bibdate: Sun Aug 18 09:31:28 2013
bibtimestamp: 2013.08.18 09:31:28 ???
note: Reprinted in cite Lovelace:1989:SAE.
keywords: Bernoulli numbers
acknowledgement: ack-nhfb
rawauthor: Ada Augusta Lovelace
rawnote: Reprinted in \cite{Lovelace:1989:SAE}.
rawtitle: Sketch of the {Analytical Engine}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
This paper contains what some view as possibly the world's first computer program, a recipe for computing Bernoulli numbers on Charles Babbage's Analytical Engine, which was not successfully constructed until more than a century after their deaths, in 1852 and 1871, respectively. It is not, however, the world's first computational algorithm: that credit is given to Euclid's procedure for fast computation of the greatest common denominator, about 300 BCE, but possibly known a few hundred years earlier.

entry:
@Article{Lovelace:1843:SAE,
  author =       "Ada Augusta Lovelace",
  title =        "Sketch of the {Analytical Engine}",
  journal =      "Scientific Memoirs",
  volume =       "3",
  number =       "??",
  pages =        "666--731",
  month =        "????",
  year =         "1843",
  bibdate =      "Sun Aug 18 09:31:28 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprinted in \cite{Lovelace:1989:SAE}.",
  acknowledgement = ack-nhfb,
  keywords =     "Bernoulli numbers",
  remark =       "This paper contains what some view as possibly the
                 world's first computer program, a recipe for computing
                 Bernoulli numbers on Charles Babbage's Analytical
                 Engine, which was not successfully constructed until
                 more than a century after their deaths, in 1852 and
                 1871, respectively. It is not, however, the world's
                 first computational algorithm: that credit is given to
                 Euclid's procedure for fast computation of the greatest
                 common denominator, about 300 BCE, but possibly known a
                 few hundred years earlier.",
}


bibtype: book
filename: elefunt.bib
label: Greenhill:1892:AEF
author: Alfred George Greenhill
title: The Applications of Elliptic Functions
publisher: pub-MACMILLAN
address: pub-MACMILLAN:adr
pages: xi + 357
year: 1892
bibdate: Wed Mar 15 08:21:33 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 08:21:33 ???
remark: Reprinted in cite Greenhill:1959:AEF.
acknowledgement: ack-nhfb
authordates: 1847--1927
rawauthor: Alfred George Greenhill
rawtitle: The Applications of Elliptic Functions
entry:
@Book{Greenhill:1892:AEF,
  author =       "Alfred George Greenhill",
  title =        "The Applications of Elliptic Functions",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  pages =        "xi + 357",
  year =         "1892",
  bibdate =      "Wed Mar 15 08:21:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1847--1927",
  remark =       "Reprinted in \cite{Greenhill:1959:AEF}.",
}


bibtype: article
filename: elefunt.bib
label: Dawson:1897:NV
author: H. G. Dawson
title: On the Numerical Value of $ int _0^h e^x^2 d x $
journal: j-PROC-LONDON-MATH-SOC-1
volume: s1-29
number: 1
pages: 519--522
month: nov
monthnumber: 11
year: 1897
CODEN: PLMTAL
DOI: https://doi.org/10.1112/plms/s1-29.1.519
ISSN: 0024-6115 (print), 1460-244X (electronic) OR 00246115 (print), 1460244X (electronic)
ISSNL: 0024-6115 OR 00246115
bibdate: Sat Jun 12:08:16 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
fjournal: Proceedings of the London Mathematical Society. First Series
remark: This paper is the origin of Dawson's integral and the function dawson(x).
journalURL: http://plms.oxfordjournals.org/content/by/year
rawauthor: H. G. Dawson
rawtitle: On the Numerical Value of $ \int_0^h e^{x^2} \, d x $
entry:
@Article{Dawson:1897:NV,
  author =       "H. G. Dawson",
  title =        "On the Numerical Value of $ \int_0^h e^{x^2} \, d x
                 $",
  journal =      j-PROC-LONDON-MATH-SOC-1,
  volume =       "s1-29",
  number =       "1",
  pages =        "519--522",
  month =        nov,
  year =         "1897",
  CODEN =        "PLMTAL",
  DOI =          "https://doi.org/10.1112/plms/s1-29.1.519",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  bibdate =      "Sat Jun 12:08:16 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  fjournal =     "Proceedings of the London Mathematical Society. First
                 Series",
  journal-URL =  "http://plms.oxfordjournals.org/content/by/year",
  remark =       "This paper is the origin of Dawson's integral and the
                 function dawson(x).",
}


bibtype: book
filename: elefunt.bib
label: Kennelly:1914:TCH
author: Arthur E. (Arthur Edwin) Kennelly
title: Tables of Complex Hyperbolic and Circular Functions
publisher: pub-HARVARD
address: pub-HARVARD:adr
pages: iii + 212
year: 1914
LCCN: QA342 .K45
bibdate: Sat Apr 1 14:49:41 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:49:41 MDT
subject: Exponential functions
acknowledgement: ack-nhfb
authordates: 1861--1939
rawauthor: Arthur E. (Arthur Edwin) Kennelly
rawtitle: Tables of Complex Hyperbolic and Circular Functions
entry:
@Book{Kennelly:1914:TCH,
  author =       "Arthur E. (Arthur Edwin) Kennelly",
  title =        "Tables of Complex Hyperbolic and Circular Functions",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "iii + 212",
  year =         "1914",
  LCCN =         "QA342 .K45",
  bibdate =      "Sat Apr 1 14:49:41 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1861--1939",
  subject =      "Exponential functions",
}


bibtype: book
filename: elefunt.bib
label: Pairman:1919:TDT
author: Eleanor Pairman
title: Tables of the Digamma and Trigamma Functions
volume: I
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: 9 + 11
year: 1919
LCCN: QA47 .T7 no.1
bibdate: Sat Mar 25 16:17:54 2017
bibtimestamp: 2017.03.25 16:17:54 ???
series: Tracts for computers
subject: Gamma functions
acknowledgement: ack-nhfb
rawauthor: Eleanor Pairman
rawtitle: Tables of the Digamma and Trigamma Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.loc.gov:7090/Voyager

remark:
Edited by Karl Pearson. According to cite Davis:1935:EPF, the author coined the phrase `polygamma function' in this booklet. English dictionaries usually do not include the word `polygamma'.

entry:
@Book{Pairman:1919:TDT,
  author =       "Eleanor Pairman",
  title =        "Tables of the Digamma and Trigamma Functions",
  volume =       "I",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "9 + 11",
  year =         "1919",
  LCCN =         "QA47 .T7 no.1",
  bibdate =      "Sat Mar 25 16:17:54 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Tracts for computers",
  acknowledgement = ack-nhfb,
  remark =       "Edited by Karl Pearson. According to
                 \cite{Davis:1935:EPF}, the author coined the phrase
                 `polygamma function' in this booklet. English
                 dictionaries usually do not include the word
                 `polygamma'.",
  subject =      "Gamma functions",
}


bibtype: book
filename: elefunt.bib
label: Kennelly:1921:TCH
author: Arthur Edwin Kennelly
title: Tables of Complex Hyperbolic and Circular Functions
publisher: pub-HARVARD
address: pub-HARVARD:adr
pages: iii + 240
year: 1921
LCCN: QA342 .K45 1921
bibdate: Sat Apr 1 14:49:41 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:49:41 MDT
subject: Functions, Exponential
acknowledgement: ack-nhfb
authordates: 1861--
rawauthor: Arthur Edwin Kennelly
rawtitle: Tables of Complex Hyperbolic and Circular Functions
entry:
@Book{Kennelly:1921:TCH,
  author =       "Arthur Edwin Kennelly",
  title =        "Tables of Complex Hyperbolic and Circular Functions",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "iii + 240",
  year =         "1921",
  LCCN =         "QA342 .K45 1921",
  bibdate =      "Sat Apr 1 14:49:41 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1861--",
  subject =      "Functions, Exponential",
}


bibtype: article
filename: elefunt.bib
label: King:1921:SNF
author: Louis Vessot King
title: On Some New Formulae for the Numerical Calculation of the Mutual Induction of Coaxial Circles
journal: j-PROC-R-SOC-LOND-SER-A-MATH-PHYS
volume: 100
number: 702
pages: 60--66
day: 4
month: oct
monthnumber: 10
year: 1921
DOI: https://doi.org/10.1098/rspa.1921.0070
ISSN: 0950-1207 (print), 2053-9150 (electronic) OR 09501207 (print), 20539150 (electronic)
bibdate: Wed Feb 03 09:07:10 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib
bibtimestamp: 2010.02.03 09:07:10 ???
URL: http://www.jstor.org/stable/93861
acknowledgement: ack-nhfb
journalURL: http://rspa.royalsocietypublishing.org/
rawauthor: Louis Vessot King
rawtitle: On Some New Formulae for the Numerical Calculation of the Mutual Induction of Coaxial Circles
note:
This is the first known publication of the AGM method, discovered by the author in 1913, for computing Jacobian elliptic functions. See also cite King:1924:DNC,King:2007:DNC.

fjournal:
Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

rawnote:
This is the first known publication of the AGM method, discovered by the author in 1913, for computing Jacobian elliptic functions. See also \cite{King:1924:DNC,King:2007:DNC}.

entry:
@Article{King:1921:SNF,
  author =       "Louis Vessot King",
  title =        "On Some New Formulae for the Numerical Calculation of
                 the Mutual Induction of Coaxial Circles",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS,
  volume =       "100",
  number =       "702",
  pages =        "60--66",
  day =          "4",
  month =        oct,
  year =         "1921",
  DOI =          "https://doi.org/10.1098/rspa.1921.0070",
  ISSN =         "0950-1207 (print), 2053-9150 (electronic)",
  bibdate =      "Wed Feb 03 09:07:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "This is the first known publication of the AGM method,
                 discovered by the author in 1913, for computing
                 Jacobian elliptic functions. See also
                 \cite{King:1924:DNC,King:2007:DNC}.",
  URL =          "http://www.jstor.org/stable/93861",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Containing Papers of a Mathematical and Physical
                 Character",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
}


bibtype: book
filename: elefunt.bib
label: King:1924:DNC
author: Louis Vessot King
title: On the Direct Numerical Calculation of Elliptic Functions and Integrals
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: viii + 42
year: 1924
LCCN: QA343
bibdate: Wed Feb 03 08:53:04 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib
bibtimestamp: 2010.02.03 08:53:04 ???
acknowledgement: ack-nhfb
rawauthor: Louis Vessot King
rawtitle: On the Direct Numerical Calculation of Elliptic Functions and Integrals
remark:
The AGM method for Jacobian elliptic functions was discovered by this book's author at McGill University in 1913, first published in cite King:1921:SNF, and then in this monograph (reprinted in cite King:2007:DNC).

entry:
@Book{King:1924:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "viii + 42",
  year =         "1924",
  LCCN =         "QA343",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic functions was
                 discovered by this book's author at McGill University
                 in 1913, first published in \cite{King:1921:SNF}, and
                 then in this monograph (reprinted in
                 \cite{King:2007:DNC}).",
}


bibtype: book
filename: elefunt.bib
label: Johnson:1925:TCT
author: K. S. (Kenneth Simonds) Johnson
title: Transmission Circuits for Telephonic Communication: Methods of Analysis and Design
publisher: D. Van Nostrand Company
address: New York, NY, USA
pages: 334
year: 1925
bibdate: Tue Apr 29 09:51:33 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.04.29 09:51:33 ???
note: Second Printing --- Corrected (1925); Third printing, with corrections and additions (1927).
URL: TK6301 .J6 1927
acknowledgement: ack-nhfb
rawauthor: K. S. (Kenneth Simonds) Johnson
rawnote: Second Printing --- Corrected (1925); Third printing, with corrections and additions (1927).
rawtitle: Transmission Circuits for Telephonic Communication: Methods of Analysis and Design
remark:
According to cite Dempsey:2024:PBI, this book, based on a series of lectures at Bell Telephone Laboratories, was a key source of tabulations of branch cuts for various inverse functions.

entry:
@Book{Johnson:1925:TCT,
  author =       "K. S. (Kenneth Simonds) Johnson",
  title =        "Transmission Circuits for Telephonic Communication:
                 Methods of Analysis and Design",
  publisher =    "D. Van Nostrand Company",
  address =      "New York, NY, USA",
  pages =        "334",
  year =         "1925",
  bibdate =      "Tue Apr 29 09:51:33 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Second Printing --- Corrected (1925); Third printing,
                 with corrections and additions (1927).",
  URL =          "TK6301 .J6 1927",
  acknowledgement = ack-nhfb,
  remark =       "According to \cite{Dempsey:2024:PBI}, this book, based
                 on a series of lectures at Bell Telephone Laboratories,
                 was a key source of tabulations of branch cuts for
                 various inverse functions.",
}


bibtype: article
filename: elefunt.bib
label: Ritt:1925:EFT
author: J. F. Ritt
title: Elementary functions and their inverses
journal: j-TRANS-AM-MATH-SOC
volume: 27
number: 1
pages: 68--90
year: 1925
CODEN: TAMTAM
DOI: https://doi.org/10.1090/S0002-9947-1925-1501299-9
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 30A05 (33B10)
MRnumber: MR1501299
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
URL: http://www.ams.org/journals/tran/1925-027-01/S0002-9947-1925-1501299-9/
fjournal: Transactions of the American Mathematical Society
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/tran/
rawauthor: J. F. Ritt
rawtitle: Elementary functions and their inverses
entry:
@Article{Ritt:1925:EFT,
  author =       "J. F. Ritt",
  title =        "Elementary functions and their inverses",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "27",
  number =       "1",
  pages =        "68--90",
  year =         "1925",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-1925-1501299-9",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "30A05 (33B10)",
  MRnumber =     "MR1501299",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journals/tran/1925-027-01/S0002-9947-1925-1501299-9/",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
}


bibtype: article
filename: elefunt.bib
label: Dederick:1926:QDDc
author: L. S. Dederick
title: Questions and Discussions: Discussions: a Modified Method for Cube Roots and Fifth Roots
journal: j-AMER-MATH-MONTHLY
volume: 33
number: 9
pages: 469--472
month: nov
monthnumber: 11
year: 1926
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:38:12 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1999.06.28 12:38:12 MDT
URL: http://www.jstor.org/stable/2299613
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: L. S. Dederick
rawtitle: Questions and Discussions: Discussions: a Modified Method for Cube Roots and Fifth Roots
entry:
@Article{Dederick:1926:QDDc,
  author =       "L. S. Dederick",
  title =        "Questions and Discussions: Discussions: a Modified
                 Method for Cube Roots and Fifth Roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "33",
  number =       "9",
  pages =        "469--472",
  month =        nov,
  year =         "1926",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:12 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2299613",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Mahler:1930:NUG
author: K. Mahler
journal: j-REND-CIRC-MAT
volume: 54
pages: 1--41
year: 1930
CODEN: RCMMAR
ISSN: 0009-725X (print), 1973-4409 (electronic) OR 0009725X (print), 19734409 (electronic)
ISSNL: 0009-725X OR 0009725X
bibdate: Sat Feb 18 14:57:12 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 14:57:12 ???
fjournal: Rendiconti del Circolo matematico di Palermo
language: German
remark: Based on doctoral dissertation, Frankfurt, Germany (1927).
acknowledgement: ack-nhfb
rawauthor: K. Mahler
title:
Uber die Nullstellen der unvollstaendigen Gammafunktionen. (German) [On the zeros of the incomplete gamma-functions]

URL:
https://carma.newcastle.edu.au/mahler/collected.html; https://carma.newcastle.edu.au/mahler/docs/002.pdf

rawtitle:
{{\"U}ber die Nullstellen der unvollstaendigen Gammafunktionen}. ({German}) [{On} the zeros of the incomplete gamma-functions]

entry:
@Article{Mahler:1930:NUG,
  author =       "K. Mahler",
  title =        "{{\"U}ber die Nullstellen der unvollstaendigen
                 Gammafunktionen}. ({German}) [{On} the zeros of the
                 incomplete gamma-functions]",
  journal =      j-REND-CIRC-MAT,
  volume =       "54",
  number =       "??",
  pages =        "1--41",
  month =        "????",
  year =         "1930",
  CODEN =        "RCMMAR",
  ISSN =         "0009-725X (print), 1973-4409 (electronic)",
  ISSN-L =       "0009-725X",
  bibdate =      "Sat Feb 18 14:57:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://carma.newcastle.edu.au/mahler/collected.html;
                 https://carma.newcastle.edu.au/mahler/docs/002.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Rendiconti del Circolo matematico di Palermo",
  language =     "German",
  remark =       "Based on doctoral dissertation, Frankfurt, Germany
                 (1927).",
}


bibtype: book
filename: elefunt.bib
label: Hobson:1931:TSE
author: Ernest William Hobson
title: The Theory of Spherical and Ellipsoidal Harmonics
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xi + 500
year: 1931
LCCN: QA406 .H7
bibdate: Sat Apr 1 14:40:56 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:40:56 MDT
subject: Spherical harmonics; Lame's functions
acknowledgement: ack-nhfb
authordates: 1856--1933
rawauthor: Ernest William Hobson
rawtitle: The Theory of Spherical and Ellipsoidal Harmonics
entry:
@Book{Hobson:1931:TSE,
  author =       "Ernest William Hobson",
  title =        "The Theory of Spherical and Ellipsoidal Harmonics",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xi + 500",
  year =         "1931",
  LCCN =         "QA406 .H7",
  bibdate =      "Sat Apr 1 14:40:56 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1856--1933",
  subject =      "Spherical harmonics; Lam{\'e}'s functions",
}


bibtype: article
filename: elefunt.bib
label: Kalbfell:1934:QDN
author: D. C. Kalbfell
title: Questions, Discussions and Notes: On a Method for Calculating Square Roots
journal: j-AMER-MATH-MONTHLY
volume: 41
number: 8
pages: 504--506
month: oct
monthnumber: 10
year: 1934
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:37:31 MDT 1999
bibtimestamp: 1999.06.28 12:37:31 MDT
URL: http://www.jstor.org/stable/2300417
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: D. C. Kalbfell
rawtitle: Questions, Discussions and Notes: On a Method for Calculating Square Roots
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

entry:
@Article{Kalbfell:1934:QDN,
  author =       "D. C. Kalbfell",
  title =        "Questions, Discussions and Notes: On a Method for
                 Calculating Square Roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "41",
  number =       "8",
  pages =        "504--506",
  month =        oct,
  year =         "1934",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:31 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2300417",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: book
filename: elefunt.bib
label: McLachlan:1934:BFE
author: N. W. (Norman William) McLachlan
title: Bessel Functions for Engineers
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
pages: xi + 1 + 192
year: 1934
LCCN: QA408 .M3
bibdate: Sat Apr 1 14:44:36 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:44:36 MDT
series: The Oxford engineering science series
subject: Bessel functions
acknowledgement: ack-nhfb
authordates: 1888--
rawauthor: N. W. (Norman William) McLachlan
rawtitle: {Bessel} Functions for Engineers
entry:
@Book{McLachlan:1934:BFE,
  author =       "N. W. (Norman William) McLachlan",
  title =        "{Bessel} Functions for Engineers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 1 + 192",
  year =         "1934",
  LCCN =         "QA408 .M3",
  bibdate =      "Sat Apr 1 14:44:36 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Oxford engineering science series",
  acknowledgement = ack-nhfb,
  author-dates = "1888--",
  subject =      "Bessel functions",
}


bibtype: article
filename: elefunt.bib
label: Davis:1935:EPF
author: H. T. Davis
title: An extension to polygamma functions of a theorem of Gauss
journal: j-BULL-AMS
volume: 41
number: 4
pages: 243--248
month: apr
monthnumber: 4
year: 1935
CODEN: BAMOAD
DOI: https://doi.org/10.1090/s0002-9904-1935-06055-0
ISSN: 0002-9904 (print), 1936-881X (electronic) OR 00029904 (print), 1936881X (electronic)
ISSNL: 0002-9904 OR 00029904
bibdate: Sat Mar 25 16:16:08 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib
bibtimestamp: 2017.03.25 16:16:08 ???
fjournal: Bulletin of the American Mathematical Society
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/bull/all_issues.html
rawauthor: H. T. Davis
rawtitle: An extension to polygamma functions of a theorem of {Gauss}
remark:
A footnote on the first page says ``The name polygamma is suggested by the paper, booktitle Tables of the Digamma and Trigamma Functions, by Eleanor Pairman, Tracts for Computers, No. 1, 1919'' cite Pairman:1919:TDT.

entry:
@Article{Davis:1935:EPF,
  author =       "H. T. Davis",
  title =        "An extension to polygamma functions of a theorem of
                 {Gauss}",
  journal =      j-BULL-AMS,
  volume =       "41",
  number =       "4",
  pages =        "243--248",
  month =        apr,
  year =         "1935",
  CODEN =        "BAMOAD",
  DOI =          "https://doi.org/10.1090/s0002-9904-1935-06055-0",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Sat Mar 25 16:16:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  remark =       "A footnote on the first page says ``The name polygamma
                 is suggested by the paper, \booktitle{Tables of the
                 Digamma and Trigamma Functions}, by Eleanor Pairman,
                 Tracts for Computers, No. 1, 1919''
                 \cite{Pairman:1919:TDT}.",
}


bibtype: article
filename: elefunt.bib
label: Airey:1937:CFA
author: J. R. Airey
journal: j-PHILOS-MAG
volume: 24
number: 162
pages: 521--552
year: 1937
CODEN: PHMAA4
DOI: https://doi.org/10.1080/14786443708565133
ISSN: 0031-8086 OR 00318086
ISSNL: 0031-8086 OR 00318086
bibdate: Thu Dec 01 14:26:37 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 14:26:37 ???
fjournal: Philosophical Magazine
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/tphm19
rawauthor: J. R. Airey
title:
The ``converging factor'' in asymptotic series and the calculation of Bessel, Laguerre and other functions

rawtitle:
The ``converging factor'' in asymptotic series and the calculation of {Bessel}, {Laguerre} and other functions

entry:
@Article{Airey:1937:CFA,
  author =       "J. R. Airey",
  title =        "The ``converging factor'' in asymptotic series and the
                 calculation of {Bessel}, {Laguerre} and other
                 functions",
  journal =      j-PHILOS-MAG,
  volume =       "24",
  number =       "162",
  pages =        "521--552",
  month =        "????",
  year =         "1937",
  CODEN =        "PHMAA4",
  DOI =          "https://doi.org/10.1080/14786443708565133",
  ISSN =         "0031-8086",
  ISSN-L =       "0031-8086",
  bibdate =      "Thu Dec 01 14:26:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Magazine",
  journal-URL =  "http://www.tandfonline.com/loi/tphm19",
}


bibtype: article
filename: elefunt.bib
label: Escott:1937:QDN
author: E. B. Escott
title: Questions, Discussions, and Notes: Rapid Method for Extracting a Square Root
journal: j-AMER-MATH-MONTHLY
volume: 44
number: 10
pages: 644--646
month: dec
monthnumber: 12
year: 1937
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:38:44 MDT 1999
bibtimestamp: 1999.06.28 12:38:44 MDT
URL: http://www.jstor.org/stable/2301484
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: E. B. Escott
rawtitle: Questions, Discussions, and Notes: Rapid Method for Extracting a Square Root
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

entry:
@Article{Escott:1937:QDN,
  author =       "E. B. Escott",
  title =        "Questions, Discussions, and Notes: Rapid Method for
                 Extracting a Square Root",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "44",
  number =       "10",
  pages =        "644--646",
  month =        dec,
  year =         "1937",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:44 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2301484",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Ostrowski:1937:KAN
author: A. M. Ostrowski
journal: Rec. Math.
volume: 2
pages: 1073--1098
year: 1937
bibdate: Mon Oct 23 14:58:35 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.23 14:58:35 ???
language: German
acknowledgement: ack-nhfb
rawauthor: A. M. Ostrowski
title:
Uber die Konvergenz und die Abrundungsfestigkeit des Newtonschen Verfahren. (German) [On the convergence and rounding strength of Newton's method]

rawtitle:
{{\"U}ber die Konvergenz und die Abr{\"u}ndungsfestigkeit des Newtonschen Verfahren}. ({German}) [{On} the convergence and rounding strength of {Newton}'s method]

entry:
@Article{Ostrowski:1937:KAN,
  author =       "A. M. Ostrowski",
  title =        "{{\"U}ber die Konvergenz und die
                 Abr{\"u}ndungsfestigkeit des Newtonschen Verfahren}.
                 ({German}) [{On} the convergence and rounding strength
                 of {Newton}'s method]",
  journal =      "Rec. Math.",
  volume =       "2",
  number =       "??",
  pages =        "1073--1098",
  month =        "????",
  year =         "1937",
  bibdate =      "Mon Oct 23 14:58:35 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Ostrowski:1938:NMA
author: A. M. Ostrowski
title: On Newton's method of approximation
journal: British Association for the Advancement of Science
pages: 392--??
year: 1938
bibdate: Mon Oct 23 14:57:22 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.23 14:57:22 ???
acknowledgement: ack-nhfb
rawauthor: A. M. Ostrowski
rawtitle: On {Newton}'s method of approximation
entry:
@Article{Ostrowski:1938:NMA,
  author =       "A. M. Ostrowski",
  title =        "On {Newton}'s method of approximation",
  journal =      "British Association for the Advancement of Science",
  volume =       "??",
  number =       "??",
  pages =        "392--??",
  month =        "????",
  year =         "1938",
  bibdate =      "Mon Oct 23 14:57:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Emde:1940:TEF
author: Fritz Emde
title: Tafeln Elementarer Funktionen (German) [Tables of Elementary Functions]
publisher: B. T. Teubner
address: Leipzig, Germany and Berlin, Germany
pages: xii + 181
year: 1940
LCCN: QA47 .E5
bibdate: Fri Jun 11 12:34:09 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.06.11 12:34:09 ???
URL: http://lccn.loc.gov/45006177
language: German
acknowledgement: ack-nhfb
authordates: 1873--1951
rawauthor: Fritz Emde
rawtitle: {Tafeln Elementarer Funktionen} ({German}) [Tables of Elementary Functions]
entry:
@Book{Emde:1940:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "B. T. Teubner",
  address =      "Leipzig, Germany and Berlin, Germany",
  pages =        "xii + 181",
  year =         "1940",
  LCCN =         "QA47 .E5",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://lccn.loc.gov/45006177",
  acknowledgement = ack-nhfb,
  author-dates = "1873--1951",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Stoner:1941:FEF
author: Paul Matthew Stoner
title: Fitting the Exponential Function and the Gompertz Function by the Method of Least Squares
journal: j-J-AM-STAT-ASSOC
volume: 36
number: 216
pages: 515--518
month: dec
monthnumber: 12
year: 1941
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:05:24 MST 2012
bibtimestamp: 2012.01.25 08:05:24 MST
URL: http://www.jstor.org/stable/2278959
fjournal: Journal of the American Statistical Association
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: Paul Matthew Stoner
rawtitle: Fitting the Exponential Function and the {Gompertz} Function by the Method of Least Squares
bibsource:
http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314095; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib

entry:
@Article{Stoner:1941:FEF,
  author =       "Paul Matthew Stoner",
  title =        "Fitting the Exponential Function and the {Gompertz}
                 Function by the Method of Least Squares",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "36",
  number =       "216",
  pages =        "515--518",
  month =        dec,
  year =         "1941",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:24 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314095;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
  URL =          "http://www.jstor.org/stable/2278959",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}


bibtype: book
filename: elefunt.bib
label: Stratton:1941:ECS
author: Julius Adams Stratton and Philip M. (Philip McCord) Morse and Lan Jen Chu and Reina Albagli Hutner
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xii + 127
year: 1941
LCCN: QC174.2 .S78
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
remark: A publication of the Technology Press, Massachusetts Institute of Technology.
subject: Wave mechanics; Mathematics; Tables
acknowledgement: ack-nhfb
authordates: 1901--1994
rawauthor: Julius Adams Stratton and Philip M. (Philip McCord) Morse and Lan Jen Chu and Reina Albagli Hutner
title:
Elliptic cylinder and spheroidal wave functions, including tables of separation constants and coefficients

rawtitle:
Elliptic cylinder and spheroidal wave functions, including tables of separation constants and coefficients

entry:
@Book{Stratton:1941:ECS,
  author =       "Julius Adams Stratton and Philip M. (Philip McCord)
                 Morse and Lan Jen Chu and Reina Albagli Hutner",
  title =        "Elliptic cylinder and spheroidal wave functions,
                 including tables of separation constants and
                 coefficients",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 127",
  year =         "1941",
  LCCN =         "QC174.2 .S78",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1901--1994",
  remark =       "A publication of the Technology Press, Massachusetts
                 Institute of Technology.",
  subject =      "Wave mechanics; Mathematics; Tables",
}


bibtype: phdthesis
filename: elefunt.bib
label: Dopper:1942:AOV
author: Herman Pieter Dopper
type: Ph.D. thesis
school: Rijksuniversiteit Groningen
address: Groningen, The Netherlands
year: 1942
bibdate: Sat Feb 18 14:32:59 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 14:32:59 ???
language: Dutch
remark: Cited in cite Paris:2016:UAE.
acknowledgement: ack-nhfb
rawauthor: Herman Pieter Dopper
title:
Asymptotische Ontwikkelingen van de Onvolledige Gammafuncties. (Dutch) [Asymptotic developments of the Incomplete Gamma Functions]

rawtitle:
Asymptotische Ontwikkelingen van de Onvolledige Gammafuncties. ({Dutch}) [{Asymptotic} developments of the Incomplete Gamma Functions]

entry:
@PhdThesis{Dopper:1942:AOV,
  author =       "Herman Pieter Dopper",
  title =        "Asymptotische Ontwikkelingen van de Onvolledige
                 Gammafuncties. ({Dutch}) [{Asymptotic} developments of
                 the Incomplete Gamma Functions]",
  type =         "{Ph.D.} thesis",
  school =       "Rijksuniversiteit Groningen",
  address =      "Groningen, The Netherlands",
  pages =        "????",
  year =         "1942",
  bibdate =      "Sat Feb 18 14:32:59 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Dutch",
  remark =       "Cited in \cite{Paris:2016:UAE}.",
}


bibtype: article
filename: elefunt.bib
label: Lancaster:1942:MME
author: Otis E. Lancaster
title: Machine Method for the Extraction of Cube Root
journal: j-J-AM-STAT-ASSOC
volume: 37
number: 217
pages: 112--115
month: mar
monthnumber: 3
year: 1942
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:05:24 MST 2012
bibtimestamp: 2012.01.25 08:05:24 MST
URL: http://www.jstor.org/stable/2279437
fjournal: Journal of the American Statistical Association
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: Otis E. Lancaster
rawtitle: Machine Method for the Extraction of Cube Root
bibsource:
http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib

entry:
@Article{Lancaster:1942:MME,
  author =       "Otis E. Lancaster",
  title =        "Machine Method for the Extraction of Cube Root",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "37",
  number =       "217",
  pages =        "112--115",
  month =        mar,
  year =         "1942",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:24 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314096;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
  URL =          "http://www.jstor.org/stable/2279437",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}


bibtype: article
filename: elefunt.bib
label: Archibald:1943:TTF
author: Raymond Clare Archibald
title: Tables of Trigonometric Functions in Non-Sexagesimal Arguments
journal: j-MATH-TABLES-AIDS-COMPUT
volume: 1
number: 2
pages: 33--44
month: apr
monthnumber: 4
year: 1943
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-43-99136-7
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Raymond Clare Archibald
rawtitle: Tables of Trigonometric Functions in Non-Sexagesimal Arguments
remark:
Original journal has only `R. C. A.' as author: possibly R. C. Archibald. AMS metadata now shows the full name.

entry:
@Article{Archibald:1943:TTF,
  author =       "Raymond Clare Archibald",
  title =        "Tables of Trigonometric Functions in Non-Sexagesimal
                 Arguments",
  journal =      j-MATH-TABLES-AIDS-COMPUT,
  volume =       "1",
  number =       "2",
  pages =        "33--44",
  month =        apr,
  year =         "1943",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-43-99136-7",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Original journal has only `R. C. A.' as author:
                 possibly R. C. Archibald. AMS metadata now shows the
                 full name.",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1943:PFE
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: viii + 261
year: 1943
bibdate: Mon Feb 13 19:15:35 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:15:35 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
title:
Praktische Funktionenlehre. 1. Elementare und elementare transzendente Funktionen, Unterstufe. (German) [Practical functional theory. 1. Elementary and elementary transcendental functions, lower stage]

rawtitle:
{Praktische Funktionenlehre. 1. Elementare und elementare transzendente Funktionen, Unterstufe}. ({German}) [{Practical} functional theory. 1. {Elementary} and elementary transcendental functions, lower stage]

entry:
@Book{Tolke:1943:PFE,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 1. Elementare und
                 elementare transzendente Funktionen, Unterstufe}.
                 ({German}) [{Practical} functional theory. 1.
                 {Elementary} and elementary transcendental functions,
                 lower stage]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 261",
  year =         "1943",
  bibdate =      "Mon Feb 13 19:15:35 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Turing:1943:MCZ
author: A. M. Turing
title: A method for the calculation of the zeta-function
journal: j-PROC-LONDON-MATH-SOC-2
volume: 48
pages: 180--197
year: 1943
ISSN: 0024-6115 (print), 1460-244X (electronic) OR 00246115 (print), 1460244X (electronic)
ISSNL: 0024-6115 OR 00246115
MRclass: 10.0X
MRnumber: MR0009612 (5,173a)
MRreviewer: C. L. Siegel
bibdate: Sat Nov 19 13:23:32 2005
bibtimestamp: 2005.11.19 13:23:32 ???
URL: http://turing.ecs.soton.ac.uk/browse.php/B/17
fjournal: Proceedings of the London Mathematical Society. Second Series
ZMnumber: 0061.08304
acknowledgement: ack-nhfb
rawauthor: A. M. Turing
rawtitle: A method for the calculation of the zeta-function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
According to cite [page 260]Newman:1955:AMT, publication was delayed four years by war-time difficulties.

entry:
@Article{Turing:1943:MCZ,
  author =       "A. M. Turing",
  title =        "A method for the calculation of the zeta-function",
  journal =      j-PROC-LONDON-MATH-SOC-2,
  volume =       "48",
  pages =        "180--197",
  year =         "1943",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  MRclass =      "10.0X",
  MRnumber =     "MR0009612 (5,173a)",
  MRreviewer =   "C. L. Siegel",
  bibdate =      "Sat Nov 19 13:23:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://turing.ecs.soton.ac.uk/browse.php/B/17",
  ZMnumber =     "0061.08304",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the London Mathematical Society. Second
                 Series",
  received =     "7 March 1939",
  remark =       "According to \cite[page 260]{Newman:1955:AMT},
                 publication was delayed four years by war-time
                 difficulties.",
}


bibtype: article
filename: elefunt.bib
label: Bateman:1944:GTB
author: Harry Bateman and Raymond Clare Archibald
title: A Guide to Tables of Bessel Functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 1
number: 7
pages: 205--308
month: jul
monthnumber: 7
year: 1944
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1944-0011175-4
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
MRnumber: 6,132b
MRreviewer: G. Szeg{\H{o}}
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Harry Bateman and Raymond Clare Archibald
rawtitle: A Guide to Tables of {Bessel} Functions
entry:
@Article{Bateman:1944:GTB,
  author =       "Harry Bateman and Raymond Clare Archibald",
  title =        "A Guide to Tables of {Bessel} Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "7",
  pages =        "205--308",
  month =        jul,
  year =         "1944",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1944-0011175-4",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRnumber =     "6,132b",
  MRreviewer =   "G. Szeg{\H{o}}",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Lehmer:1944:NCB
author: Derrick Henry Lehmer
title: Note on the Computation of the Bessel Function $ I_n(X) $
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 1
number: 5
pages: 133--135
month: apr
monthnumber: 4
year: 1944
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-44-99053-8
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Derrick Henry Lehmer
rawtitle: Note on the Computation of the {Bessel} Function {$ I_n(X) $}
remark:
Original journal has only `D. H. L.' as author: probably D. H. Lehmer. AMS metadata now shows the full name.

entry:
@Article{Lehmer:1944:NCB,
  author =       "Derrick Henry Lehmer",
  title =        "Note on the Computation of the {Bessel} Function {$
                 I_n(X) $}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "5",
  pages =        "133--135",
  month =        apr,
  year =         "1944",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-44-99053-8",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Original journal has only `D. H. L.' as author:
                 probably D. H. Lehmer. AMS metadata now shows the full
                 name.",
}


bibtype: book
filename: elefunt.bib
label: Lewis:1944:SCH
author: Charles J. Lewis
title: A survey of the confluent hypergeometric function
address: Washington, DC, USA
pages: 155
year: 1944
LCCN: QA351 .L53
bibdate: Sat Oct 30 21:06:31 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:06:31 MDT
subject: Hypergeometric functions
acknowledgement: ack-nhfb
rawauthor: Charles J. Lewis
rawtitle: A survey of the confluent hypergeometric function
entry:
@Book{Lewis:1944:SCH,
  author =       "Charles J. Lewis",
  title =        "A survey of the confluent hypergeometric function",
  publisher =    "????",
  address =      "Washington, DC, USA",
  pages =        "155",
  year =         "1944",
  LCCN =         "QA351 .L53",
  bibdate =      "Sat Oct 30 21:06:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions",
}


bibtype: article
filename: elefunt.bib
label: Abramowitz:1945:ZCB
author: Milton Abramowitz
title: Zeros of certain Bessel functions of fractional order
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 1
number: 9
pages: 353--354
month: jan
monthnumber: 1
year: 1945
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1945-0011176-7
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
MRclass: 65.0X
MRnumber: 6,132c
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Milton Abramowitz
rawtitle: Zeros of certain {Bessel} functions of fractional order
entry:
@Article{Abramowitz:1945:ZCB,
  author =       "Milton Abramowitz",
  title =        "Zeros of certain {Bessel} functions of fractional
                 order",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "9",
  pages =        "353--354",
  month =        jan,
  year =         "1945",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1945-0011176-7",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "6,132c",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Briggs:1945:TAL
author: Lyman J. Briggs and Arnold N. Lowan
title: Tables of Associated Legendre Functions
publisher: pub-U-COLUMBIA
address: pub-U-COLUMBIA:adr
pages: xlvi + 303 + 3
year: 1945
LCCN: QA406 .U5 1945
bibdate: Sat Apr 1 14:47:02 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:47:02 MDT
subject: Legendre's functions
acknowledgement: ack-nhfb
rawauthor: Lyman J. Briggs and Arnold N. Lowan
rawtitle: Tables of Associated {Legendre} Functions
remark:
Prepared by the Mathematical Tables Project and conducted under the sponsorship of the National bureau of Standards. Present volume begun under the auspices of the Work Projects Administration for the City of New York and completed with the support of the Office of Scientific Research and Development. Lyman J. Briggs, Director, National Bureau of Standards and official sponsor. Arnold N. Lowan, Project Director, Mathematical Tables Project. Reproduced by a photo offset process.

entry:
@Book{Briggs:1945:TAL,
  author =       "Lyman J. Briggs and Arnold N. Lowan",
  title =        "Tables of Associated {Legendre} Functions",
  publisher =    pub-U-COLUMBIA,
  address =      pub-U-COLUMBIA:adr,
  pages =        "xlvi + 303 + 3",
  year =         "1945",
  LCCN =         "QA406 .U5 1945",
  bibdate =      "Sat Apr 1 14:47:02 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Prepared by the Mathematical Tables Project and
                 conducted under the sponsorship of the National bureau
                 of Standards. Present volume begun under the auspices
                 of the Work Projects Administration for the City of New
                 York and completed with the support of the Office of
                 Scientific Research and Development. Lyman J. Briggs,
                 Director, National Bureau of Standards and official
                 sponsor. Arnold N. Lowan, Project Director,
                 Mathematical Tables Project. Reproduced by a photo
                 offset process.",
  subject =      "Legendre's functions",
}


bibtype: book
filename: elefunt.bib
label: Emde:1945:TEF
author: Fritz Emde
title: Tafeln Elementarer Funktionen (German) [Tables of Elementary Functions]
publisher: Edwards Bros.
address: Ann Arbor, MI, USA
pages: xii + 181
year: 1945
bibdate: Fri Jun 11 12:34:09 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.06.11 12:34:09 ???
note: Original edition published in 1940.
language: German
acknowledgement: ack-nhfb
rawauthor: Fritz Emde
rawnote: Original edition published in 1940.
rawtitle: {Tafeln Elementarer Funktionen} ({German}) [Tables of Elementary Functions]
entry:
@Book{Emde:1945:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "Edwards Bros.",
  address =      "Ann Arbor, MI, USA",
  pages =        "xii + 181",
  year =         "1945",
  LCCN =         "????",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Original edition published in 1940.",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1946:MZC
author: Anonymous
title: More Zeros of Certain Bessel Functions of Fractional Order
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 2
number: 15
pages: 118--119
month: jul
monthnumber: 7
year: 1946
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1946-0016689-0
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Anonymous
rawtitle: More Zeros of Certain {Bessel} Functions of Fractional Order
entry:
@Article{Anonymous:1946:MZC,
  author =       "Anonymous",
  title =        "More Zeros of Certain {Bessel} Functions of Fractional
                 Order",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "2",
  number =       "15",
  pages =        "118--119",
  month =        jul,
  year =         "1946",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1946-0016689-0",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Anonymous:1948:TBF
author: Anonymous
volume: 1
publisher: pub-US-GPO
address: pub-US-GPO:adr
pages: ix + 60
year: 1948
LCCN: QA3 .U5 no. 1
bibdate: Sat Nov 04 16:47:30 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.04 16:47:30 ???
series: ser-APPL-MATH-SER-NBS
acknowledgement: ack-nhfb
rawauthor: Anonymous
title:
Tables of the Bessel Functions $ Y_0 (x) $, $ Y_1 (x) $, $ K_0 (x) $, $ K_1 (x) $, $ 0 leq x leq 1 $

rawtitle:
Tables of the {Bessel} Functions {$ Y_0 (x) $}, {$ Y_1 (x) $}, {$ K_0 (x) $}, {$ K_1 (x) $}, $ 0 \leq x \leq 1 $

entry:
@Book{Anonymous:1948:TBF,
  author =       "Anonymous",
  title =        "Tables of the {Bessel} Functions {$ Y_0 (x) $}, {$ Y_1
                 (x) $}, {$ K_0 (x) $}, {$ K_1 (x) $}, $ 0 \leq x \leq 1
                 $",
  volume =       "1",
  publisher =    pub-US-GPO,
  address =      pub-US-GPO:adr,
  pages =        "ix + 60",
  year =         "1948",
  LCCN =         "QA3 .U5 no. 1",
  bibdate =      "Sat Nov 04 16:47:30 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       ser-APPL-MATH-SER-NBS,
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Emde:1948:TEF
author: Fritz Emde
title: Tafeln Elementarer Funktionen (German) [Tables of Elementary Functions]
publisher: pub-TEUBNER
address: pub-TEUBNER:adr
edition: Second
pages: xii + 181
year: 1948
LCCN: QA55 .E5 1948
MRclass: 65.0X
MRnumber: 11,263k
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: German
acknowledgement: ack-nhfb
rawauthor: Fritz Emde
rawtitle: {Tafeln Elementarer Funktionen} ({German}) [Tables of Elementary Functions]
entry:
@Book{Emde:1948:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  edition =      "Second",
  pages =        "xii + 181",
  year =         "1948",
  LCCN =         "QA55 .E5 1948",
  MRclass =      "65.0X",
  MRnumber =     "11,263k",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: techreport
filename: elefunt.bib
label: Tukey:1948:NSR
author: John W. Tukey
title: A note on the square-root iteration
type: SRG Memorandum report
number: 10
institution: inst-PRINCETON
address: inst-PRINCETON:adr
pages: 18
year: 1948
bibdate: Tue May 15 08:00:09 2012
bibtimestamp: 2012.05.15 08:00:09 ???
acknowledgement: ack-nhfb
rawauthor: John W. Tukey
rawtitle: A note on the square-root iteration
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Tukey:1948:NSR,
  author =       "John W. Tukey",
  title =        "A note on the square-root iteration",
  type =         "SRG Memorandum report",
  number =       "10",
  institution =  inst-PRINCETON,
  address =      inst-PRINCETON:adr,
  pages =        "18",
  year =         "1948",
  bibdate =      "Tue May 15 08:00:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Wise:1948:IBF
author: M. E. Wise
title: The Incomplete Beta Function and the Incomplete Gamma Function: An Acknowledgment
journal: j-J-R-STAT-SOC-SER-B-METHODOL
volume: 10
number: 2
pages: 264--264
year: 1948
CODEN: JSTBAJ
DOI: https://doi.org/10.2307/2983781
ISSN: 0035-9246 OR 00359246
ISSNL: 0035-9246 OR 00359246
bibdate: Fri Jan 23 11:53:21 MST 2015
bibtimestamp: 2015.01.23 11:53:21 MST
URL: http://www.jstor.org/stable/2983781
fjournal: Journal of the Royal Statistical Society. Series B (Methodological)
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00359246.html
rawauthor: M. E. Wise
rawtitle: The Incomplete Beta Function and the Incomplete Gamma Function: An Acknowledgment
bibsource:
http://www.jstor.org/stable/i349688; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jrss-b.bib

entry:
@Article{Wise:1948:IBF,
  author =       "M. E. Wise",
  title =        "The Incomplete Beta Function and the Incomplete Gamma
                 Function: An Acknowledgment",
  journal =      j-J-R-STAT-SOC-SER-B-METHODOL,
  volume =       "10",
  number =       "2",
  pages =        "264--264",
  month =        "????",
  year =         "1948",
  CODEN =        "JSTBAJ",
  DOI =          "https://doi.org/10.2307/2983781",
  ISSN =         "0035-9246",
  ISSN-L =       "0035-9246",
  bibdate =      "Fri Jan 23 11:53:21 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349688;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-b.bib",
  URL =          "http://www.jstor.org/stable/2983781",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series B
                 (Methodological)",
  journal-URL =  "http://www.jstor.org/journals/00359246.html",
}


bibtype: article
filename: elefunt.bib
label: Hartree:1949:NIP
author: D. R. Hartree
title: Notes on iterative processes
journal: j-PROC-CAMBRIDGE-PHIL-SOC
volume: 45
number: 2
pages: 230--236
month: apr
monthnumber: 4
year: 1949
CODEN: PCPSA4
DOI: https://doi.org/10.1017/s0305004100024762
ISSN: 0008-1981 OR 00081981
ISSNL: 0008-1981 OR 00081981
MRclass: 65.0X
MRnumber: 29268
MRreviewer: E. Bodewig
bibdate: Thu Aug 3 09:15:52 2023
bibtimestamp: 2023.08.03 09:15:52 ???
URL: https://ui.adsabs.harvard.edu/abs/1949PCPS...45..230H
fjournal: Proceedings of the Cambridge Philosophical Society
keywords: $1/p$-th root; iterative process; reciprocal square root; square root
ZMnumber: 0033.19003
acknowledgement: ack-nhfb
authordates: Douglas Rayner Hartree (27 March 1897--12 February 1958)
journalURL: http://journals.cambridge.org/action/displayJournal?jid=PSP
rawauthor: D. R. Hartree
rawtitle: Notes on iterative processes
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
Correction: in equation (29) at the bottom of page 233, replace the denominator term $ 2 y_0 $ by $ 2 y_1 $, matching the denominator in equation (32) on page 234.

rawnote:
Correction: in equation (29) at the bottom of page 233, replace the denominator term $ 2 y_0 $ by $ 2 y_1 $, matching the denominator in equation (32) on page 234.

entry:
@Article{Hartree:1949:NIP,
  author =       "D. R. Hartree",
  title =        "Notes on iterative processes",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "45",
  number =       "2",
  pages =        "230--236",
  month =        apr,
  year =         "1949",
  CODEN =        "PCPSA4",
  DOI =          "https://doi.org/10.1017/s0305004100024762",
  ISSN =         "0008-1981",
  ISSN-L =       "0008-1981",
  MRclass =      "65.0X",
  MRnumber =     "29268",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Thu Aug 3 09:15:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Correction: in equation (29) at the bottom of page
                 233, replace the denominator term $ 2 y_0 $ by $ 2 y_1
                 $, matching the denominator in equation (32) on page
                 234.",
  URL =          "https://ui.adsabs.harvard.edu/abs/1949PCPS...45..230H",
  ZMnumber =     "0033.19003",
  acknowledgement = ack-nhfb,
  author-dates = "Douglas Rayner Hartree (27 March 1897--12 February
                 1958)",
  fjournal =     "Proceedings of the Cambridge Philosophical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  keywords =     "$1/p$-th root; iterative process; reciprocal square
                 root; square root",
  ZBmath =       "3051117",
}


bibtype: article
filename: elefunt.bib
label: Lowan:1949:CLN
author: Arnold N. Lowan
title: The Computation Laboratory of the National Bureau of Standards
journal: j-SCRIPTA-MATH
volume: 15
pages: 33--63
year: 1949
ISSN: 0036-9713 OR 00369713
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
ZMnumber: 0034.07002
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: Arnold N. Lowan
rawtitle: The {Computation Laboratory of the National Bureau of Standards}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/scripta-math.bib

fjournal:
Scripta Mathematica: A Quarterly Journal Devoted to the Philosophy, History, and Expository Treatment of Mathematics

entry:
@Article{Lowan:1949:CLN,
  author =       "Arnold N. Lowan",
  title =        "The {Computation Laboratory of the National Bureau of
                 Standards}",
  journal =      j-SCRIPTA-MATH,
  volume =       "15",
  number =       "??",
  pages =        "33--63",
  month =        "????",
  year =         "1949",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0034.07002",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  ZBmath =       "3052129",
}


bibtype: book
filename: elefunt.bib
label: Magnus:1949:FTS
author: Wilhelm Magnus and Fritz Oberhettinger
title: Formulas and theorems for the special functions of mathematical physics
publisher: Chelsea Pub. Co.
address: New York, NY, USA
pages: 172
year: 1949
LCCN: QA41 M19e
bibdate: Sat Oct 30 18:44:51 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 18:44:51 ???
note: Translated from the German by John Wermer.
acknowledgement: ack-nhfb
rawauthor: Wilhelm Magnus and Fritz Oberhettinger
rawnote: Translated from the German by John Wermer.
rawtitle: Formulas and theorems for the special functions of mathematical physics
entry:
@Book{Magnus:1949:FTS,
  author =       "Wilhelm Magnus and Fritz Oberhettinger",
  title =        "Formulas and theorems for the special functions of
                 mathematical physics",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "172",
  year =         "1949",
  LCCN =         "QA41 M19e",
  bibdate =      "Sat Oct 30 18:44:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from the German by John Wermer.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Mitchell:1949:TFA
author: K. Mitchell
journal: j-PHILOS-MAG
volume: 40
number: 302
pages: 351--368
year: 1949
CODEN: PHMAA4
DOI: https://doi.org/10.1080/14786444908561256
ISSN: 0031-8086 OR 00318086
bibdate: Sat Jun 17 17:47:16 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.06.17 17:47:16 ???
URL: https://www.tandfonline.com/doi/abs/10.1080/14786444908561256
fjournal: Philosophical Magazine
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/tphm19
rawauthor: K. Mitchell
title:
Tables of the function $ int _0^z - log |1 - y| / y d y $ with an account of some properties of this and related functions

rawtitle:
Tables of the function $ \int_0^z - \log |1 - y| / y \, d y $ with an account of some properties of this and related functions

entry:
@Article{Mitchell:1949:TFA,
  author =       "K. Mitchell",
  title =        "Tables of the function $ \int_0^z - \log |1 - y| / y
                 \, d y $ with an account of some properties of this and
                 related functions",
  journal =      j-PHILOS-MAG,
  volume =       "40",
  number =       "302",
  pages =        "351--368",
  year =         "1949",
  CODEN =        "PHMAA4",
  DOI =          "https://doi.org/10.1080/14786444908561256",
  ISSN =         "0031-8086",
  bibdate =      "Sat Jun 17 17:47:16 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.tandfonline.com/doi/abs/10.1080/14786444908561256",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Magazine",
  journal-URL =  "http://www.tandfonline.com/loi/tphm19",
  received =     "9 April 1948",
}


bibtype: inproceedings
filename: elefunt.bib
label: Polya:1949:RCP
author: G. Polya
editor: J. Neyman
booktitle: Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability
title: Remarks on computing the probability integral in one and two dimensions
publisher: pub-U-CALIFORNIA-PRESS
address: pub-U-CALIFORNIA-PRESS:adr
pages: 63--78
year: 1949
bibdate: Sat Dec 16 17:23:49 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 17:23:49 ???
acknowledgement: ack-nhfb
rawauthor: G. P{\'o}lya
rawbooktitle: Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability
raweditor: J. Neyman
rawtitle: Remarks on computing the probability integral in one and two dimensions
entry:
@InProceedings{Polya:1949:RCP,
  author =       "G. P{\'o}lya",
  editor =       "J. Neyman",
  booktitle =    "Proceedings of the First Berkeley Symposium on
                 Mathematical Statistics and Probability",
  title =        "Remarks on computing the probability integral in one
                 and two dimensions",
  publisher =    pub-U-CALIFORNIA-PRESS,
  address =      pub-U-CALIFORNIA-PRESS:adr,
  pages =        "63--78",
  year =         "1949",
  bibdate =      "Sat Dec 16 17:23:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: USNBSCL:1949:TCH
author: United States National Bureau of Standards Computation Laboratory
title: Tables of the confluent hypergeometric function $ F(n / 2, 1 / 2, x) $ and related functions
volume: 3
publisher: pub-US-GPO
address: pub-US-GPO:adr
pages: xxii + 73
year: 1949
LCCN: QA3 .U5 no. 3
bibdate: Sat Oct 30 21:06:31 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:06:31 MDT
series: Applied mathematics series
subject: Hypergeometric functions; Mathematics; Tables
acknowledgement: ack-nhfb
rawauthor: {United States National Bureau of Standards Computation Laboratory }
rawtitle: Tables of the confluent hypergeometric function {$ F(n / 2, 1 / 2, x) $ and related functions}
URL:
http://openlibrary.org/works/OL1218358W/Tables_of_the_confluent_hypergeometric_function_F%28n_2_1_2_x%29_and_related_functions

entry:
@Book{USNBSCL:1949:TCH,
  author =       "{United States National Bureau of Standards
                 Computation Laboratory }",
  title =        "Tables of the confluent hypergeometric function {$ F(n
                 / 2, 1 / 2, x) $ and related functions}",
  volume =       "3",
  publisher =    pub-US-GPO,
  address =      pub-US-GPO:adr,
  pages =        "xxii + 73",
  year =         "1949",
  LCCN =         "QA3 .U5 no. 3",
  bibdate =      "Sat Oct 30 21:06:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applied mathematics series",
  URL =          "http://openlibrary.org/works/OL1218358W/Tables_of_the_confluent_hypergeometric_function_F%28n_2_1_2_x%29_and_related_functions",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Mathematics; Tables",
}


bibtype: article
filename: elefunt.bib
label: Norlund:1950:HF
author: Niels Erik Norlund
title: Hypergeometric functions
journal: Mat. Tidsskr. B.
volume: 1950
pages: 18--21
year: 1950
MRclass: 33.0X
MRnumber: MR0045259 (13,554e)
MRreviewer: S. C. van Veen
bibdate: Thu Dec 01 12:41:44 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 12:41:44 ???
language: Danish
ZMnumber: 0067.29402
acknowledgement: ack-nhfb
rawauthor: Niels Erik N{\o}rlund
rawtitle: Hypergeometric functions
entry:
@Article{Norlund:1950:HF,
  author =       "Niels Erik N{\o}rlund",
  title =        "Hypergeometric functions",
  journal =      "Mat. Tidsskr. B.",
  volume =       "1950",
  number =       "??",
  pages =        "18--21",
  year =         "1950",
  MRclass =      "33.0X",
  MRnumber =     "MR0045259 (13,554e)",
  MRreviewer =   "S. C. van Veen",
  bibdate =      "Thu Dec 01 12:41:44 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0067.29402",
  acknowledgement = ack-nhfb,
  language =     "Danish",
}


bibtype: techreport
filename: elefunt.bib
label: Stanley:1950:TRG
author: John Pearson Stanley and Maurice V. Wilkes
title: Table of the reciprocal of the gamma function for complex argument
type: Report
institution: Computation Centre, University of Toronto
address: Toronto, ON, Canada
year: 1950
MRclass: 65.0X
MRnumber: 48144
MRreviewer: S. C. van Veen
bibdate: Sat Sep 07 16:52:05 2024
bibtimestamp: 2024.09.07 16:52:05 ???
abstract: Toronto, ON, Canada
ZMnumber: 0040.06903
acknowledgement: ack-nhfb
authordates: Sir Maurice Vincent Wilkes (26 June 1913--29 November 2010)
rawabstract: Toronto, ON, Canada
rawauthor: John Pearson Stanley and Maurice V. Wilkes
rawtitle: Table of the reciprocal of the gamma function for complex argument
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Stanley:1950:TRG,
  author =       "John Pearson Stanley and Maurice V. Wilkes",
  title =        "Table of the reciprocal of the gamma function for
                 complex argument",
  type =         "Report",
  institution =  "Computation Centre, University of Toronto",
  address =      "Toronto, ON, Canada",
  pages =        "????",
  year =         "1950",
  MRclass =      "65.0X",
  MRnumber =     "48144",
  MRreviewer =   "S. C. van Veen",
  bibdate =      "Sat Sep 07 16:52:05 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0040.06903",
  abstract =     "Toronto, ON, Canada",
  acknowledgement = ack-nhfb,
  author-dates = "Sir Maurice Vincent Wilkes (26 June 1913--29 November
                 2010)",
  RSBM-number =  "22",
  ZBmath =       "3060432",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1950:PFE
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: xi + 440
year: 1950
bibdate: Mon Feb 13 19:12:35 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:12:35 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
title:
Praktische Funktionenlehre. 1. Elementare und elementare transzendente Funktionen. (German) [Practical functional theory. 1. Elementary and elementary transcendental functions]

rawtitle:
{Praktische Funktionenlehre. 1. Elementare und elementare transzendente Funktionen}. ({German}) [{Practical} functional theory. 1. {Elementary} and elementary transcendental functions]

entry:
@Book{Tolke:1950:PFE,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 1. Elementare und
                 elementare transzendente Funktionen}. ({German})
                 [{Practical} functional theory. 1. {Elementary} and
                 elementary transcendental functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 440",
  year =         "1950",
  bibdate =      "Mon Feb 13 19:12:35 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Tricomi:1950:AEU
author: F. G. Tricomi
journal: j-MATH-Z
volume: 53
number: 2
pages: 136--148
month: apr
monthnumber: 4
year: 1950
CODEN: MAZEAX
DOI: https://doi.org/10.1007/BF01162409
ISSN: 0025-5874 (print), 1432-1823 (electronic) OR 00255874 (print), 14321823 (electronic)
ISSNL: 0025-5874 OR 00255874
bibdate: Sat Feb 18 14:47:24 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 14:47:24 ???
URL: http://link.springer.com/article/10.1007/BF01162409
fjournal: Mathematische Zeitschrift
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/209
rawauthor: F. G. Tricomi
title:
Asymptotische Eigenschaften der unvollstandigen Gammafunktion. (German) [Asymptotic properties of the incomplete gamma function]

rawtitle:
{Asymptotische Eigenschaften der unvollst{\"a}ndigen Gammafunktion}. ({German}) [{Asymptotic} properties of the incomplete gamma function]

entry:
@Article{Tricomi:1950:AEU,
  author =       "F. G. Tricomi",
  title =        "{Asymptotische Eigenschaften der unvollst{\"a}ndigen
                 Gammafunktion}. ({German}) [{Asymptotic} properties of
                 the incomplete gamma function]",
  journal =      j-MATH-Z,
  volume =       "53",
  number =       "2",
  pages =        "136--148",
  month =        apr,
  year =         "1950",
  CODEN =        "MAZEAX",
  DOI =          "https://doi.org/10.1007/BF01162409",
  ISSN =         "0025-5874 (print), 1432-1823 (electronic)",
  ISSN-L =       "0025-5874",
  bibdate =      "Sat Feb 18 14:47:24 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01162409",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Zeitschrift",
  journal-URL =  "http://link.springer.com/journal/209",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Cadwell:1951:BNI
author: J. H. Cadwell
title: The Bivariate Normal Integral
journal: j-BIOMETRIKA
volume: 38
number: 3/4
pages: 475--479
month: dec
monthnumber: 12
year: 1951
CODEN: BIOKAX
DOI: https://doi.org/10.2307/2332596
ISSN: 0006-3444 (print), 1464-3510 (electronic) OR 00063444 (print), 14643510 (electronic)
ISSNL: 0006-3444 OR 00063444
MRclass: 60.0X
MRnumber: 0045960 (13,662h)
MRreviewer: G. E. Noether
bibdate: Sat Jun 21 14:32:38 MDT 2014
bibtimestamp: 2014.06.21 14:32:38 MDT
URL: http://www.jstor.org/stable/2332596
fjournal: Biometrika
acknowledgement: ack-nhfb
journalURL: http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html
rawauthor: J. H. Cadwell
rawtitle: The Bivariate Normal Integral
bibsource:
http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315418; https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Cadwell:1951:BNI,
  author =       "J. H. Cadwell",
  title =        "The Bivariate Normal Integral",
  journal =      j-BIOMETRIKA,
  volume =       "38",
  number =       "3/4",
  pages =        "475--479",
  month =        dec,
  year =         "1951",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2332596",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "60.0X",
  MRnumber =     "0045960 (13,662h)",
  MRreviewer =   "G. E. Noether",
  bibdate =      "Sat Jun 21 14:32:38 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315418;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2332596",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
}


bibtype: article
filename: elefunt.bib
label: Fogel:1951:FTE
author: E. K. Fogel'
title: A finite theory of elementary functions. I. Logarithmic and exponential functions. (Russian)
journal: Latvijas PSR Zinatnu Akad. Vestis
volume: 5
number: 46
pages: 801--813
year: 1951
MRclass: 33.0X
MRnumber: 15,218b
MRreviewer: H. N. Shapiro
bibdate: Sat Apr 25 13:05:19 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.04.25 13:05:19 ???
language: Russian
acknowledgement: ack-nhfb
rawauthor: {\`E}. K. Fogel'
rawtitle: A finite theory of elementary functions. {I}. {Logarithmic} and exponential functions. ({Russian})
entry:
@Article{Fogel:1951:FTE,
  author =       "{\`E}. K. Fogel'",
  title =        "A finite theory of elementary functions. {I}.
                 {Logarithmic} and exponential functions. ({Russian})",
  journal =      "Latvijas PSR Zin{\=a}t{\c{n}}u Akad. V{\=e}stis",
  volume =       "5",
  number =       "46",
  pages =        "801--813",
  year =         "1951",
  MRclass =      "33.0X",
  MRnumber =     "15,218b",
  MRreviewer =   "H. N. Shapiro",
  bibdate =      "Sat Apr 25 13:05:19 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gellman:1951:CCH
author: Harvey Gellman
title: The Calculation of Complex Hypergeometric Functions with the IBM Type 602-A Calculating Punch
publisher: IBM
address: New York, NY, USA
pages: 161--168
year: 1951
bibdate: Mon Jun 18 06:09:24 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.06.18 06:09:24 ???
acknowledgement: ack-nhfb
rawauthor: Harvey Gellman
rawtitle: The Calculation of Complex Hypergeometric Functions with the {IBM Type 602-A} Calculating Punch
booktitle:
Proceedings of a Computation Seminar [IBM Department of Education, Endicot, NY, from December 5 to 9, 1949]

remark:
A Computation Seminar, sponsored by the International Business Machines Corporation, was held in the IBM Department of Education, Endicot, NY, from December 5 to 9, 1949. Attending the Seminar were one hundred and seven research engineers and scientists who are experienced both in applying mathematical methods to the solution of physical problems and in the associated punched card methods of computation.

rawbooktitle:
Proceedings of a Computation Seminar [{IBM Department of Education, Endicot, NY, from December 5 to 9, 1949}]

entry:
@InProceedings{Gellman:1951:CCH,
  author =       "Harvey Gellman",
  booktitle =    "Proceedings of a Computation Seminar [{IBM Department
                 of Education, Endicot, NY, from December 5 to 9,
                 1949}]",
  title =        "The Calculation of Complex Hypergeometric Functions
                 with the {IBM Type 602-A} Calculating Punch",
  publisher =    "IBM",
  address =      "New York, NY, USA",
  pages =        "161--168",
  year =         "1951",
  bibdate =      "Mon Jun 18 06:09:24 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "A Computation Seminar, sponsored by the International
                 Business Machines Corporation, was held in the IBM
                 Department of Education, Endicot, NY, from December 5
                 to 9, 1949. Attending the Seminar were one hundred and
                 seven research engineers and scientists who are
                 experienced both in applying mathematical methods to
                 the solution of physical problems and in the associated
                 punched card methods of computation.",
}


bibtype: article
filename: elefunt.bib
label: Rutishauser:1951:BAK
author: Heinz Rutishauser
journal: j-Z-ANGE-MATH-PHYS
volume: 2
number: 4
pages: 292--293
month: jul
monthnumber: 7
year: 1951
CODEN: ZAMPDB
DOI: https://doi.org/10.1007/bf02579691
ISSN: 0044-2275 (print), 1420-9039 (electronic) OR 00442275 (print), 14209039 (electronic)
ISSNL: 0044-2275 OR 00442275
MRclass: 26.1X
MRnumber: 44598
MRreviewer: F. J. Murray
bibdate: Mon Aug 24 21:56:15 2020
bibtimestamp: 2020.08.24 21:56:15 ???
language: German
acknowledgement: ack-nhfb
authordates: Heinz Rutishauser (30 January 1918--10 November 1970)
journalURL: http://link.springer.com/journal/33
rawauthor: Heinz Rutishauser
title:
Bemerkungen zur Arbeit von K. Emden ``Eine Losung fur $ int e^b(x + a cos x) d x $''. (German) [Remarks on the work by K. Emden, ``A solution for $ int e^b (x + a cos x) d x $'']

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

fjournal:
Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees

rawtitle:
{Bemerkungen zur Arbeit von K. Emden ``Eine L{\"o}sung f{\"u}r $ \int e^{b(x + a \cos x)} \, d x $}''. ({German}) [{Remarks} on the work by {K. Emden, ``A solution for $ \int e^{b (x + a \ cos x)} \, d x $''}]

entry:
@Article{Rutishauser:1951:BAK,
  author =       "Heinz Rutishauser",
  title =        "{Bemerkungen zur Arbeit von K. Emden ``Eine L{\"o}sung
                 f{\"u}r $ \int e^{b(x + a \cos x)} \, d x $}''.
                 ({German}) [{Remarks} on the work by {K. Emden, ``A
                 solution for $ \int e^{b (x + a \ cos x)} \, d x
                 $''}]",
  journal =      j-Z-ANGE-MATH-PHYS,
  volume =       "2",
  number =       "4",
  pages =        "292--293",
  month =        jul,
  year =         "1951",
  CODEN =        "ZAMPDB",
  DOI =          "https://doi.org/10.1007/bf02579691",
  ISSN =         "0044-2275 (print), 1420-9039 (electronic)",
  ISSN-L =       "0044-2275",
  MRclass =      "26.1X",
  MRnumber =     "44598",
  MRreviewer =   "F. J. Murray",
  bibdate =      "Mon Aug 24 21:56:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Heinz Rutishauser (30 January 1918--10 November
                 1970)",
  fjournal =     "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
                 ZAMP. Journal of Applied Mathematics and Physics.
                 Journal de Math\'{e}matiques et de Physique
                 Appliqu\'{e}es",
  journal-URL =  "http://link.springer.com/journal/33",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Salzer:1951:FCE
author: H. E. Salzer
title: Formulas for Calculating the Error Function of a Complex Variable
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 5
number: 34
pages: 67--70
month: apr
monthnumber: 4
year: 1951
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1951-0048150-3
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. E. Salzer
rawtitle: Formulas for Calculating the Error Function of a Complex Variable
entry:
@Article{Salzer:1951:FCE,
  author =       "H. E. Salzer",
  title =        "Formulas for Calculating the Error Function of a
                 Complex Variable",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "34",
  pages =        "67--70",
  month =        apr,
  year =         "1951",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1951-0048150-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Salzer:1951:RTT
author: H. E. Salzer
title: Radix Table for Trigonometric Functions and their Inverses to High Accuracy
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 5
number: 33
pages: 9--11
month: jan
monthnumber: 1
year: 1951
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-51-99447-1
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. E. Salzer
rawtitle: Radix Table for Trigonometric Functions and their Inverses to High Accuracy
entry:
@Article{Salzer:1951:RTT,
  author =       "H. E. Salzer",
  title =        "Radix Table for Trigonometric Functions and their
                 Inverses to High Accuracy",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "33",
  pages =        "9--11",
  month =        jan,
  year =         "1951",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-51-99447-1",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Wilkes:1951:PPE
author: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
title: The Preparation of Programs for an Electronic Digital Computer
publisher: pub-AW
address: pub-AW:adr
pages: 167
year: 1951
LCCN: QA76.5 .W55 1951
bibdate: Mon Feb 10 09:42:47 2020
bibtimestamp: 2020.02.10 09:42:47 ???
note: See also second edition cite Wilkes:1957:PPE, and reprint cite Wilkes:1982:PPE.
acknowledgement: ack-nhfb
rawauthor: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
rawnote: See also second edition \cite{Wilkes:1957:PPE}, and reprint \cite{Wilkes:1982:PPE}.
rawtitle: The Preparation of Programs for an Electronic Digital Computer
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
Part I Chapter 1. The Design of Programs for Electronic Computing Machines / 1 1-1 Introduction / 1 1-2 Types of automatic computing machines / 2 1-3 Description of the EDSAC / 3 1-4 The EDSAC order code / 5 1-5 Notes on the order code / 6 1-6 The use of conditional orders / 7 1-7 Modification of orders by the program / 8 1-8 Multiaddress codes / 11 1-9 Binary--decimal conversion / 12 1-10 Checking facilities / 14 Chapter 2. Input of Orders / 15 2-1 Initial orders / 15 2-2 Pseudo-orders / 17 2-3 Examples / 17 2-4 Control combinations / 17 2-5 Starting the program / 18 2-6 Use of code letters / 19 2-7 Constants / 20 2-8 Notation / 20 Chapter 3. Subroutines and Parameters / 22 3-1 Open subroutines / 22 3-2 closed subroutines / 22 3-3 preset parameters / 23 3-4 program parameters / 23 Chapter 4. Library Subroutines and their Use in Constructing Programs / 25 4-1 Library catalog / 25 4-2 Input and output subroutines / 25 4-3 Division subroutines / 27 4-4 Trigonometrical and other functions / 27 4-5 Quadrature / 27 4-6 Assembly subroutines / 27 4-7 Integration of differential equations / 32 4-8 Processes, Interpretive subroutines / 34 Chapter 5. Pitfalls / 38 5-1 Proofreading of programs, points to be checked / 38 5-2 Location of mistakes in a program / 39 5-3 Counting operations / 41 Chapter 6. Use of the EDSAC & Its Associated Equipment / 42 6-1 Tape Punching & editing facilities / 42 6-2 Storage of library subroutines / 43 6-3 EDSAC organization / 43 6-4 EDSAC controls / 43 Chapter 7. Examples / 45 7-1 Example 1. Calculation of $exp (-sin x)$ / 45 7-2 Example 2. Calculation of $pi $ by evaluation of definite integral / 48 7-3 Alternative method for Example 2 / 52 7-4 Example 2, with extra print orders for checking / 53 7-5 Application of checking subroutine C11 to Example 2 / 54 7-6 Example of integration of an ordinary differential equation / 46 7-7 Evaluation of a definite integral / 61 7-8 Program to facilitate the solution of algebraic equation / 66 Part II. Specifications of Library Subroutines / 72 A. Subroutines to carry out floating point arithmetic / 73 B. Subroutines to carry out arithmetical operations on complex numbers / 78 C. Checking subroutines / 79 D. Division subroutines / 82 E. Exponential subroutines / 83 F. General routines relating to functions / 84 G. Subroutines for integration of ordinary differential equations / 86 J. Subroutines for calculating special functions [Legendre polynomials] / 88 K. Subroutines for the summation of power series / 88 L. Subroutines for evaluating logarithms / 91 M. Miscellaneous subroutines / 91 P. Print subroutines / 92 Q. Quadrature subroutines / 95 R. Input subroutines / 96 S. Subroutines for evaluation of fractional powers / 98 T. Subroutines for calculating trigonometrical functions / 99 U. Subroutines for counting operations / 101 V1. Multiplication of vector by symmetric matrix / 102 V2. Addition and subtraction of $n$ dimensional vectors / 103 Part III. Programs of Selected Library Subroutines / 104 Appendix A. Keyboard perforator code, etc. / 158 Appendix B. The initial orders / 159 Appendix C. Control combinations / 161 Appendix D. Interpretive subroutines: example of packing of orders / 162 Appendix E. Methods of counting in a simple cycle / 164 Index

rawTOC:
Part I \\ Chapter 1. The Design of Programs for Electronic Computing Machines / 1 \\ 1-1 Introduction / 1 \\ 1-2 Types of automatic computing machines / 2 \\ 1-3 Description of the EDSAC / 3 \\ 1-4 The EDSAC order code / 5 \\ 1-5 Notes on the order code / 6 \\ 1-6 The use of conditional orders / 7 \\ 1-7 Modification of orders by the program / 8 \\ 1-8 Multiaddress codes / 11 \\ 1-9 Binary--decimal conversion / 12 \\ 1-10 Checking facilities / 14 \\ Chapter 2. Input of Orders / 15 \\ 2-1 Initial orders / 15 \\ 2-2 Pseudo-orders / 17 \\ 2-3 Examples / 17 \\ 2-4 Control combinations / 17 \\ 2-5 Starting the program / 18 \\ 2-6 Use of code letters / 19 \\ 2-7 Constants / 20 \\ 2-8 Notation / 20 \\ Chapter 3. Subroutines and Parameters / 22 \\ 3-1 Open subroutines / 22 \\ 3-2 closed subroutines / 22 \\ 3-3 preset parameters / 23 \\ 3-4 program parameters / 23 \\ Chapter 4. Library Subroutines and their Use in Constructing Programs / 25 \\ 4-1 Library catalog / 25 \\ 4-2 Input and output subroutines / 25 \\ 4-3 Division subroutines / 27 \\ 4-4 Trigonometrical and other functions / 27 \\ 4-5 Quadrature / 27 \\ 4-6 Assembly subroutines / 27 \\ 4-7 Integration of differential equations / 32 \\ 4-8 Processes, Interpretive subroutines / 34 \\ Chapter 5. Pitfalls / 38 \\ 5-1 Proofreading of programs, points to be checked / 38 \\ 5-2 Location of mistakes in a program / 39 \\ 5-3 Counting operations / 41 \\ Chapter 6. Use of the EDSAC \& Its Associated Equipment / 42 \\ 6-1 Tape Punching \& editing facilities / 42 \\ 6-2 Storage of library subroutines / 43 \\ 6-3 EDSAC organization / 43 \\ 6-4 EDSAC controls / 43 \\ Chapter 7. Examples / 45 \\ 7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\ 7-2 Example 2. Calculation of $\pi$ by evaluation of definite integral / 48 \\ 7-3 Alternative method for Example 2 / 52 \\ 7-4 Example 2, with extra print orders for checking / 53 \\ 7-5 Application of checking subroutine C11 to Example 2 / 54 \\ 7-6 Example of integration of an ordinary differential equation / 46 \\ 7-7 Evaluation of a definite integral / 61 \\ 7-8 Program to facilitate the solution of algebraic equation / 66 \\ Part II. Specifications of Library Subroutines / 72 \\ A. Subroutines to carry out floating point arithmetic / 73 \\ B. Subroutines to carry out arithmetical operations on complex numbers / 78 \\ C. Checking subroutines / 79 \\ D. Division subroutines / 82 \\ E. Exponential subroutines / 83 \\ F. General routines relating to functions / 84 \\ G. Subroutines for integration of ordinary differential equations / 86 \\ J. Subroutines for calculating special functions [Legendre polynomials] / 88 \\ K. Subroutines for the summation of power series / 88 \\ L. Subroutines for evaluating logarithms / 91 \\ M. Miscellaneous subroutines / 91 \\ P. Print subroutines / 92 \\ Q. Quadrature subroutines / 95 \\ R. Input subroutines / 96 \\ S. Subroutines for evaluation of fractional powers / 98 \\ T. Subroutines for calculating trigonometrical functions / 99 \\ U. Subroutines for counting operations / 101 \\ V1. Multiplication of vector by symmetric matrix / 102 \\ V2. Addition and subtraction of $n$ dimensional vectors / 103 \\ Part III. Programs of Selected Library Subroutines / 104 \\ Appendix A. Keyboard perforator code, etc. / 158 \\ Appendix B. The initial orders / 159 \\ Appendix C. Control combinations / 161 \\ Appendix D. Interpretive subroutines: example of packing of orders / 162 \\ Appendix E. Methods of counting in a simple cycle / 164 \\ Index

entry:
@Book{Wilkes:1951:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "167",
  year =         "1951",
  LCCN =         "QA76.5 .W55 1951",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also second edition \cite{Wilkes:1957:PPE}, and
                 reprint \cite{Wilkes:1982:PPE}.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I \\
                 Chapter 1. The Design of Programs for Electronic
                 Computing Machines / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machines / 2 \\
                 1-3 Description of the EDSAC / 3 \\
                 1-4 The EDSAC order code / 5 \\
                 1-5 Notes on the order code / 6 \\
                 1-6 The use of conditional orders / 7 \\
                 1-7 Modification of orders by the program / 8 \\
                 1-8 Multiaddress codes / 11 \\
                 1-9 Binary--decimal conversion / 12 \\
                 1-10 Checking facilities / 14 \\
                 Chapter 2. Input of Orders / 15 \\
                 2-1 Initial orders / 15 \\
                 2-2 Pseudo-orders / 17 \\
                 2-3 Examples / 17 \\
                 2-4 Control combinations / 17 \\
                 2-5 Starting the program / 18 \\
                 2-6 Use of code letters / 19 \\
                 2-7 Constants / 20 \\
                 2-8 Notation / 20 \\
                 Chapter 3. Subroutines and Parameters / 22 \\
                 3-1 Open subroutines / 22 \\
                 3-2 closed subroutines / 22 \\
                 3-3 preset parameters / 23 \\
                 3-4 program parameters / 23 \\
                 Chapter 4. Library Subroutines and their Use in
                 Constructing Programs / 25 \\
                 4-1 Library catalog / 25 \\
                 4-2 Input and output subroutines / 25 \\
                 4-3 Division subroutines / 27 \\
                 4-4 Trigonometrical and other functions / 27 \\
                 4-5 Quadrature / 27 \\
                 4-6 Assembly subroutines / 27 \\
                 4-7 Integration of differential equations / 32 \\
                 4-8 Processes, Interpretive subroutines / 34 \\
                 Chapter 5. Pitfalls / 38 \\
                 5-1 Proofreading of programs, points to be checked / 38
                 \\
                 5-2 Location of mistakes in a program / 39 \\
                 5-3 Counting operations / 41 \\
                 Chapter 6. Use of the EDSAC \& Its Associated Equipment
                 / 42 \\
                 6-1 Tape Punching \& editing facilities / 42 \\
                 6-2 Storage of library subroutines / 43 \\
                 6-3 EDSAC organization / 43 \\
                 6-4 EDSAC controls / 43 \\
                 Chapter 7. Examples / 45 \\
                 7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
                 7-2 Example 2. Calculation of $\pi$ by evaluation of
                 definite integral / 48 \\
                 7-3 Alternative method for Example 2 / 52 \\
                 7-4 Example 2, with extra print orders for checking /
                 53 \\
                 7-5 Application of checking subroutine C11 to Example 2
                 / 54 \\
                 7-6 Example of integration of an ordinary differential
                 equation / 46 \\
                 7-7 Evaluation of a definite integral / 61 \\
                 7-8 Program to facilitate the solution of algebraic
                 equation / 66 \\
                 Part II. Specifications of Library Subroutines / 72 \\
                 A. Subroutines to carry out floating point arithmetic /
                 73 \\
                 B. Subroutines to carry out arithmetical operations on
                 complex numbers / 78 \\
                 C. Checking subroutines / 79 \\
                 D. Division subroutines / 82 \\
                 E. Exponential subroutines / 83 \\
                 F. General routines relating to functions / 84 \\
                 G. Subroutines for integration of ordinary differential
                 equations / 86 \\
                 J. Subroutines for calculating special functions
                 [Legendre polynomials] / 88 \\
                 K. Subroutines for the summation of power series / 88
                 \\
                 L. Subroutines for evaluating logarithms / 91 \\
                 M. Miscellaneous subroutines / 91 \\
                 P. Print subroutines / 92 \\
                 Q. Quadrature subroutines / 95 \\
                 R. Input subroutines / 96 \\
                 S. Subroutines for evaluation of fractional powers / 98
                 \\
                 T. Subroutines for calculating trigonometrical
                 functions / 99 \\
                 U. Subroutines for counting operations / 101 \\
                 V1. Multiplication of vector by symmetric matrix / 102
                 \\
                 V2. Addition and subtraction of $n$ dimensional vectors
                 / 103 \\
                 Part III. Programs of Selected Library Subroutines /
                 104 \\
                 Appendix A. Keyboard perforator code, etc. / 158 \\
                 Appendix B. The initial orders / 159 \\
                 Appendix C. Control combinations / 161 \\
                 Appendix D. Interpretive subroutines: example of
                 packing of orders / 162 \\
                 Appendix E. Methods of counting in a simple cycle / 164
                 \\
                 Index",
}


bibtype: book
filename: elefunt.bib
label: Anonymous:1952:BFP
author: Anonymous
title: Bessel Functions, Part II
volume: 10
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
year: 1952
bibdate: Tue Nov 14 14:59:31 2023
bibtimestamp: 2023.11.14 14:59:31 ???
series: British Association Mathematical Tables
remark: TO DO: was Leslie Fox a co-author?? Who were the authors?? Page count??
acknowledgement: ack-nhfb
authordates: Leslie Fox (30 September 1918--1 August 1992)
rawauthor: Anonymous
rawtitle: {Bessel} Functions, {Part II}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Book{Anonymous:1952:BFP,
  author =       "Anonymous",
  title =        "{Bessel} Functions, {Part II}",
  volume =       "10",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "????",
  year =         "1952",
  bibdate =      "Tue Nov 14 14:59:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "British Association Mathematical Tables",
  acknowledgement = ack-nhfb,
  author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
  remark =       "TO DO: was Leslie Fox a co-author?? Who were the
                 authors?? Page count??",
}


bibtype: inbook
filename: elefunt.bib
label: Goncarov:1952:EFC
author: V. L. Goncarov
title: Elementary functions of a complex variable
publisher: Gosudarstv. Izdat. Tehn-Teoret. Lit.
address: Moscow-Leningrad, USSR
pages: 491--552
year: 1952
MRclass: 30.0X
MRnumber: 14,1073c
MRreviewer: R. P. Boas, Jr.
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: V. L. Gon{\v{c}}arov
rawtitle: Elementary functions of a complex variable
booktitle:
Encyclopaedia of elementary mathematics. Book III. Functions and limits (the foundations of analysis)

rawbooktitle:
Encyclopaedia of elementary mathematics. {Book III}. {Functions} and limits (the foundations of analysis)

entry:
@InBook{Goncarov:1952:EFC,
  author =       "V. L. Gon{\v{c}}arov",
  booktitle =    "Encyclopaedia of elementary mathematics. {Book III}.
                 {Functions} and limits (the foundations of analysis)",
  title =        "Elementary functions of a complex variable",
  publisher =    "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
  address =      "Moscow-Leningrad, USSR",
  pages =        "491--552",
  year =         "1952",
  MRclass =      "30.0X",
  MRnumber =     "14,1073c",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: elefunt.bib
label: Goncarov:1952:EFR
author: V. L. Goncarov
publisher: Gosudarstv. Izdat. Tehn-Teoret. Lit.
address: Moscow-Leningrad, USSR
pages: 9--296
year: 1952
MRclass: 27.2X
MRnumber: 14,1070d
MRreviewer: R. P. Boas, Jr.
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: V. L. Gon{\v{c}}arov
booktitle:
Encyclopaedia of elementary mathematics. Book III. Functions and limits (the foundations of analysis)

title:
Elementary functions of a real variable. Limits of sequences and functions. The general concept of a function

rawbooktitle:
Encyclopaedia of elementary mathematics. {Book III}. {Functions} and limits (the foundations of analysis)

rawtitle:
Elementary functions of a real variable. Limits of sequences and functions. {The} general concept of a function

entry:
@InCollection{Goncarov:1952:EFR,
  author =       "V. L. Gon{\v{c}}arov",
  booktitle =    "Encyclopaedia of elementary mathematics. {Book III}.
                 {Functions} and limits (the foundations of analysis)",
  title =        "Elementary functions of a real variable. Limits of
                 sequences and functions. {The} general concept of a
                 function",
  publisher =    "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
  address =      "Moscow-Leningrad, USSR",
  pages =        "9--296",
  year =         "1952",
  MRclass =      "27.2X",
  MRnumber =     "14,1070d",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kuipers:1952:PSE
author: L. Kuipers
title: Properties of some elementary functions
journal: Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes Math.
volume: 55
number: 14
pages: 388--393
year: 1952
MRclass: 27.0X
MRnumber: 14,360e
MRreviewer: E. Frank
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: L. Kuipers
rawtitle: Properties of some elementary functions
entry:
@Article{Kuipers:1952:PSE,
  author =       "L. Kuipers",
  title =        "Properties of some elementary functions",
  journal =      "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes
                 Math.",
  volume =       "55",
  number =       "14",
  pages =        "388--393",
  year =         "1952",
  MRclass =      "27.0X",
  MRnumber =     "14,360e",
  MRreviewer =   "E. Frank",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Bowman:1953:IEF
author: Frank Bowman
title: Introduction to Elliptic Functions with Applications
publisher: English Universities Press
address: London, UK
pages: 115
year: 1953
LCCN: QA343 .B76 1953
bibdate: Wed Mar 15 06:50:49 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 06:50:49 MDT
subject: Elliptic functions; Elliptische functies
acknowledgement: ack-nhfb
rawauthor: Frank Bowman
rawtitle: Introduction to Elliptic Functions with Applications
entry:
@Book{Bowman:1953:IEF,
  author =       "Frank Bowman",
  title =        "Introduction to Elliptic Functions with Applications",
  publisher =    "English Universities Press",
  address =      "London, UK",
  pages =        "115",
  year =         "1953",
  LCCN =         "QA343 .B76 1953",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  subject =      "Elliptic functions; Elliptische functies",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lovelace:1953:AET
author: Ada Augusta Lovelace
title: Appendix 1: Extracts From booktitle Taylor's Scientific Memoirs, Vol. III
crossref: Bowden:1953:FTT
pages: 341--408
year: 1953
bibdate: Fri Jun 08 08:33:30 2018
bibtimestamp: 2018.06.08 08:33:30 ???
acknowledgement: ack-nhfb
rawauthor: Ada Augusta Lovelace
rawtitle: {Appendix 1}: {Extracts} From {{\booktitle{Taylor's Scientific Memoirs}}, Vol. III}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
Reprint of cite Lovelace:1843:SAE. Pages 400--408 describe the computation of the Bernoulli numbers.

rawnote:
Reprint of \cite{Lovelace:1843:SAE}. Pages 400--408 describe the computation of the Bernoulli numbers.

entry:
@InProceedings{Lovelace:1953:AET,
  author =       "Ada Augusta Lovelace",
  title =        "{Appendix 1}: {Extracts} From {{\booktitle{Taylor's
                 Scientific Memoirs}}, Vol. III}",
  crossref =     "Bowden:1953:FTT",
  pages =        "341--408",
  year =         "1953",
  bibdate =      "Fri Jun 08 08:33:30 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Lovelace:1843:SAE}. Pages 400--408
                 describe the computation of the Bernoulli numbers.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Salzer:1953:RTO
author: Herbert E. Salzer
title: Radix Table for Obtaining Hyperbolic and Inverse Hyperbolic Functions to Many Places
journal: j-J-MATH-PHYS-MIT
volume: 32
number: 1--4
pages: 197--202
month: apr
monthnumber: 4
year: 1953
CODEN: JMPHA9
DOI: https://doi.org/10.1002/sapm1953321197
ISSN: 0097-1421 OR 00971421
ISSNL: 0097-1421 OR 00971421
bibdate: Sat Aug 19 13:35:59 MDT 2023
bibtimestamp: 2023.08.19 13:35:59 MDT
URL: https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1953321197
fjournal: Journal of Mathematics and Physics (MIT)
acknowledgement: ack-nhfb
ajournal: J. Math. Phys. (MIT)
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590
onlinedate: April 1953
rawauthor: Herbert E. Salzer
rawtitle: Radix Table for Obtaining Hyperbolic and Inverse Hyperbolic Functions to Many Places
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib

entry:
@Article{Salzer:1953:RTO,
  author =       "Herbert E. Salzer",
  title =        "Radix Table for Obtaining Hyperbolic and Inverse
                 Hyperbolic Functions to Many Places",
  journal =      j-J-MATH-PHYS-MIT,
  volume =       "32",
  number =       "1--4",
  pages =        "197--202",
  month =        apr,
  year =         "1953",
  CODEN =        "JMPHA9",
  DOI =          "https://doi.org/10.1002/sapm1953321197",
  ISSN =         "0097-1421",
  ISSN-L =       "0097-1421",
  bibdate =      "Sat Aug 19 13:35:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1953321197",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Phys. (MIT)",
  fjournal =     "Journal of Mathematics and Physics (MIT)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
  onlinedate =   "April 1953",
}


bibtype: article
filename: elefunt.bib
label: Scherberg:1953:ACP
author: Max G. Scherberg and John F. Riordan
title: Analogue Calculation of Polynomial and Trigonometric Expansions (in Other Aids to Computation)
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 7
number: 41
pages: 61--65
month: jan
monthnumber: 1
year: 1953
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-53-99373-9
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Max G. Scherberg and John F. Riordan
rawtitle: Analogue Calculation of Polynomial and Trigonometric Expansions (in {Other Aids to Computation})
entry:
@Article{Scherberg:1953:ACP,
  author =       "Max G. Scherberg and John F. Riordan",
  title =        "Analogue Calculation of Polynomial and Trigonometric
                 Expansions (in {Other Aids to Computation})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "7",
  number =       "41",
  pages =        "61--65",
  month =        jan,
  year =         "1953",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-53-99373-9",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Stiefel:1953:ITF
author: E. Stiefel
journal: j-Z-ANGE-MATH-MECH
volume: 33
pages: 260--262
year: 1953
CODEN: ZAMMAX
DOI: https://doi.org/10.1002/zamm.19530330806
ISSN: 0044-2267 (print), 1521-4001 (electronic) OR 00442267 (print), 15214001 (electronic)
ISSNL: 0044-2267 OR 00442267
MRclass: 65.0X
MRnumber: 59061
MRreviewer: D. C. Gilles
bibdate: Wed Sep 2 16:23:13 2020
bibtimestamp: 2020.09.02 16:23:13 ???
fjournal: Zeitschrift fur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten
language: German
acknowledgement: ack-nhfb
authordates: Eduard Stiefel (21 April 1909--25 November 1978)
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001
rawauthor: E. Stiefel
title:
Zur Interpolation von tabellierten Funktionen durch Exponentialsummen und zur Berechnung von Eigenwerten aus den Schwarzschen Konstanten. (German) [On interpolation of tabulated functions by exponential sums and on the calculation of eigenvalues from the Schwarz's constants]

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
{Zur Interpolation von tabellierten Funktionen durch Exponentialsummen und zur Berechnung von Eigenwerten aus den Schwarzschen Konstanten}. ({German}) [{On} interpolation of tabulated functions by exponential sums and on the calculation of eigenvalues from the {Schwarz}'s constants]

entry:
@Article{Stiefel:1953:ITF,
  author =       "E. Stiefel",
  title =        "{Zur Interpolation von tabellierten Funktionen durch
                 Exponentialsummen und zur Berechnung von Eigenwerten
                 aus den Schwarzschen Konstanten}. ({German}) [{On}
                 interpolation of tabulated functions by exponential
                 sums and on the calculation of eigenvalues from the
                 {Schwarz}'s constants]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "33",
  pages =        "260--262",
  year =         "1953",
  CODEN =        "ZAMMAX",
  DOI =          "https://doi.org/10.1002/zamm.19530330806",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "65.0X",
  MRnumber =     "59061",
  MRreviewer =   "D. C. Gilles",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
  fjournal =     "Zeitschrift f{\"{u}}r Angewandte Mathematik und
                 Mechanik. Ingenieurwissenschaftliche
                 Forschungsarbeiten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Turing:1953:SCR
author: A. M. Turing
title: Some calculations of the Riemann zeta-function
journal: j-PROC-LONDON-MATH-SOC-3
volume: 3
number: 3
pages: 99--117
year: 1953
CODEN: PLMTAL
ISSN: 0024-6115 (print), 1460-244X (electronic) OR 00246115 (print), 1460244X (electronic)
ISSNL: 0024-6115 OR 00246115
MRclass: 65.0X
MRnumber: MR0055785 (14,1126e)
MRreviewer: D. H. Lehmer
bibdate: Sat Nov 19 13:23:32 2005
bibtimestamp: 2005.11.19 13:23:32 ???
URL: http://turing.ecs.soton.ac.uk/browse.php/B/21
fjournal: Proceedings of the London Mathematical Society. Third Series
ZMnumber: 0050.08101
acknowledgement: ack-nhfb
rawauthor: A. M. Turing
rawtitle: Some calculations of the {Riemann} zeta-function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
See corrections and improvements cite Lehman:1970:DZR, and cite Trudgian:2011:ITM. The latter comments: ``Turing's Method has become the standard technique used in modern verification of the Riemann hypothesis.'' See also cite Lehmer:1956:RRZ.

rawnote:
See corrections and improvements \cite{Lehman:1970:DZR}, and \cite{Trudgian:2011:ITM}. The latter comments: ``Turing's Method has become the standard technique used in modern verification of the Riemann hypothesis.'' See also \cite{Lehmer:1956:RRZ}.

entry:
@Article{Turing:1953:SCR,
  author =       "A. M. Turing",
  title =        "Some calculations of the {Riemann} zeta-function",
  journal =      j-PROC-LONDON-MATH-SOC-3,
  volume =       "3",
  number =       "3",
  pages =        "99--117",
  year =         "1953",
  CODEN =        "PLMTAL",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  MRclass =      "65.0X",
  MRnumber =     "MR0055785 (14,1126e)",
  MRreviewer =   "D. H. Lehmer",
  bibdate =      "Sat Nov 19 13:23:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See corrections and improvements
                 \cite{Lehman:1970:DZR}, and \cite{Trudgian:2011:ITM}.
                 The latter comments: ``Turing's Method has become the
                 standard technique used in modern verification of the
                 Riemann hypothesis.'' See also
                 \cite{Lehmer:1956:RRZ}.",
  URL =          "http://turing.ecs.soton.ac.uk/browse.php/B/21",
  ZMnumber =     "0050.08101",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the London Mathematical Society. Third
                 Series",
}


bibtype: article
filename: elefunt.bib
label: Aaboe:1954:AKI
author: Asger Aaboe
title: Al-Kashi's iteration method for the determination of $ sin 1^circ $
journal: j-SCRIPTA-MATH
volume: 20
pages: 24--29
year: 1954
ISSN: 0036-9713 OR 00369713
ISSNL: 0036-9713 OR 00369713
MRclass: 01.0X
MRnumber: 62046
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
ZMnumber: 0055.00104
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: Asger Aaboe
rawtitle: {Al-K{\=a}sh{\v{\i}}}'s iteration method for the determination of $ \sin 1^\circ $
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/scripta-math.bib

fjournal:
Scripta Mathematica: A Quarterly Journal Devoted to the Philosophy, History, and Expository Treatment of Mathematics

entry:
@Article{Aaboe:1954:AKI,
  author =       "Asger Aaboe",
  title =        "{Al-K{\=a}sh{\v{\i}}}'s iteration method for the
                 determination of $ \sin 1^\circ $",
  journal =      j-SCRIPTA-MATH,
  volume =       "20",
  number =       "??",
  pages =        "24--29",
  month =        "????",
  year =         "1954",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  MRclass =      "01.0X",
  MRnumber =     "62046",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0055.00104",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  ZBmath =       "3086736",
}


bibtype: article
filename: elefunt.bib
label: Atta:1954:CGH
author: Susie E. Atta and Ward C. Sangren
title: Calculation of Generalized Hypergeometric Series
journal: j-J-ACM
volume: 1
number: 4
pages: 170--172
month: oct
monthnumber: 10
year: 1954
CODEN: JACOAH
DOI: https://doi.org/10.1145/320783.320785
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Tue Nov 08 21:50:00 1994
bibtimestamp: 1994.11.08 21:50:00 ???
fjournal: Journal of the Association for Computing Machinery
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Susie E. Atta and Ward C. Sangren
rawtitle: Calculation of Generalized Hypergeometric Series
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib

entry:
@Article{Atta:1954:CGH,
  author =       "Susie E. Atta and Ward C. Sangren",
  title =        "Calculation of Generalized Hypergeometric Series",
  journal =      j-J-ACM,
  volume =       "1",
  number =       "4",
  pages =        "170--172",
  month =        oct,
  year =         "1954",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/320783.320785",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 08 21:50:00 1994",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: article
filename: elefunt.bib
label: Cahill:1954:PCH
author: W. F. Cahill
title: Programs for Computing the Hypergeometric Series (in Automatic Computing Machinery; Discussions)
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 8
number: 45
pages: 36--37
month: jan
monthnumber: 1
year: 1954
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-54-99344-8
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. F. Cahill
rawtitle: Programs for Computing the Hypergeometric Series (in Automatic Computing Machinery; Discussions)
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

entry:
@Article{Cahill:1954:PCH,
  author =       "W. F. Cahill",
  title =        "Programs for Computing the Hypergeometric Series (in
                 Automatic Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "45",
  pages =        "36--37",
  month =        jan,
  year =         "1954",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-54-99344-8",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1954:PAE
author: C. W. Clenshaw
title: Polynomial approximations to elementary functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 8
number: 47
pages: 143--147
month: jul
monthnumber: 7
year: 1954
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1954-0063487-2
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
MRclass: 41.1X
MRnumber: 16,128f
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: C. W. Clenshaw
rawtitle: Polynomial approximations to elementary functions
entry:
@Article{Clenshaw:1954:PAE,
  author =       "C. W. Clenshaw",
  title =        "Polynomial approximations to elementary functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "47",
  pages =        "143--147",
  month =        jul,
  year =         "1954",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1954-0063487-2",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "41.1X",
  MRnumber =     "16,128f",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Fox:1954:STB
author: L. Fox
title: A Short Table for Bessel Functions of Integer Orders and Large Arguments
volume: 3
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: 28
year: 1954
MRclass: 65.0X
MRnumber: 65245
MRreviewer: R. C. Archibald
bibdate: Mon Nov 13 14:02:18 2023
bibtimestamp: 2023.11.13 14:02:18 ???
series: Royal Society Shorter Mathematical Tables
acknowledgement: ack-nhfb
authordates: Leslie Fox (30 September 1918--1 August 1992)
rawauthor: L. Fox
rawtitle: A Short Table for {Bessel} Functions of Integer Orders and Large Arguments
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Book{Fox:1954:STB,
  author =       "L. Fox",
  title =        "A Short Table for {Bessel} Functions of Integer Orders
                 and Large Arguments",
  volume =       "3",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "28",
  year =         "1954",
  MRclass =      "65.0X",
  MRnumber =     "65245",
  MRreviewer =   "R. C. Archibald",
  bibdate =      "Mon Nov 13 14:02:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Royal Society Shorter Mathematical Tables",
  acknowledgement = ack-nhfb,
  author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: techreport
filename: elefunt.bib
label: Franklin:1954:CARa
author: J. Franklin and B. Friedman
title: A convergent asymptotic representation for integrals
institution: Division of Electromagnetic Research, Institute of Mathematical Sciences, New York University
address: New York, NY, USA
pages: i + 17
year: 1954
MRclass: 40.0X
MRnumber: 0068019
MRreviewer: J. G. van der Corput
bibdate: Tue Feb 06 15:03:36 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.02.06 15:03:36 ???
series: Res. Rep. No. BR-9
remark: See applications in cite Temme:2015:AMI,Navas-Palencia:2018:HPC.
acknowledgement: ack-nhfb
rawauthor: J. Franklin and B. Friedman
rawtitle: A convergent asymptotic representation for integrals
entry:
@TechReport{Franklin:1954:CARa,
  author =       "J. Franklin and B. Friedman",
  title =        "A convergent asymptotic representation for integrals",
  institution =  "Division of Electromagnetic Research, Institute of
                 Mathematical Sciences, New York University",
  address =      "New York, NY, USA",
  pages =        "i + 17",
  year =         "1954",
  MRclass =      "40.0X",
  MRnumber =     "0068019",
  MRreviewer =   "J. G. van der Corput",
  bibdate =      "Tue Feb 06 15:03:36 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Res. Rep. No. BR-9",
  acknowledgement = ack-nhfb,
  remark =       "See applications in
                 \cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}


bibtype: article
filename: elefunt.bib
label: LaFara:1954:MCI
author: Robert L. LaFara
title: A Method for Calculating Inverse Trigonometric Functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 8
number: 47
pages: 132--139
month: jul
monthnumber: 7
year: 1954
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1954-0063150-8
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Robert L. LaFara
rawtitle: A Method for Calculating Inverse Trigonometric Functions
entry:
@Article{LaFara:1954:MCI,
  author =       "Robert L. LaFara",
  title =        "A Method for Calculating Inverse Trigonometric
                 Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "47",
  pages =        "132--139",
  month =        jul,
  year =         "1954",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1954-0063150-8",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: incollection
filename: elefunt.bib
label: Ostrowski:1954:TPA
author: A. M. Ostrowski
title: On two problems in abstract algebra connected with Horner's rule
crossref: Birkhoff:1954:SMM
pages: 40--48
year: 1954
bibdate: Fri Oct 20 10:13:10 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 10:13:10 ???
keywords: number of multiplications to evaluate a polynomial
remark: TO DO: Find copy of this book section.
acknowledgement: ack-nhfb
rawauthor: A. M. Ostrowski
rawtitle: On two problems in abstract algebra connected with {Horner}'s rule
entry:
@InCollection{Ostrowski:1954:TPA,
  author =       "A. M. Ostrowski",
  title =        "On two problems in abstract algebra connected with
                 {Horner}'s rule",
  crossref =     "Birkhoff:1954:SMM",
  pages =        "40--48",
  year =         "1954",
  bibdate =      "Fri Oct 20 10:13:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "TO DO: Find copy of this book section.",
}


bibtype: article
filename: elefunt.bib
label: Shenton:1954:INI
author: L. R. Shenton
title: Inequalities for the Normal Integral Including a New Continued Fraction
journal: j-BIOMETRIKA
volume: 41
number: 1/2
pages: 177--189
month: jun
monthnumber: 6
year: 1954
CODEN: BIOKAX
DOI: https://doi.org/10.2307/2333015
ISSN: 0006-3444 (print), 1464-3510 (electronic) OR 00063444 (print), 14643510 (electronic)
ISSNL: 0006-3444 OR 00063444
MRclass: 62.0X
MRnumber: 0061785 (15,884e)
MRreviewer: E. Lukacs
bibdate: Sat Jun 21 14:32:43 MDT 2014
bibtimestamp: 2014.06.21 14:32:43 MDT
URL: http://www.jstor.org/stable/2333015
fjournal: Biometrika
acknowledgement: ack-nhfb
journalURL: http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html
rawauthor: L. R. Shenton
rawtitle: Inequalities for the Normal Integral Including a New Continued Fraction
bibsource:
http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315422; https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Shenton:1954:INI,
  author =       "L. R. Shenton",
  title =        "Inequalities for the Normal Integral Including a New
                 Continued Fraction",
  journal =      j-BIOMETRIKA,
  volume =       "41",
  number =       "1/2",
  pages =        "177--189",
  month =        jun,
  year =         "1954",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2333015",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62.0X",
  MRnumber =     "0061785 (15,884e)",
  MRreviewer =   "E. Lukacs",
  bibdate =      "Sat Jun 21 14:32:43 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315422;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2333015",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
}


bibtype: inproceedings
filename: elefunt.bib
label: Todd:1954:MWN
author: John Todd
booktitle: Transactions of 2nd Symposium on Applied Mathematics, 29 April 1954, University of Chicago
title: Motivation for working on numerical analysis
publisher: pub-AMS
address: pub-AMS:adr
year: 1954
bibdate: Fri Oct 20 13:28:45 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 13:28:45 ???
remark: Sponsored by the American Mathematical Society and the Office of Ordnance Research
acknowledgement: ack-nhfb
rawauthor: John Todd
rawbooktitle: Transactions of {2nd Symposium on Applied Mathematics, 29 April 1954, University of Chicago}
rawtitle: Motivation for working on numerical analysis
entry:
@InProceedings{Todd:1954:MWN,
  author =       "John Todd",
  editor =       "????",
  booktitle =    "Transactions of {2nd Symposium on Applied Mathematics,
                 29 April 1954, University of Chicago}",
  title =        "Motivation for working on numerical analysis",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "????",
  year =         "1954",
  bibdate =      "Fri Oct 20 13:28:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Sponsored by the American Mathematical Society and the
                 Office of Ordnance Research",
}


bibtype: article
filename: elefunt.bib
label: Booth:1955:NAP
author: A. D. Booth
title: A note on approximating polynomials for trigonometric functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 9
number: 49
pages: 21--23
month: jan
monthnumber: 1
year: 1955
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1955-0069579-7
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
MRclass: 65.0X
MRnumber: 69579
MRreviewer: L. Fox
bibdate: Tue Nov 14 17:19:58 2023
bibtimestamp: 2023.11.14 17:19:58 ???
fjournal: Mathematical Tables and other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: A. D. Booth
rawtitle: A note on approximating polynomials for trigonometric functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib

entry:
@Article{Booth:1955:NAP,
  author =       "A. D. Booth",
  title =        "A note on approximating polynomials for trigonometric
                 functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  number =       "49",
  pages =        "21--23",
  month =        jan,
  year =         "1955",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1955-0069579-7",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "69579",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: techreport
filename: elefunt.bib
label: Carlson:1955:RAF
author: Bengt Carlson and Max Goldstein
title: Rational Approximations of Functions
type: Report
number: LA-1943
institution: inst-LASL
address: inst-LASL:adr
pages: iv + 46
month: aug
monthnumber: 8
year: 1955
DOI: https://doi.org/10.2172/4374577
bibdate: Sat Dec 27 09:41:36 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2014.12.27 09:41:36 ???
remark: Cited in cite [page 71]Abramowitz:1964:HMF.
acknowledgement: ack-nhfb
rawauthor: Bengt Carlson and Max Goldstein
rawtitle: Rational Approximations of Functions
URL:
http://www.osti.gov/scitech/biblio/4374577-0deJO9/; http://www.osti.gov/scitech/servlets/purl/4374577

keywords:
$-ln (x)/(1 - x)$; $art (x) / x$; $cos (x)$; $exp (-x)$; $sin (x) / x$; $tan (x) / x$; $x cot (x)$; $x**(1/2)$; $x**(1/3)$; $x**(1/4)$; $x**(1/5)$; $x**(1/6)$; $x**(1/7)$; continued fractions; rational approximations

entry:
@TechReport{Carlson:1955:RAF,
  author =       "Bengt Carlson and Max Goldstein",
  title =        "Rational Approximations of Functions",
  type =         "Report",
  number =       "LA-1943",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "iv + 46",
  month =        aug,
  year =         "1955",
  DOI =          "https://doi.org/10.2172/4374577",
  bibdate =      "Sat Dec 27 09:41:36 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.osti.gov/scitech/biblio/4374577-0deJO9/;
                 http://www.osti.gov/scitech/servlets/purl/4374577",
  acknowledgement = ack-nhfb,
  keywords =     "$-\ln(x)/(1 - x)$; $\art(x) / x$; $\cos(x)$;
                 $\exp(-x)$; $\sin(x) / x$; $\tan(x) / x$; $x \cot(x)$;
                 $x**(1/2)$; $x**(1/3)$; $x**(1/4)$; $x**(1/5)$;
                 $x**(1/6)$; $x**(1/7)$; continued fractions; rational
                 approximations",
  remark =       "Cited in \cite[page 71]{Abramowitz:1964:HMF}.",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1955:NSC
author: C. W. Clenshaw
title: A Note on the Summation of Chebyshev Series
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 9
number: 51
pages: 118--120
month: jul
monthnumber: 7
year: 1955
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1955-0071856-0
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
MRclass: 65.0X
MRnumber: 0071856
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
keywords: Chebyshev series; Clenshaw algorithm; Clenshaw summation; Horner polynomial evaluation
acknowledgement: ack-nhfb
authordates: Charles William Clenshaw (15 March 1926--23 September 2004)
journalURL: http://www.ams.org/mcom/
rawauthor: C. W. Clenshaw
rawtitle: A Note on the Summation of {Chebyshev} Series
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

remark:
Hidden inside cite Brenner:1955:TNS, but important in its own right for commentary on the recursive algorithm for summation of Chebyshev series, and a brief analysis of its accuracy.

entry:
@Article{Clenshaw:1955:NSC,
  author =       "C. W. Clenshaw",
  title =        "A Note on the Summation of {Chebyshev} Series",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  number =       "51",
  pages =        "118--120",
  month =        jul,
  year =         "1955",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "0071856",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev series; Clenshaw algorithm; Clenshaw
                 summation; Horner polynomial evaluation",
  remark =       "Hidden inside \cite{Brenner:1955:TNS}, but important
                 in its own right for commentary on the recursive
                 algorithm for summation of Chebyshev series, and a
                 brief analysis of its accuracy.",
}


bibtype: article
filename: elefunt.bib
label: Froberg:1955:NTC
author: Carl-Erik Froberg
title: Numerical Treatment of Coulomb Wave Functions
journal: j-REV-MOD-PHYS
volume: 27
number: 4
pages: 399--411
month: oct
monthnumber: 10
year: 1955
CODEN: RMPHAT
DOI: https://doi.org/10.1103/RevModPhys.27.399
ISSNL: 0034-6861 OR 00346861
bibdate: Tue May 22 16:36:44 MDT 2012
bibtimestamp: 2012.05.22 16:36:44 MDT
URL: http://link.aps.org/doi/10.1103/RevModPhys.27.399; http://rmp.aps.org/abstract/RMP/v27/i4/p399_1
fjournal: Reviews of Modern Physics
acknowledgement: ack-nhfb
journalURL: http://rmp.aps.org/browse
rawauthor: Carl-Erik Fr{\"o}berg
rawtitle: Numerical Treatment of {Coulomb} Wave Functions
ISSN:
0034-6861 (print), 1538-4527 (electronic), 1539-0756 OR 00346861 (print), 15384527 (electronic), 15390756

bibsource:
http://rmp.aps.org/toc/RMP/v27/i4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/revmodphys1950.bib

entry:
@Article{Froberg:1955:NTC,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "Numerical Treatment of {Coulomb} Wave Functions",
  journal =      j-REV-MOD-PHYS,
  volume =       "27",
  number =       "4",
  pages =        "399--411",
  month =        oct,
  year =         "1955",
  CODEN =        "RMPHAT",
  DOI =          "https://doi.org/10.1103/RevModPhys.27.399",
  ISSN =         "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
  ISSN-L =       "0034-6861",
  bibdate =      "Tue May 22 16:36:44 MDT 2012",
  bibsource =    "http://rmp.aps.org/toc/RMP/v27/i4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/revmodphys1950.bib",
  URL =          "http://link.aps.org/doi/10.1103/RevModPhys.27.399;
                 http://rmp.aps.org/abstract/RMP/v27/i4/p399_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Reviews of Modern Physics",
  journal-URL =  "http://rmp.aps.org/browse",
}


bibtype: book
filename: elefunt.bib
label: Hastings:1955:ADC
author: Cecil Hastings, Jr.
title: Approximations for Digital Computers
publisher: pub-PRINCETON
address: pub-PRINCETON:adr
pages: viii + 201
year: 1955
ISBN: 0-691-07914-5 OR 0691079145
ISBN13: 978-0-691-07914-1 OR 9780691079141
LCCN: QA76 .H37
bibdate: Mon Oct 01 15:59:48 2007
bibtimestamp: 2007.10.01 15:59:48 ???
note: Assisted by Jeanne T. Hayward and James P. Wong, Jr.
series: The Rand series
subject: Electronic digital computers; Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Cecil {Hastings, Jr.}
rawnote: Assisted by Jeanne T. Hayward and James P. Wong, Jr.
rawtitle: Approximations for Digital Computers
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager

TOC:
Preface / v Part I 1: Concerning Best Fit / 3 2: Linear Weights / 19 3: An Iterative Procedure / 27 4: Solution of Equations / 35 5: Chebyshev Polynomials / 47 6: Concerning Weights / 65 7: Function With a Peak / 75 8: Rates of Convergence / 83 9: Choice of Form / 95 10: A Scoring-Camera Problem / 115 Part II 1: $log _10 x$ / 125 5: $phi (x) = (1 - e^-x) / x$ / 129 8: $arctan x$ / 132 14: $sin (pi /2) x$ / 138 17: $10^x$ / 141 21: $W(x) = e^-x / (1 + e^-x)^2$ / 145 24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 27: $E'(x) = (1 / sqrt 2 pi ) e^-(1/2)x^2$ / 151 30: ``Total Klein-Nishina Cross Section'' Function / 154 31: $Gamma (1 + x)$ / 155 35: $arcsin x$ / 159 40: $log _2 x$ / 164 43: $Phi (x) = (2 / sqrt pi ) int _0^x e^-t^2 dt$ / 167 46: $K(k) = int _0^pi /2 (1 / sqrt 1 - k^2 sin ^2 phi ) dphi $ / 170 49: $E(k) = int _0^pi /2 (sqrt 1 - k^2 sin ^2 phi ) dphi $ / 173 52: $ln (1 + x)$ / 176 57: $e^-x$ / 181 61: $Phi (x) = (2 / sqrt pi ) int _0^x e^-t^2 dt$ / 185 64: $-rm Ei(-x) = int _x^infty (e^-t / t) dt$ / 188 67: $q = (1 / sqrt 2 pi ) int _x(q)^infty e^-(1/2)t^2 dt$ / 191 69: $W(z) = int _0^infty (e^(-u z) / (K_1^2(u) + pi ^2 I_1^2(u))) (1/u) du$ / 193 71: $P(x) = int _x^infty (sin (t - x) / t) dt$ / 195 74: $Q(x) = int _x^infty (cos (t - x) / t) dt$ / 195 References for Part II / 201

rawTOC:
Preface / v \\ Part I \\ 1: Concerning Best Fit / 3 \\ 2: Linear Weights / 19 \\ 3: An Iterative Procedure / 27 \\ 4: Solution of Equations / 35 \\ 5: Chebyshev Polynomials / 47 \\ 6: Concerning Weights / 65 \\ 7: Function With a Peak / 75 \\ 8: Rates of Convergence / 83 \\ 9: Choice of Form / 95 \\ 10: A Scoring-Camera Problem / 115 \\ Part II \\ 1: $\log_{10} x$ / 125 \\ 5: $\phi(x) = (1 - e^{-x}) / x$ / 129 \\ 8: $\arctan x$ / 132 \\ 14: $\sin (\pi/2) x$ / 138 \\ 17: $10^x$ / 141 \\ 21: $W(x) = e^{-x} / (1 + e^{-x})^2$ / 145 \\ 24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 \\ 27: $E'(x) = (1 / \sqrt{2 \pi}) e^{-(1/2)x^2}$ / 151 \\ 30: ``Total Klein-Nishina Cross Section'' Function / 154 \\ 31: $\Gamma(1 + x)$ / 155 \\ 35: $\arcsin x$ / 159 \\ 40: $\log_2 x$ / 164 \\ 43: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \, dt$ / 167 \\ 46: $K(k) = \int_0^{\pi/2} (1 / \sqrt{1 - k^2 \sin^2 \phi}) \, d\phi$ / 170 \\ 49: $E(k) = \int_0^{\pi/2} (\sqrt{1 - k^2 \sin^2 \phi}) \, d\phi$ / 173 \\ 52: $\ln(1 + x)$ / 176 \\ 57: $e^{-x}$ / 181 \\ 61: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \, dt$ / 185 \\ 64: $-{\rm Ei}(-x) = \int_x^\infty (e^{-t} / t) \, dt$ / 188 \\ 67: $q = (1 / \sqrt{2 \pi}) \int_{x(q)}^\infty e^{-(1/2)t^2} \, dt$ / 191 \\ 69: $W(z) = \int_0^\infty (e^(-u z) / (K_1^2(u) + \pi^2 I_1^2(u))) (1/u) \, du$ / 193 \\ 71: $P(x) = \int_x^\infty (\sin(t - x) / t) \, dt$ / 195 \\ 74: $Q(x) = \int_x^\infty (\cos(t - x) / t) \, dt$ / 195 \\ References for Part II / 201

entry:
@Book{Hastings:1955:ADC,
  author =       "Cecil {Hastings, Jr.}",
  title =        "Approximations for Digital Computers",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 201",
  year =         "1955",
  ISBN =         "0-691-07914-5",
  ISBN-13 =      "978-0-691-07914-1",
  LCCN =         "QA76 .H37",
  bibdate =      "Mon Oct 01 15:59:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Assisted by Jeanne T. Hayward and James P. Wong, Jr.",
  series =       "The Rand series",
  acknowledgement = ack-nhfb,
  remark-1 =     "Reprinted 1957, 1959, 1962, 1966, and 1970. I have
                 fourth printing (1962).",
  remark-2 =     "Hastings gives a polynomial approximation for
                 computing random numbers from a normal distribution.",
  subject =      "Electronic digital computers; Numerical analysis",
  tableofcontents = "Preface / v \\
                 Part I \\
                 1: Concerning Best Fit / 3 \\
                 2: Linear Weights / 19 \\
                 3: An Iterative Procedure / 27 \\
                 4: Solution of Equations / 35 \\
                 5: Chebyshev Polynomials / 47 \\
                 6: Concerning Weights / 65 \\
                 7: Function With a Peak / 75 \\
                 8: Rates of Convergence / 83 \\
                 9: Choice of Form / 95 \\
                 10: A Scoring-Camera Problem / 115 \\
                 Part II \\
                 1: $\log_{10} x$ / 125 \\
                 5: $\phi(x) = (1 - e^{-x}) / x$ / 129 \\
                 8: $\arctan x$ / 132 \\
                 14: $\sin (\pi/2) x$ / 138 \\
                 17: $10^x$ / 141 \\
                 21: $W(x) = e^{-x} / (1 + e^{-x})^2$ / 145 \\
                 24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 \\
                 27: $E'(x) = (1 / \sqrt{2 \pi}) e^{-(1/2)x^2}$ / 151
                 \\
                 30: ``Total Klein-Nishina Cross Section'' Function /
                 154 \\
                 31: $\Gamma(1 + x)$ / 155 \\
                 35: $\arcsin x$ / 159 \\
                 40: $\log_2 x$ / 164 \\
                 43: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
                 dt$ / 167 \\
                 46: $K(k) = \int_0^{\pi/2} (1 / \sqrt{1 - k^2 \sin^2
                 \phi}) \, d\phi$ / 170 \\
                 49: $E(k) = \int_0^{\pi/2} (\sqrt{1 - k^2 \sin^2 \phi})
                 \, d\phi$ / 173 \\
                 52: $\ln(1 + x)$ / 176 \\
                 57: $e^{-x}$ / 181 \\
                 61: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
                 dt$ / 185 \\
                 64: $-{\rm Ei}(-x) = \int_x^\infty (e^{-t} / t) \, dt$
                 / 188 \\
                 67: $q = (1 / \sqrt{2 \pi}) \int_{x(q)}^\infty
                 e^{-(1/2)t^2} \, dt$ / 191 \\
                 69: $W(z) = \int_0^\infty (e^(-u z) / (K_1^2(u) + \pi^2
                 I_1^2(u))) (1/u) \, du$ / 193 \\
                 71: $P(x) = \int_x^\infty (\sin(t - x) / t) \, dt$ /
                 195 \\
                 74: $Q(x) = \int_x^\infty (\cos(t - x) / t) \, dt$ /
                 195 \\
                 References for Part II / 201",
}


bibtype: book
filename: elefunt.bib
label: Hobson:1955:TSE
author: Ernest William Hobson
title: The Theory of Spherical and Ellipsoidal Harmonics
publisher: Chelsea Pub. Co.
address: New York, NY, USA
pages: 500
year: 1955
LCCN: QA406 .H7 1955
bibdate: Sat Apr 1 14:40:56 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:40:56 MDT
subject: Spherical harmonics; Lame's functions
acknowledgement: ack-nhfb
authordates: 1856--1933
rawauthor: Ernest William Hobson
rawtitle: The Theory of Spherical and Ellipsoidal Harmonics
entry:
@Book{Hobson:1955:TSE,
  author =       "Ernest William Hobson",
  title =        "The Theory of Spherical and Ellipsoidal Harmonics",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "500",
  year =         "1955",
  LCCN =         "QA406 .H7 1955",
  bibdate =      "Sat Apr 1 14:40:56 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1856--1933",
  subject =      "Spherical harmonics; Lam{\'e}'s functions",
}


bibtype: book
filename: elefunt.bib
label: McLachlan:1955:BFE
author: N. W. (Norman William) McLachlan
title: Bessel Functions for Engineers
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
edition: Second
pages: xii + 239
year: 1955
LCCN: QA408 .M3 1955
bibdate: Sat Apr 1 14:44:36 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:44:36 MDT
series: The Oxford engineering science series
subject: Bessel functions
acknowledgement: ack-nhfb
authordates: 1888--
rawauthor: N. W. (Norman William) McLachlan
rawtitle: {Bessel} Functions for Engineers
entry:
@Book{McLachlan:1955:BFE,
  author =       "N. W. (Norman William) McLachlan",
  title =        "{Bessel} Functions for Engineers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  edition =      "Second",
  pages =        "xii + 239",
  year =         "1955",
  LCCN =         "QA408 .M3 1955",
  bibdate =      "Sat Apr 1 14:44:36 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Oxford engineering science series",
  acknowledgement = ack-nhfb,
  author-dates = "1888--",
  subject =      "Bessel functions",
}


bibtype: article
filename: elefunt.bib
label: Motzkin:1955:EP
author: T. S. Motzkin
title: Evaluation of polynomials
journal: j-BULL-AMS
volume: 61
number: 2
pages: 163--163
month: mar
monthnumber: 3
year: 1955
CODEN: BAMOAD
ISSN: 0002-9904 (print), 1936-881X (electronic) OR 00029904 (print), 1936881X (electronic)
ISSNL: 0002-9904 OR 00029904
bibdate: Fri Oct 20 09:06:44 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 09:06:44 ???
fjournal: Bulletin of the American Mathematical Society
keywords: number of multiplications to evaluate a polynomial
remark: One-paragraph abstract only, with reference-less mention of Ostrowski.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/bull/all_issues.html
issue: 635
rawauthor: T. S. Motzkin
rawtitle: Evaluation of polynomials
entry:
@Article{Motzkin:1955:EP,
  author =       "T. S. Motzkin",
  title =        "Evaluation of polynomials",
  journal =      j-BULL-AMS,
  volume =       "61",
  number =       "2",
  pages =        "163--163",
  month =        mar,
  year =         "1955",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Fri Oct 20 09:06:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the American Mathematical Society",
  issue =        "635",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  keywords =     "number of multiplications to evaluate a polynomial",
  received =     "12 November 1954",
  remark =       "One-paragraph abstract only, with reference-less
                 mention of Ostrowski.",
}


bibtype: article
filename: elefunt.bib
label: Motzkin:1955:ERF
author: T. S. Motzkin
title: Evaluation of rational functions
journal: j-BULL-AMS
volume: 61
number: 2
pages: 163--163
month: mar
monthnumber: 3
year: 1955
CODEN: BAMOAD
ISSN: 0002-9904 (print), 1936-881X (electronic) OR 00029904 (print), 1936881X (electronic)
ISSNL: 0002-9904 OR 00029904
bibdate: Fri Oct 20 09:06:44 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 09:06:44 ???
fjournal: Bulletin of the American Mathematical Society
keywords: number of multiplications to evaluate a polynomial
remark: One-paragraph abstract only, with reference to Ostrowski.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/bull/all_issues.html
issue: 635
rawauthor: T. S. Motzkin
rawtitle: Evaluation of rational functions
entry:
@Article{Motzkin:1955:ERF,
  author =       "T. S. Motzkin",
  title =        "Evaluation of rational functions",
  journal =      j-BULL-AMS,
  volume =       "61",
  number =       "2",
  pages =        "163--163",
  month =        mar,
  year =         "1955",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Fri Oct 20 09:06:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the American Mathematical Society",
  issue =        "635",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  keywords =     "number of multiplications to evaluate a polynomial",
  received =     "12 November 1954",
  remark =       "One-paragraph abstract only, with reference to
                 Ostrowski.",
}


bibtype: article
filename: elefunt.bib
label: Norlund:1955:HF
author: Niels Erik Norlund
title: Hypergeometric functions
journal: j-ACTA-MATH
volume: 94
pages: 289--349
year: 1955
CODEN: ACMAA8
DOI: https://doi.org/10.1007/BF02392494
ISSN: 0001-5962 (print), 1871-2509 (electronic) OR 00015962 (print), 18712509 (electronic)
ISSNL: 0001-5962 OR 00015962
MRclass: 33.0X
MRnumber: MR0074585 (17,610d)
MRreviewer: A. Erd{\'e}lyi
bibdate: Thu Dec 01 10:09:47 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:09:47 ???
fjournal: Acta Mathematica
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11511
rawauthor: Niels Erik N{\o}rlund
rawtitle: Hypergeometric functions
entry:
@Article{Norlund:1955:HF,
  author =       "Niels Erik N{\o}rlund",
  title =        "Hypergeometric functions",
  journal =      j-ACTA-MATH,
  volume =       "94",
  number =       "??",
  pages =        "289--349",
  month =        "????",
  year =         "1955",
  CODEN =        "ACMAA8",
  DOI =          "https://doi.org/10.1007/BF02392494",
  ISSN =         "0001-5962 (print), 1871-2509 (electronic)",
  ISSN-L =       "0001-5962",
  MRclass =      "33.0X",
  MRnumber =     "MR0074585 (17,610d)",
  MRreviewer =   "A. Erd{\'e}lyi",
  bibdate =      "Thu Dec 01 10:09:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Mathematica",
  journal-URL =  "http://link.springer.com/journal/11511",
}


bibtype: article
filename: elefunt.bib
label: Preston:1955:ACS
author: F. S. Preston
title: An Analog Computer for the Solution of Tangents
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-4
number: 3
pages: 101--106
year: 1955
CODEN: IRELAO
DOI: https://doi.org/10.1109/IRETELC.1955.507908
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 15:10:37 MDT 2011
bibtimestamp: 2011.06.30 15:10:37 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407908
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: F. S. Preston
rawtitle: An Analog Computer for the Solution of Tangents
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Preston:1955:ACS,
  author =       "F. S. Preston",
  title =        "An Analog Computer for the Solution of Tangents",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-4",
  number =       "3",
  pages =        "101--106",
  month =        "????",
  year =         "1955",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/IRETELC.1955.507908",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:10:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407908",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: elefunt.bib
label: Robinson:1955:EAC
author: A. S. Robinson
title: An Electronic Analog Computing Technique for the Solution of Trigonometric Problems
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-4
number: 3
pages: 95--101
year: 1955
CODEN: IRELAO
DOI: https://doi.org/10.1109/IRETELC.1955.5407907
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 15:10:37 MDT 2011
bibtimestamp: 2011.06.30 15:10:37 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407907
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: A. S. Robinson
rawtitle: An Electronic Analog Computing Technique for the Solution of Trigonometric Problems
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Robinson:1955:EAC,
  author =       "A. S. Robinson",
  title =        "An Electronic Analog Computing Technique for the
                 Solution of Trigonometric Problems",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-4",
  number =       "3",
  pages =        "95--101",
  month =        "????",
  year =         "1955",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/IRETELC.1955.5407907",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:10:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407907",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: elefunt.bib
label: Salzer:1955:CZE
author: Herbert E. Salzer
title: Complex zeros of the error function
journal: j-J-FRANKLIN-INST
volume: 260
number: 3
pages: 209--211
month: sep
monthnumber: 9
year: 1955
CODEN: JFINAB
DOI: https://doi.org/10.1016/0016-0032(55)90732-8
ISSN: 0016-0032 (print), 1879-2693 (electronic) OR 00160032 (print), 18792693 (electronic)
ISSNL: 0016-0032 OR 00160032
MRclass: 65.1X
MRnumber: 71880
MRreviewer: L. Fox
bibdate: Tue Nov 14 17:19:58 2023
bibtimestamp: 2023.11.14 17:19:58 ???
fjournal: Journal of the Franklin Institute
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00160032
rawauthor: Herbert E. Salzer
rawtitle: Complex zeros of the error function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Salzer:1955:CZE,
  author =       "Herbert E. Salzer",
  title =        "Complex zeros of the error function",
  journal =      j-J-FRANKLIN-INST,
  volume =       "260",
  number =       "3",
  pages =        "209--211",
  month =        sep,
  year =         "1955",
  CODEN =        "JFINAB",
  DOI =          "https://doi.org/10.1016/0016-0032(55)90732-8",
  ISSN =         "0016-0032 (print), 1879-2693 (electronic)",
  ISSN-L =       "0016-0032",
  MRclass =      "65.1X",
  MRnumber =     "71880",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Franklin Institute",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00160032",
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: article
filename: elefunt.bib
label: Todd:1955:MWN
author: John Todd
title: Motivation for working in numerical analysis
journal: j-COMM-PURE-APPL-MATH
volume: 8
number: 1
pages: 97--116
month: feb
monthnumber: 2
year: 1955
CODEN: CPAMAT, CPMAMV
DOI: https://doi.org/10.1002/cpa.3160080107
ISSN: 0010-3640 (print), 1097-0312 (electronic) OR 00103640 (print), 10970312 (electronic)
ISSNL: 0010-3640 OR 00103640
MRclass: 65.0X
MRnumber: 70251
MRreviewer: G. E. Forsythe
bibdate: Fri Oct 20 08:38:37 2023
bibtimestamp: 2023.10.20 08:38:37 ???
fjournal: Communications on Pure and Applied Mathematics (New York)
ZMnumber: 0064.37402
acknowledgement: ack-nhfb
ajournal: Comm. Pure Appl. Math.
authordates: John Todd (16 May 1911--21 June 2007)
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312
rawauthor: John Todd
rawtitle: Motivation for working in numerical analysis
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

keywords:
characteristic roots (eigenvalues) of finite matrices; game theory; integral equations; modified differences; Monte Carlo; number of multiplications to evaluate a polynomial; polynomial evaluation; quadrature; recent activity in numerical analysis; sequence convergence acceleration; theory of machines (automata)

entry:
@Article{Todd:1955:MWN,
  author =       "John Todd",
  title =        "Motivation for working in numerical analysis",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "8",
  number =       "1",
  pages =        "97--116",
  month =        feb,
  year =         "1955",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160080107",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "65.0X",
  MRnumber =     "70251",
  MRreviewer =   "G. E. Forsythe",
  bibdate =      "Fri Oct 20 08:38:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0064.37402",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Pure Appl. Math.",
  author-dates = "John Todd (16 May 1911--21 June 2007)",
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  keywords =     "characteristic roots (eigenvalues) of finite matrices;
                 game theory; integral equations; modified differences;
                 Monte Carlo; number of multiplications to evaluate a
                 polynomial; polynomial evaluation; quadrature; recent
                 activity in numerical analysis; sequence convergence
                 acceleration; theory of machines (automata)",
  remark-1 =     "This may be the earliest paper to note that a
                 polynomial of degree $n$ can be evaluated with fewer
                 than $n$ multiplications, but requiring more than $n$
                 additions. The normal Horner form requires $n$ multiply
                 and $n$ add operations: $ h = a_n $, $ h = x h + a_k $
                 (for $ k = n - 1 $ to $0$), and on modern hardware can
                 be conveniently evaluated in $n$ consecutive fused
                 multiply-add operations. However, the evaluation of the
                 altered forms often has terms of differing signs, and
                 may be subject to catastrophic leading digit loss, when
                 the original polynomial, if it had coefficients of the
                 same sign, might have been computed stably for $ x >
                 0$. In some cases, the new coefficients are complex,
                 even when those of the original polynomial are real
                 numbers. See also related publications
                 \cite{Ostrowski:1954:TPA, Todd:1954:MWN,
                 Motzkin:1955:EP, Motzkin:1955:ERF, Belaga:1958:SPI,
                 Pan:1959:CSC, Pan:1959:SCP, Floyd:1961:ACE,
                 Dorn:1962:GHR, Knuth:1962:EPC, Eisman:1963:PER,
                 Eve:1964:EP, Rice:1965:CPR, Winograd:1970:NMN,
                 Rabin:1972:FEP, Miller:1975:CCN, Knuth:1998:EP,
                 Kusterer:1979:SEP, Ceberio:2002:HRI, Cameron:2024:AHM}.
                 Rice reports extreme numerical instability of the
                 Belaga and Motzkin forms, and moderate instability of
                 the Pan forms, while the Chebyshev form is never
                 unstable. Todd cites Motzkin's work as ``to appear'',
                 and those two one-paragraph abstracts were received 12
                 November 1954 and published in March 1955, but Todd's
                 paper has no received date, so we cannot determine
                 their relative priority. Entry
                 \cite{Ostrowski:1954:TPA} may be prior art, but a copy
                 of that work has not yet been located. The quotation in
                 entry \cite{Eve:1964:E} summarizes the bounds on the
                 number of add and multiply operations.",
  remark-2 =     "Knuth's treatment (Knuth:1962:EPC) concentrates on
                 operation counts, because the polynomial variable need
                 not be a real scalar floating-point number: it could be
                 complex, multiple precision, matrix, series, ..., where
                 multiplication is relatively expensive. Knuth remarks
                 on page 485 that ``numerical analysis of the accuracy
                 achieved \ldots{} is beyond the scope of this book: the
                 reader should be careful to investigate the accuracy of
                 any calculations undertaken with floating-point
                 arithmetic.'' On page 486, Knuth notes that the nested
                 form is often attributed to Horner:1819:XNM, but that
                 Isaac Newton used it in unpublished notes 150 years
                 earlier, and it was employed by the Chinese in the 13th
                 century CE.",
  remark-3 =     "The year of this paper is erroneously cited in
                 reference lists of several sources as 1951, rather than
                 the correct 1955.",
  ZBmath =       "3109832",
}


bibtype: book
filename: elefunt.bib
label: Achieser:1956:TA
author: N. I. Achieser
title: Theory of Approximation
publisher: Frederick Ungar Publishing Company
address: New York, NY, USA
pages: x + 307
year: 1956
LCCN: QA221 .A533 1956
bibdate: Fri Oct 20 08:06:59 MDT 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 08:06:59 MDT
subject: Mathematical analysis
acknowledgement: ack-nhfb
rawauthor: N. I. Achieser
rawtitle: Theory of Approximation
remark:
Translation of Russian original, Leketisii po teorii approksimaetisii. Reprinted in cite Achieser:1992:TA.

TOC:
Approximation Problems in Linear Normalized Spaces Formulation of the Principal Problem in the Theory of Approximation / 1 The Concept of Metric Space / 1 The Concept of Linear Normalized Space / 2 Examples of Linear Normalized Spaces / 3 The Inequalities of Holder and Minkowski / 4 Additional Examples of Linear Normalized Spaces / 7 Hilbert Space / 8 The Fundamental Theorem of Approximation Theory in Linear Normalized Spaces / 10 Strictly Normalized Spaces / 11 An Example of Approximation in the Space $L^p$ / 12 Geometric Interpretation / 13 Separable and Complete Spaces / 14 Approximation Theorems in Hilbert Space / 15 An Example of Approximation in Hilbert Space / 19 More About the Approximation Problem in Hilbert Space / 21 Orthonormalized Vector Systems in Hilbert Space / 22 Orthogonalization of Vector Systems / 23 Infinite Orthonormalized Systems / 25 An Example of a Non-Separable System / 29 Weierstrass' First Theorem / 29 Weierstrass' Second Theorem / 32 The Separability of the Space C / 33 The Separability of the Space $L^p$ / 34 Generalization of Weierstrass' Theorem to the Space $L^p$ / 37 The Completeness of the Space $L^p$ / 38 Examples of Complete Orthonormalized Systems in L[superscript 2] / 40 Muntz's Theorem / 43 The Concept of the Linear Functional / 46 F. Riesz's Theorem / 47 A Criterion for the Closure of a Set of Vectors in Linear Normalized Spaces / 49 P. L. Tchebysheff's Domain of Ideas Statement of the Problem / 51 A Generalization of the Theorem of de la Vallee-Poussin / 52 The Existence Theorem / 53 Tchebysheff's Theorem / 55 A Special Case of Tchebysheff's Theorem / 57 The Tchebysheff Polynomials of Least Deviation from Zero / 57 A Further Example of P. Tchebysheff's Theorem / 58 An Example for the Application of the General Theorem of de la Vallee-Poussin / 60 An Example for the Application of P. L. Tchebysheff's General Theorem / 62 The Passage to Periodic Functions / 64 An Example of Approximating with the Aid of Periodic Functions / 66 The Weierstrass Function / 66 Haar's Problem / 67 Proof of the Necessity of Haar's Condition / 68 Proof of the Sufficiency of Haar's Condition / 69 An Example Related to Haar's Problem / 72 P. L. Tchebysheff's Systems of Functions / 73 Generalization of P. L. Tchebysheff's Theorem / 74 On a Question Pertaining to the Approximation of a Continuous Function in the Space $L$ / 76 A. A. Markoff's Theorem / 82 Special Cases of the Theorem of A. A. Markoff / 85 Elements of Harmonic Analysis The Simplest Properties of Fourier Series / 89 Fourier Series for Functions of Bounded Variation / 93 The Parseval Equation for Fourier Series / 97 Examples of Fourier Series / 98 Trigonometric Integrals / 101 The Riemann--Lebesgue Theorem / 103 Plancherel's Theory / 104 Watson's Theorem / 106 Plancherel's Theorem / 108 Fejer's Theorem / 110 Integral-Operators of the Fejer Type / 113 The Theorem of Young and Hardy / 116 Examples of Kernels of the Fejer Type / 118 The Fourier Transformation of Integrable Functions / 120 The Faltung of two Functions / 122 V. A. Stekloff's Functions / 123 Multimonotonic Functions / 125 Conjugate Functions / 126 Certain Extremal Properties of Integral Transcendental Functions of the Exponential Type Integral Functions of the Exponential Type / 130 The Borel Transformation / 132 The Theorem of Wiener and Paley / 134 Integral Functions of the Exponential Type which are Bounded along the Real Axis / 137 S. N. Bernstein's Inequality / 140 B. M. Levitan's Polynomials / 146 The Theorem of Fejer and Riesz. A Generalization of This Theorem / 152 A Criterion for the Representation of Continuous Functions as Fourier--Stieltjes Integrals / 154 Questions Regarding the Best Harmonic Approximation of Functions Preliminary Remarks / 160 The Modulus of Continuity / 161 The Generalization to the Space $L^p$ ($p geq 1$) / 162 An Example of Harmonic Approximation / 165 Some Estimates for Fourier Coefficients / 169 More about V. A. Stekloff's Functions / 173 Two Lemmas / 175 The Direct Problem of Harmonic Approximation / 176 A Criterion due to B. Sz.-Nagy / 183 The Best Approximation of Differentiable Functions / 187 Direct Observations Concerning Periodic Functions / 195 Jackson's Second Theorem / 199 The Generalized Fejer Method / 201 Berstein's Theorem / 206 Priwaloff's Theorem / 210 Generalizations of Bernstein's Theorems to the Space $L^p$ ($p geq 1$) / 211 The Best Harmonic Approximation of Analytic Functions / 214 A Different Formulation of the Result of the Preceding Section / 218 The Converse of Bernstein's Theorem / 221 Wiener's Theorem on Approximation Wiener's Problem / 224 The Necessity of Wiener's Condition / 224 Some Definitions and Notation / 225 Several Lemmas / 227 The Wiener--Levy Theorem / 230 Proof of the Sufficiency of Wiener's Condition / 233 Wiener's General Tauber Theorem / 234 Weakly Decreasing Functions / 235 Remarks on the Terminology / 237 Ikehara's Theorem / 238 Carleman's Tauber Theorem / 241 Various Addenda and Problems Elementary Extremal Problems and Certain Closure Criteria / 243 Szego's Theorem and Some of Its Applications / 256 Further Examples of Closed Sequences of Functions / 267 The Caratheodory--Fejer Problem and Similar Problems / 270 Solotareff's Problems and Related Problems / 280 The Best Harmonic Approximation of the Simplest Analytic Functions / 289 Notes / 296 Index / 306

rawTOC:
Approximation Problems in Linear Normalized Spaces \\ Formulation of the Principal Problem in the Theory of Approximation / 1 \\ The Concept of Metric Space / 1 \\ The Concept of Linear Normalized Space / 2 \\ Examples of Linear Normalized Spaces / 3 \\ The Inequalities of Holder and Minkowski / 4 \\ Additional Examples of Linear Normalized Spaces / 7 \\ Hilbert Space / 8 \\ The Fundamental Theorem of Approximation Theory in Linear Normalized Spaces / 10 \\ Strictly Normalized Spaces / 11 \\ An Example of Approximation in the Space $L^p$ / 12 \\ Geometric Interpretation / 13 \\ Separable and Complete Spaces / 14 \\ Approximation Theorems in Hilbert Space / 15 \\ An Example of Approximation in Hilbert Space / 19 \\ More About the Approximation Problem in Hilbert Space / 21 \\ Orthonormalized Vector Systems in Hilbert Space / 22 \\ Orthogonalization of Vector Systems / 23 \\ Infinite Orthonormalized Systems / 25 \\ An Example of a Non-Separable System / 29 \\ Weierstrass' First Theorem / 29 \\ Weierstrass' Second Theorem / 32 \\ The Separability of the Space C / 33 \\ The Separability of the Space $L^p$ / 34 \\ Generalization of Weierstrass' Theorem to the Space $L^p$ / 37 \\ The Completeness of the Space $L^p$ / 38 \\ Examples of Complete Orthonormalized Systems in L[superscript 2] / 40 \\ Muntz's Theorem / 43 \\ The Concept of the Linear Functional / 46 \\ F. Riesz's Theorem / 47 \\ A Criterion for the Closure of a Set of Vectors in Linear Normalized Spaces / 49 \\ P. L. Tchebysheff's Domain of Ideas \\ Statement of the Problem / 51 \\ A Generalization of the Theorem of de la Vallee-Poussin / 52 \\ The Existence Theorem / 53 \\ Tchebysheff's Theorem / 55 \\ A Special Case of Tchebysheff's Theorem / 57 \\ The Tchebysheff Polynomials of Least Deviation from Zero / 57 \\ A Further Example of P. Tchebysheff's Theorem / 58 \\ An Example for the Application of the General Theorem of de la Vallee-Poussin / 60 \\ An Example for the Application of P. L. Tchebysheff's General Theorem / 62 \\ The Passage to Periodic Functions / 64 \\ An Example of Approximating with the Aid of Periodic Functions / 66 \\ The Weierstrass Function / 66 \\ Haar's Problem / 67 \\ Proof of the Necessity of Haar's Condition / 68 \\ Proof of the Sufficiency of Haar's Condition / 69 \\ An Example Related to Haar's Problem / 72 \\ P. L. Tchebysheff's Systems of Functions / 73 \\ Generalization of P. L. Tchebysheff's Theorem / 74 \\ On a Question Pertaining to the Approximation of a Continuous Function in the Space $L$ / 76 \\ A. A. Markoff's Theorem / 82 \\ Special Cases of the Theorem of A. A. Markoff / 85 \\ Elements of Harmonic Analysis \\ The Simplest Properties of Fourier Series / 89 \\ Fourier Series for Functions of Bounded Variation / 93 \\ The Parseval Equation for Fourier Series / 97 \\ Examples of Fourier Series / 98 \\ Trigonometric Integrals / 101 \\ The Riemann--Lebesgue Theorem / 103 \\ Plancherel's Theory / 104 \\ Watson's Theorem / 106 \\ Plancherel's Theorem / 108 \\ Fejer's Theorem / 110 \\ Integral-Operators of the Fejer Type / 113 \\ The Theorem of Young and Hardy / 116 \\ Examples of Kernels of the Fejer Type / 118 \\ The Fourier Transformation of Integrable Functions / 120 \\ The Faltung of two Functions / 122 \\ V. A. Stekloff's Functions / 123 \\ Multimonotonic Functions / 125 \\ Conjugate Functions / 126 \\ Certain Extremal Properties of Integral Transcendental Functions of the Exponential Type \\ Integral Functions of the Exponential Type / 130 \\ The Borel Transformation / 132 \\ The Theorem of Wiener and Paley / 134 \\ Integral Functions of the Exponential Type which are Bounded along the Real Axis / 137 \\ S. N. Bernstein's Inequality / 140 \\ B. M. Levitan's Polynomials / 146 \\ The Theorem of Fejer and Riesz. A Generalization of This Theorem / 152 \\ A Criterion for the Representation of Continuous Functions as Fourier--Stieltjes Integrals / 154 \\ Questions Regarding the Best Harmonic Approximation of Functions Preliminary Remarks / 160 \\ The Modulus of Continuity / 161 \\ The Generalization to the Space $L^p$ ($p \geq 1$) / 162 \\ An Example of Harmonic Approximation / 165 \\ Some Estimates for Fourier Coefficients / 169 \\ More about V. A. Stekloff's Functions / 173 \\ Two Lemmas / 175 \\ The Direct Problem of Harmonic Approximation / 176 \\ A Criterion due to B. Sz.-Nagy / 183 \\ The Best Approximation of Differentiable Functions / 187 \\ Direct Observations Concerning Periodic Functions / 195 \\ Jackson's Second Theorem / 199 \\ The Generalized Fejer Method / 201 \\ Berstein's Theorem / 206 \\ Priwaloff's Theorem / 210 \\ Generalizations of Bernstein's Theorems to the Space $L^p$ ($p \geq 1$) / 211 \\ The Best Harmonic Approximation of Analytic Functions / 214 \\ A Different Formulation of the Result of the Preceding Section / 218 \\ The Converse of Bernstein's Theorem / 221 \\ Wiener's Theorem on Approximation \\ Wiener's Problem / 224 \\ The Necessity of Wiener's Condition / 224 \\ Some Definitions and Notation / 225 \\ Several Lemmas / 227 \\ The Wiener--Levy Theorem / 230 \\ Proof of the Sufficiency of Wiener's Condition / 233 \\ Wiener's General Tauber Theorem / 234 \\ Weakly Decreasing Functions / 235 \\ Remarks on the Terminology / 237 \\ Ikehara's Theorem / 238 \\ Carleman's Tauber Theorem / 241 \\ Various Addenda and Problems \\ Elementary Extremal Problems and Certain Closure Criteria / 243 \\ Szego's Theorem and Some of Its Applications / 256 \\ Further Examples of Closed Sequences of Functions / 267 \\ The Caratheodory--Fejer Problem and Similar Problems / 270 \\ Solotareff's Problems and Related Problems / 280 \\ The Best Harmonic Approximation of the Simplest Analytic Functions / 289 \\ Notes / 296 \\ Index / 306

entry:
@Book{Achieser:1956:TA,
  author =       "N. I. Achieser",
  title =        "Theory of Approximation",
  publisher =    "Frederick Ungar Publishing Company",
  address =      "New York, NY, USA",
  pages =        "x + 307",
  year =         "1956",
  LCCN =         "QA221 .A533 1956",
  bibdate =      "Fri Oct 20 08:06:59 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Russian original, Lek{\"e}t{\`\i}sii po
                 teorii approksima{\"e}t{\`\i}sii. Reprinted in
                 \cite{Achieser:1992:TA}.",
  subject =      "Mathematical analysis",
  tableofcontents = "Approximation Problems in Linear Normalized Spaces
                 \\
                 Formulation of the Principal Problem in the Theory of
                 Approximation / 1 \\
                 The Concept of Metric Space / 1 \\
                 The Concept of Linear Normalized Space / 2 \\
                 Examples of Linear Normalized Spaces / 3 \\
                 The Inequalities of Holder and Minkowski / 4 \\
                 Additional Examples of Linear Normalized Spaces / 7 \\
                 Hilbert Space / 8 \\
                 The Fundamental Theorem of Approximation Theory in
                 Linear Normalized Spaces / 10 \\
                 Strictly Normalized Spaces / 11 \\
                 An Example of Approximation in the Space $L^p$ / 12 \\
                 Geometric Interpretation / 13 \\
                 Separable and Complete Spaces / 14 \\
                 Approximation Theorems in Hilbert Space / 15 \\
                 An Example of Approximation in Hilbert Space / 19 \\
                 More About the Approximation Problem in Hilbert Space /
                 21 \\
                 Orthonormalized Vector Systems in Hilbert Space / 22
                 \\
                 Orthogonalization of Vector Systems / 23 \\
                 Infinite Orthonormalized Systems / 25 \\
                 An Example of a Non-Separable System / 29 \\
                 Weierstrass' First Theorem / 29 \\
                 Weierstrass' Second Theorem / 32 \\
                 The Separability of the Space C / 33 \\
                 The Separability of the Space $L^p$ / 34 \\
                 Generalization of Weierstrass' Theorem to the Space
                 $L^p$ / 37 \\
                 The Completeness of the Space $L^p$ / 38 \\
                 Examples of Complete Orthonormalized Systems in
                 L[superscript 2] / 40 \\
                 Muntz's Theorem / 43 \\
                 The Concept of the Linear Functional / 46 \\
                 F. Riesz's Theorem / 47 \\
                 A Criterion for the Closure of a Set of Vectors in
                 Linear Normalized Spaces / 49 \\
                 P. L. Tchebysheff's Domain of Ideas \\
                 Statement of the Problem / 51 \\
                 A Generalization of the Theorem of de la Vallee-Poussin
                 / 52 \\
                 The Existence Theorem / 53 \\
                 Tchebysheff's Theorem / 55 \\
                 A Special Case of Tchebysheff's Theorem / 57 \\
                 The Tchebysheff Polynomials of Least Deviation from
                 Zero / 57 \\
                 A Further Example of P. Tchebysheff's Theorem / 58 \\
                 An Example for the Application of the General Theorem
                 of de la Vallee-Poussin / 60 \\
                 An Example for the Application of P. L. Tchebysheff's
                 General Theorem / 62 \\
                 The Passage to Periodic Functions / 64 \\
                 An Example of Approximating with the Aid of Periodic
                 Functions / 66 \\
                 The Weierstrass Function / 66 \\
                 Haar's Problem / 67 \\
                 Proof of the Necessity of Haar's Condition / 68 \\
                 Proof of the Sufficiency of Haar's Condition / 69 \\
                 An Example Related to Haar's Problem / 72 \\
                 P. L. Tchebysheff's Systems of Functions / 73 \\
                 Generalization of P. L. Tchebysheff's Theorem / 74 \\
                 On a Question Pertaining to the Approximation of a
                 Continuous Function in the Space $L$ / 76 \\
                 A. A. Markoff's Theorem / 82 \\
                 Special Cases of the Theorem of A. A. Markoff / 85 \\
                 Elements of Harmonic Analysis \\
                 The Simplest Properties of Fourier Series / 89 \\
                 Fourier Series for Functions of Bounded Variation / 93
                 \\
                 The Parseval Equation for Fourier Series / 97 \\
                 Examples of Fourier Series / 98 \\
                 Trigonometric Integrals / 101 \\
                 The Riemann--Lebesgue Theorem / 103 \\
                 Plancherel's Theory / 104 \\
                 Watson's Theorem / 106 \\
                 Plancherel's Theorem / 108 \\
                 Fejer's Theorem / 110 \\
                 Integral-Operators of the Fejer Type / 113 \\
                 The Theorem of Young and Hardy / 116 \\
                 Examples of Kernels of the Fejer Type / 118 \\
                 The Fourier Transformation of Integrable Functions /
                 120 \\
                 The Faltung of two Functions / 122 \\
                 V. A. Stekloff's Functions / 123 \\
                 Multimonotonic Functions / 125 \\
                 Conjugate Functions / 126 \\
                 Certain Extremal Properties of Integral Transcendental
                 Functions of the Exponential Type \\
                 Integral Functions of the Exponential Type / 130 \\
                 The Borel Transformation / 132 \\
                 The Theorem of Wiener and Paley / 134 \\
                 Integral Functions of the Exponential Type which are
                 Bounded along the Real Axis / 137 \\
                 S. N. Bernstein's Inequality / 140 \\
                 B. M. Levitan's Polynomials / 146 \\
                 The Theorem of Fejer and Riesz. A Generalization of
                 This Theorem / 152 \\
                 A Criterion for the Representation of Continuous
                 Functions as Fourier--Stieltjes Integrals / 154 \\
                 Questions Regarding the Best Harmonic Approximation of
                 Functions Preliminary Remarks / 160 \\
                 The Modulus of Continuity / 161 \\
                 The Generalization to the Space $L^p$ ($p \geq 1$) /
                 162 \\
                 An Example of Harmonic Approximation / 165 \\
                 Some Estimates for Fourier Coefficients / 169 \\
                 More about V. A. Stekloff's Functions / 173 \\
                 Two Lemmas / 175 \\
                 The Direct Problem of Harmonic Approximation / 176 \\
                 A Criterion due to B. Sz.-Nagy / 183 \\
                 The Best Approximation of Differentiable Functions /
                 187 \\
                 Direct Observations Concerning Periodic Functions / 195
                 \\
                 Jackson's Second Theorem / 199 \\
                 The Generalized Fejer Method / 201 \\
                 Berstein's Theorem / 206 \\
                 Priwaloff's Theorem / 210 \\
                 Generalizations of Bernstein's Theorems to the Space
                 $L^p$ ($p \geq 1$) / 211 \\
                 The Best Harmonic Approximation of Analytic Functions /
                 214 \\
                 A Different Formulation of the Result of the Preceding
                 Section / 218 \\
                 The Converse of Bernstein's Theorem / 221 \\
                 Wiener's Theorem on Approximation \\
                 Wiener's Problem / 224 \\
                 The Necessity of Wiener's Condition / 224 \\
                 Some Definitions and Notation / 225 \\
                 Several Lemmas / 227 \\
                 The Wiener--Levy Theorem / 230 \\
                 Proof of the Sufficiency of Wiener's Condition / 233
                 \\
                 Wiener's General Tauber Theorem / 234 \\
                 Weakly Decreasing Functions / 235 \\
                 Remarks on the Terminology / 237 \\
                 Ikehara's Theorem / 238 \\
                 Carleman's Tauber Theorem / 241 \\
                 Various Addenda and Problems \\
                 Elementary Extremal Problems and Certain Closure
                 Criteria / 243 \\
                 Szego's Theorem and Some of Its Applications / 256 \\
                 Further Examples of Closed Sequences of Functions / 267
                 \\
                 The Caratheodory--Fejer Problem and Similar Problems /
                 270 \\
                 Solotareff's Problems and Related Problems / 280 \\
                 The Best Harmonic Approximation of the Simplest
                 Analytic Functions / 289 \\
                 Notes / 296 \\
                 Index / 306",
}


bibtype: inproceedings
filename: elefunt.bib
label: Haynes:1956:EIE
author: John G. Haynes
booktitle: ACM'56: Proceedings of the 1956 11th ACM national meeting
title: Evaluation of incomplete elliptic integrals by Gaussian integration
publisher: pub-ACM
address: pub-ACM:adr
pages: 56--59
year: 1956
DOI: https://doi.org/10.1145/800258.808948
bibdate: Fri Dec 21 08:53:15 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.12.21 08:53:15 ???
URL: https://dl.acm.org/ft_gateway.cfm?id=808948
acknowledgement: ack-nhfb
rawauthor: John G. Haynes
rawbooktitle: {ACM'56: Proceedings of the 1956 11th ACM national meeting}
rawtitle: Evaluation of incomplete elliptic integrals by {Gaussian} integration
entry:
@InProceedings{Haynes:1956:EIE,
  author =       "John G. Haynes",
  editor =       "????",
  booktitle =    "{ACM'56: Proceedings of the 1956 11th ACM national
                 meeting}",
  title =        "Evaluation of incomplete elliptic integrals by
                 {Gaussian} integration",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "56--59",
  year =         "1956",
  DOI =          "https://doi.org/10.1145/800258.808948",
  bibdate =      "Fri Dec 21 08:53:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=808948",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Jeffreys:1956:MMP
author: Harold Jeffreys and Bertha Swirles Jeffreys
title: Methods of Mathematical Physics
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Third
pages: 714
year: 1956
LCCN: QA401 .J4 1956
bibdate: Thu Aug 17 10:48:45 2023
bibtimestamp: 2023.08.17 10:48:45 ???
URL: https://en.wikipedia.org/wiki/Bertha_Swirles; https://en.wikipedia.org/wiki/Harold_Jeffreys
remark: References to Douglas Hartree in
acknowledgement: ack-nhfb
subjectdates: Douglas Rayner Hartree (27 March 1897--12 February 1958)
rawauthor: Harold Jeffreys and Bertha {Swirles Jeffreys}
rawtitle: Methods of Mathematical Physics
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
Preface Authors' Notes 1: The Real Variable 2: Scalars and Vectors 3: Tensors 4: Matrices 5: Multiple Integrals 6: Potential Theory 7: Operational Methods 8: Physical Applications of the Operational Method 9: Numerical Methods 10: Calculus of Variations 11: Functions of a Complex Variable 12: Contour Integration and Bromwich's Integral 13: Conformal Representation 14: Fourier's Theorem 15: The Factorial and Related Functions 16: Solution of Linear Differential Equation 17: Asymptotic Expansions 18: The Equations of Potential, Waves, and Heat Conduction 19: Waves in One Dimension and Waves With Spherical Symmetry 20: Conduction of Heat in One and Three Dimensions 21: Bessel Functions 22: Applications of Bessel Functions 23: The Confluent Hypergeometric Function 24: Legendre Functions and Associated Functions 25: Elliptic Functions Notes Appendix on Notation Index

authordates:
Sir Harold Jeffreys (22 April 1891--18 March 1989); Lady Bertha Swirles Jeffreys (22 May 1903--18 December 1999)

rawTOC:
Preface \\ Authors' Notes \\ 1: The Real Variable \\ 2: Scalars and Vectors \\ 3: Tensors \\ 4: Matrices \\ 5: Multiple Integrals \\ 6: Potential Theory \\ 7: Operational Methods \\ 8: Physical Applications of the Operational Method \\ 9: Numerical Methods \\ 10: Calculus of Variations \\ 11: Functions of a Complex Variable \\ 12: Contour Integration and Bromwich's Integral \\ 13: Conformal Representation \\ 14: Fourier's Theorem \\ 15: The Factorial and Related Functions \\ 16: Solution of Linear Differential Equation \\ 17: Asymptotic Expansions \\ 18: The Equations of Potential, Waves, and Heat Conduction \\ 19: Waves in One Dimension and Waves With Spherical Symmetry \\ 20: Conduction of Heat in One and Three Dimensions \\ 21: Bessel Functions \\ 22: Applications of Bessel Functions \\ 23: The Confluent Hypergeometric Function \\ 24: Legendre Functions and Associated Functions \\ 25: Elliptic Functions \\ Notes \\ Appendix on Notation \\ Index

entry:
@Book{Jeffreys:1956:MMP,
  author =       "Harold Jeffreys and Bertha {Swirles Jeffreys}",
  title =        "Methods of Mathematical Physics",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "714",
  year =         "1956",
  LCCN =         "QA401 .J4 1956",
  bibdate =      "Thu Aug 17 10:48:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://en.wikipedia.org/wiki/Bertha_Swirles;
                 https://en.wikipedia.org/wiki/Harold_Jeffreys",
  acknowledgement = ack-nhfb,
  author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
                 Lady Bertha Swirles Jeffreys (22 May 1903--18 December
                 1999)",
  remark =       "References to Douglas Hartree in",
  remark-1 =     "First edition 1946, second edition 1950, third edition
                 1956, first paperback edition 1972, reprinted 1978,
                 1980, 1988, 1992, 1999, 2001. Third edition preface is
                 dated April 1953. Second edition preface is dated 15
                 November 1948. First edition preface is dated 1946.
                 Reprinted in \cite{Jeffreys:1999:MMP}.",
  subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
                 1958)",
  tableofcontents = "Preface \\
                 Authors' Notes \\
                 1: The Real Variable \\
                 2: Scalars and Vectors \\
                 3: Tensors \\
                 4: Matrices \\
                 5: Multiple Integrals \\
                 6: Potential Theory \\
                 7: Operational Methods \\
                 8: Physical Applications of the Operational Method \\
                 9: Numerical Methods \\
                 10: Calculus of Variations \\
                 11: Functions of a Complex Variable \\
                 12: Contour Integration and Bromwich's Integral \\
                 13: Conformal Representation \\
                 14: Fourier's Theorem \\
                 15: The Factorial and Related Functions \\
                 16: Solution of Linear Differential Equation \\
                 17: Asymptotic Expansions \\
                 18: The Equations of Potential, Waves, and Heat
                 Conduction \\
                 19: Waves in One Dimension and Waves With Spherical
                 Symmetry \\
                 20: Conduction of Heat in One and Three Dimensions \\
                 21: Bessel Functions \\
                 22: Applications of Bessel Functions \\
                 23: The Confluent Hypergeometric Function \\
                 24: Legendre Functions and Associated Functions \\
                 25: Elliptic Functions \\
                 Notes \\
                 Appendix on Notation \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Lehmer:1956:RRZ
author: D. H. Lehmer
title: On the roots of the Riemann zeta-function
journal: j-ACTA-MATH
volume: 95
number: 1
pages: 291--298
month: dec
monthnumber: 12
year: 1956
CODEN: ACMAA8
DOI: https://doi.org/10.1007/BF02401102
ISSN: 0001-5962 (print), 1871-2509 (electronic) OR 00015962 (print), 18712509 (electronic)
ISSNL: 0001-5962 OR 00015962
MRclass: 10.1X
MRnumber: 0086082 (19,121a)
MRreviewer: L. Schoenfeld
bibdate: Mon Sep 28 16:18:23 2015
bibtimestamp: 2015.09.28 16:18:23 ???
fjournal: Acta Mathematica
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11511
rawauthor: D. H. Lehmer
rawtitle: On the roots of the {Riemann} zeta-function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Lehmer:1956:RRZ,
  author =       "D. H. Lehmer",
  title =        "On the roots of the {Riemann} zeta-function",
  journal =      j-ACTA-MATH,
  volume =       "95",
  number =       "1",
  pages =        "291--298",
  month =        dec,
  year =         "1956",
  CODEN =        "ACMAA8",
  DOI =          "https://doi.org/10.1007/BF02401102",
  ISSN =         "0001-5962 (print), 1871-2509 (electronic)",
  ISSN-L =       "0001-5962",
  MRclass =      "10.1X",
  MRnumber =     "0086082 (19,121a)",
  MRreviewer =   "L. Schoenfeld",
  bibdate =      "Mon Sep 28 16:18:23 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Mathematica",
  journal-URL =  "http://link.springer.com/journal/11511",
  remark-1 =     "See \cite[references 38--39, page
                 54]{Bullynck:2015:CPT} for Turing's role in this work,
                 published two years after Turing's death in 1954.
                 Turing's incomplete work appears in
                 \cite{Turing:1953:SCR}.",
  remark-2 =     "From page 293: ``Plans to extend the work of
                 Titchmarsh [on the zeros of the Riemann zeta function]
                 by use of a differential analyzer were made in 1939 by
                 the late A. M. Turing. These were interrupted by the
                 war and later rendered obsolete by the advent of the
                 electronic digital computers.''",
  remark-3 =     "From page 293: ``In 1947 the writer programmed an
                 extension of the work of Titchmarsh [on the zeros of
                 the Riemann zeta function] for the ENIAC, the only
                 electronic computer then in operation. However, before
                 the program could be run, the ENIAC was drastically
                 modified thus rendering it useless for the problem.''",
  remark-4 =     "From page 293: ``In June 1950, Turing used the
                 Manchester University Mark 1 electronic digital
                 computer to examine the zeta-function for $24,937.96 <
                 t < 25,735.93$ (that is for $63 < \sqrt{\tau} < 6.4$)
                 and found in this region of the critical strip that
                 there are about 1070 simple zeros all with $a = 1/2$.
                 In another short run the validity of the Riemann
                 Hypothesis was verified between Titchmarsh's upper
                 limit of $t = 1468$ and $t = 1540$. Only some twenty
                 hours of machine time was used. Unfortunately no
                 further time was made available and these incomplete
                 results were published in 1953.''",
}


bibtype: inproceedings
filename: elefunt.bib
label: Luke:1956:RFAa
author: Yudell L. Luke
booktitle: ACM'56: Proceedings of the 1956 11th ACM national meeting
publisher: pub-ACM
address: pub-ACM:adr
pages: 13--16
year: 1956
DOI: https://doi.org/10.1145/800258.808937
bibdate: Fri Dec 21 08:53:15 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.12.21 08:53:15 ???
note: See errata and addenda cite Luke:1956:RFAb.
URL: https://dl.acm.org/ft_gateway.cfm?id=808937
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawbooktitle: {ACM'56: Proceedings of the 1956 11th ACM national meeting}
rawnote: See errata and addenda \cite{Luke:1956:RFAb}.
title:
On rational function approximations to the exponential function with application to the practical solution of linear differential difference equations with constant coefficients

rawtitle:
On rational function approximations to the exponential function with application to the practical solution of linear differential difference equations with constant coefficients

entry:
@InProceedings{Luke:1956:RFAa,
  author =       "Yudell L. Luke",
  editor =       "????",
  booktitle =    "{ACM'56: Proceedings of the 1956 11th ACM national
                 meeting}",
  title =        "On rational function approximations to the exponential
                 function with application to the practical solution of
                 linear differential difference equations with constant
                 coefficients",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "13--16",
  year =         "1956",
  DOI =          "https://doi.org/10.1145/800258.808937",
  bibdate =      "Fri Dec 21 08:53:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See errata and addenda \cite{Luke:1956:RFAb}.",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=808937",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Luke:1956:RFAb
author: Yudell L. Luke
booktitle: ACM'56: Proceedings of the 1956 11th ACM national meeting
publisher: pub-ACM
address: pub-ACM:adr
pages: 177--178
year: 1956
DOI: https://doi.org/10.1145/800258.808979
bibdate: Fri Dec 21 08:53:15 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.12.21 08:53:15 ???
note: See cite Luke:1956:RFAa.
URL: https://dl.acm.org/ft_gateway.cfm?id=808979
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawbooktitle: {ACM'56: Proceedings of the 1956 11th ACM national meeting}
rawnote: See \cite{Luke:1956:RFAa}.
title:
On rational function approximations to the exponential function with application to the practical solution of linear differential difference equations with constant coefficients: Errata and addenda

rawtitle:
On rational function approximations to the exponential function with application to the practical solution of linear differential difference equations with constant coefficients: Errata and addenda

entry:
@InProceedings{Luke:1956:RFAb,
  author =       "Yudell L. Luke",
  editor =       "????",
  booktitle =    "{ACM'56: Proceedings of the 1956 11th ACM national
                 meeting}",
  title =        "On rational function approximations to the exponential
                 function with application to the practical solution of
                 linear differential difference equations with constant
                 coefficients: Errata and addenda",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "177--178",
  year =         "1956",
  DOI =          "https://doi.org/10.1145/800258.808979",
  bibdate =      "Fri Dec 21 08:53:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Luke:1956:RFAa}.",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=808979",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Sneddon:1956:SFM
author: Ian Naismith Sneddon
title: Special Functions of Mathematical Physics and Chemistry
volume: 19
publisher: Oliver and Boyd
address: Edinburgh, UK
edition: Third
pages: viii + 164
year: 1956
LCCN: QA1 U588 v. 19
bibdate: Sat Oct 30 18:41:48 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 18:41:48 ???
series: University mathematical texts
remark: See second edition cite Sneddon:1961:SFM and third edition cite Sneddon:1980:SFM.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: Ian Naismith Sneddon
rawtitle: Special Functions of Mathematical Physics and Chemistry
entry:
@Book{Sneddon:1956:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "Special Functions of Mathematical Physics and
                 Chemistry",
  volume =       "19",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Third",
  pages =        "viii + 164",
  year =         "1956",
  LCCN =         "QA1 U588 v. 19",
  bibdate =      "Sat Oct 30 18:41:48 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  remark =       "See second edition \cite{Sneddon:1961:SFM} and third
                 edition \cite{Sneddon:1980:SFM}.",
  subject =      "Functions, Special",
}


bibtype: book
filename: elefunt.bib
label: Stratton:1956:SWF
author: Julius Adams Stratton
title: Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiii + 613
year: 1956
LCCN: QA405 .S8
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
subject: Wave mechanics; Spheroidal functions
acknowledgement: ack-nhfb
authordates: 1901--1994
rawauthor: Julius Adams Stratton
rawtitle: Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients
entry:
@Book{Stratton:1956:SWF,
  author =       "Julius Adams Stratton",
  title =        "Spheroidal Wave Functions, Including Tables of
                 Separation Constants and Coefficients",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 613",
  year =         "1956",
  LCCN =         "QA405 .S8",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1901--1994",
  subject =      "Wave mechanics; Spheroidal functions",
}


bibtype: book
filename: elefunt.bib
label: Edmonds:1957:AMQ
author: A. R. (Alan Robert) Edmonds
title: Angular Momentum in Quantum Mechanics
publisher: pub-PRINCETON
address: pub-PRINCETON:adr
pages: viii + 146
year: 1957
bibdate: Mon Aug 4 15:01:00 MDT 2025
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.08.04 15:01:00 MDT
series: Investigations in physics
acknowledgement: ack-nhfb
rawauthor: A. R. (Alan Robert) Edmonds
rawtitle: Angular Momentum in Quantum Mechanics
entry:
@Book{Edmonds:1957:AMQ,
  author =       "A. R. (Alan Robert) Edmonds",
  title =        "Angular Momentum in Quantum Mechanics",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 146",
  year =         "1957",
  LCCN =         "????",
  bibdate =      "Mon Aug 4 15:01:00 MDT 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Investigations in physics",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Flammer:1957:SWF
author: Carson Flammer
title: Spheroidal Wave Functions
publisher: pub-STANFORD
address: pub-STANFORD:adr
pages: ix + 220
year: 1957
LCCN: QA405 .F55
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
series: A Stanford Research Institute monograph
subject: Spheroidal functions
acknowledgement: ack-nhfb
rawauthor: Carson Flammer
rawtitle: Spheroidal Wave Functions
remark:
The basis for this monograph was work done at Stanford Research Institute for the United States Air Force Cambridge Research Center under Contract AF 19 (604)-1296.

entry:
@Book{Flammer:1957:SWF,
  author =       "Carson Flammer",
  title =        "Spheroidal Wave Functions",
  publisher =    pub-STANFORD,
  address =      pub-STANFORD:adr,
  pages =        "ix + 220",
  year =         "1957",
  LCCN =         "QA405 .F55",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "A Stanford Research Institute monograph",
  acknowledgement = ack-nhfb,
  remark =       "The basis for this monograph was work done at Stanford
                 Research Institute for the United States Air Force
                 Cambridge Research Center under Contract AF 19
                 (604)-1296.",
  subject =      "Spheroidal functions",
}


bibtype: article
filename: elefunt.bib
label: Franklin:1957:CARb
author: Joel Franklin and Bernard Friedman
title: A convergent asymptotic representation for integrals
journal: j-PROC-CAMBRIDGE-PHIL-SOC
volume: 53
pages: 612--619
year: 1957
CODEN: PCPSA4
ISSN: 0008-1981 OR 00081981
MRclass: 42.1X
MRnumber: 0090691
MRreviewer: P. Henrici
bibdate: Tue Feb 06 15:03:36 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.02.06 15:03:36 ???
fjournal: Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences
remark: See applications in cite Temme:2015:AMI,Navas-Palencia:2018:HPC.
acknowledgement: ack-nhfb
journalURL: http://journals.cambridge.org/action/displayJournal?jid=PSP
rawauthor: Joel Franklin and Bernard Friedman
rawtitle: A convergent asymptotic representation for integrals
URL:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2F167020D3A1F98182882E99549E7751/S0305004100032667a.pdf/a-convergent-asymptotic-representation-for-integrals.pdf

abstract:
This paper represents a new method for obtaining an asymptotic representation for integrals of the form $ int _0^infty e^-p x x^c - 1 f(x) d x $ when $p$ is large. It is shown that if $ f(x)$ satisfies certain conditions this representation is also convergent. Numerical calculations seem to show that the first term of the representation gives a close approximation to the value of the integral for a wide range of values of $p$.

rawabstract:
This paper represents a new method for obtaining an asymptotic representation for integrals of the form $ \int_0^\infty e^{-p x} x^{c - 1} f(x) \, d x $ when $p$ is large. It is shown that if $ f(x)$ satisfies certain conditions this representation is also convergent. Numerical calculations seem to show that the first term of the representation gives a close approximation to the value of the integral for a wide range of values of $p$.

entry:
@Article{Franklin:1957:CARb,
  author =       "Joel Franklin and Bernard Friedman",
  title =        "A convergent asymptotic representation for integrals",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "53",
  pages =        "612--619",
  year =         "1957",
  CODEN =        "PCPSA4",
  ISSN =         "0008-1981",
  MRclass =      "42.1X",
  MRnumber =     "0090691",
  MRreviewer =   "P. Henrici",
  bibdate =      "Tue Feb 06 15:03:36 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2F167020D3A1F98182882E99549E7751/S0305004100032667a.pdf/a-convergent-asymptotic-representation-for-integrals.pdf",
  abstract =     "This paper represents a new method for obtaining an
                 asymptotic representation for integrals of the form $
                 \int_0^\infty e^{-p x} x^{c - 1} f(x) \, d x $ when $p$
                 is large. It is shown that if $ f(x)$ satisfies certain
                 conditions this representation is also convergent.
                 Numerical calculations seem to show that the first term
                 of the representation gives a close approximation to
                 the value of the integral for a wide range of values of
                 $p$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Cambridge Philosophical Society.
                 Mathematical and physical sciences",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  remark =       "See applications in
                 \cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}


bibtype: article
filename: elefunt.bib
label: Hitchcock:1957:PAB
author: A. J. M. Hitchcock
title: Polynomial Approximations to Bessel Functions of Order Zero and One and to Related Functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
number: 58
pages: 86--88
month: apr
monthnumber: 4
year: 1957
CODEN: MTTCAS
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Mon Feb 27 08:05:17 2012
bibtimestamp: 2012.02.27 08:05:17 ???
URL: http://www.jstor.org/stable/2002156
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: A. J. M. Hitchcock
rawtitle: Polynomial Approximations to {Bessel} Functions of Order Zero and One and to Related Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

entry:
@Article{Hitchcock:1957:PAB,
  author =       "A. J. M. Hitchcock",
  title =        "Polynomial Approximations to {Bessel} Functions of
                 Order Zero and One and to Related Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "86--88",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002156",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Kogbetliantz:1957:CEN
author: E. G. Kogbetliantz
title: Computation of $ e^N $ for $ - infty < N < + infty $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 1
number: 2
pages: 110--115
month: apr
monthnumber: 4
year: 1957
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.12.0110
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 68.0X
MRnumber: 19,775d
bibdate: Tue Sep 06 20:55:54 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.06 20:55:54 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: W. F. Freiberger
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of {$ e^N $} for $ - \infty < {N} < + \infty $ Using an Electronic Computer
entry:
@Article{Kogbetliantz:1957:CEN,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of {$ e^N $} for $ - \infty < {N} < +
                 \infty $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "110--115",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.12.0110",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "68.0X",
  MRnumber =     "19,775d",
  bibdate =      "Tue Sep 06 20:55:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "W. F. Freiberger",
}


bibtype: article
filename: elefunt.bib
label: Linskii:1957:CEF
author: V. S. Linskii
title: Calculation of elementary functions on automatic digital machines. (Russian)
journal: Vycisl. Mat.
volume: 2
pages: 90--119
year: 1957
MRclass: 68.00
MRnumber: 21 \#982
MRreviewer: J. W. Carr, III
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. S. Linski{\u{\i}}
rawtitle: Calculation of elementary functions on automatic digital machines. ({Russian})
entry:
@Article{Linskii:1957:CEF,
  author =       "V. S. Linski{\u{\i}}",
  title =        "Calculation of elementary functions on automatic
                 digital machines. ({Russian})",
  journal =      "Vy{\v{c}}isl. Mat.",
  volume =       "2",
  pages =        "90--119",
  year =         "1957",
  MRclass =      "68.00",
  MRnumber =     "21 \#982",
  MRreviewer =   "J. W. Carr, III",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Luke:1957:C
author: Yudell L. Luke
title: On the Computation of $ log Z $ and $ operatorname arc tan Z $
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
number: 57
pages: 16--18
month: jan
monthnumber: 1
year: 1957
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1957-0084855-1
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke
rawtitle: On the Computation of $ \log {Z} $ and $ \operatorname {arc} \tan {Z} $
entry:
@Article{Luke:1957:C,
  author =       "Yudell L. Luke",
  title =        "On the Computation of $ \log {Z} $ and $ \operatorname
                 {arc} \tan {Z} $",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "57",
  pages =        "16--18",
  month =        jan,
  year =         "1957",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1957-0084855-1",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Miller:1957:NGS
author: J. C. P. Miller
title: Note on the General Solution of the Confluent Hypergeometric Equation
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
number: 58
pages: 97--99
month: apr
monthnumber: 4
year: 1957
CODEN: MTTCAS
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Mon Feb 27 08:05:17 2012
bibtimestamp: 2012.02.27 08:05:17 ???
URL: http://www.jstor.org/stable/2002156
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. C. P. Miller
rawtitle: Note on the General Solution of the Confluent Hypergeometric Equation
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

entry:
@Article{Miller:1957:NGS,
  author =       "J. C. P. Miller",
  title =        "Note on the General Solution of the Confluent
                 Hypergeometric Equation",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "97--99",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002156",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Southard:1957:ATW
author: Thomas H. Southard
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
number: 58
pages: 99--100
month: apr
monthnumber: 4
year: 1957
CODEN: MTTCAS
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Mon Feb 27 08:05:17 2012
bibtimestamp: 2012.02.27 08:05:17 ???
URL: http://www.jstor.org/stable/2002156
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Thomas H. Southard
title:
Approximation and Table of the Weierstrass $ wp $ Function in the Equianharmonic Case for Real Argument

rawtitle:
Approximation and Table of the {Weierstrass} $ \wp $ Function in the Equianharmonic Case for Real Argument

entry:
@Article{Southard:1957:ATW,
  author =       "Thomas H. Southard",
  title =        "Approximation and Table of the {Weierstrass} $ \wp $
                 Function in the Equianharmonic Case for Real Argument",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "99--100",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002156",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Stegun:1957:GBF
author: Irene A. Stegun and Milton Abramowitz
title: Generation of Bessel Functions on High Speed Computers
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
number: 60
pages: 255--257
month: oct
monthnumber: 10
year: 1957
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1957-0093939-3
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Irene A. Stegun and Milton Abramowitz
rawtitle: Generation of {Bessel} Functions on High Speed Computers
entry:
@Article{Stegun:1957:GBF,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Generation of {Bessel} Functions on High Speed
                 Computers",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "60",
  pages =        "255--257",
  month =        oct,
  year =         "1957",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1957-0093939-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: T:1957:CHS
author: C. B. T.
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
number: 58
pages: 110--110
month: apr
monthnumber: 4
year: 1957
CODEN: MTTCAS
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Mon Feb 27 08:05:17 2012
bibtimestamp: 2012.02.27 08:05:17 ???
URL: http://www.jstor.org/stable/2002157
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: C. B. T.
title:
Comment: T. H. Southard, booktitle Approximation and table of the Weierstrass $ wp $ function in the equianharmonic case for real argument. [MTAC, this issue, p. 99--100]

rawtitle:
Comment: {T. H. Southard, \booktitle{Approximation and table of the Weierstrass $ \wp $ function in the equianharmonic case for real argument}. [MTAC, this issue, p. 99--100]}

entry:
@Article{T:1957:CHS,
  author =       "C. B. T.",
  title =        "Comment: {T. H. Southard, \booktitle{Approximation and
                 table of the Weierstrass $ \wp $ function in the
                 equianharmonic case for real argument}. [MTAC, this
                 issue, p. 99--100]}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "110--110",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002157",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Wilkes:1957:PPE
author: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
title: The Preparation of Programs for an Electronic Digital Computer
publisher: pub-AW
address: pub-AW:adr
edition: Second
pages: xiv + 238
year: 1957
LCCN: QA76.5 .W52 1957
bibdate: Mon Feb 10 09:42:47 2020
bibtimestamp: 2020.02.10 09:42:47 ???
note: See also first edition cite Wilkes:1951:PPE.
URL: https://b-ok.org/book/3668116/b363ff
acknowledgement: ack-nhfb
rawauthor: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
rawnote: See also first edition \cite{Wilkes:1951:PPE}.
rawtitle: The Preparation of Programs for an Electronic Digital Computer
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 1-1 Introduction / 1 1-2 Types of automatic computing machine / 1 1-3 The EDSAC / 3 1-4 Store / 5 1-5 Arithmetical unit / 5 1-6 Form of numbers in the machine / 5 1-7 Form of orders in the machine / 6 1-8 Storage of orders / 6 1-9 Written form of orders / 7 1-10 Some simple examples / 7 Exercises A / 9 1-11 Jump orders / 9 Exercises B / 11 1-12 Repeated groups of orders / 11 1-13 The use of the B-register / 15 Exercises C / 18 1-14 Equivalence between orders and numbers; pseudo-orders / 18 1-15 Use of the arithmetical unit for constructing or modifying orders / 20 1-16 The mix order / 23 Exercises D / 24 CHAPTER 2. SUBROUTINES / 25 2-1 Introduction / 25 2-2 Relative numbering of addresses / 25 2-3 Internal and external forms of orders / 26 2-4 Reading of orders from the input tape / 28 2-5 Open and closed subroutines / 29 2-6 Entering and leaving a closed subroutine / 29 2-7 Closed B subroutines / 30 2-8 Closed A subroutines / 31 2-9 Use of library subroutines / 32 Exercises E / 33 2-10 Long numbers / 35 2-11 Some further orders in the order code / 36 2-12 Scale factors / 38 2-13 Control combinations / 39 Exercises F / 40 2-14 Relative addresses in control combinations / 41 2-15 Extension of the use of relative addresses / 41 2-16 Setting of the constants to be added by terminal code letters / 43 2-17 Complete table of terminal code letters / 44 2-18 Parameters / 45 2-19 Preset parameters / 46 2-20 Program parameters / 46 2-21 Standard procedure for setting preset parameters / 46 2-22 Interpretive subroutines / 47 Exercises G / 49 CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 3-1 Introduction / 51 3-2 Single-address codes / 52 3-3 Multi-address codes / 53 3-4 Multiplication and division / 56 3-5 Source-destination codes / 57 3-6 Representation of negative numbers / 59 3-7 Miscellaneous facilities / 60 3-8 Minimum-access coding / 61 3-9 The evaluation of an order code / 63 3-10 Use of an auxiliary store / 64 CHAPTER 4. INPUT AND OUTPUT / 66 4-1 Introduction / 66 4-2 Input of numbers / 66 4-3 Output of numbers / 67 4-4 Input of orders / 69 4-5 Recognition of the code letter S / 72 4-6 Economy of input and output time / 72 4-7 Some features of input systems used with other machines / 73 4-8 Punched tape / 73 4-9 Punched cards / 75 CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 5-1 Introduction / 80 5-2 Library catalog / 80 5-3 Input subroutines / 81 5-4 Output subroutines / 81 5-5 Division subroutines / 82 5-6 Trigonometric and other functions / 82 5-7 The economization of a power series by the use of Chebyshev polynomials / 83 5-8 Quadrature / 86 5-9 Integration of ordinary differential equations / 87 5-10 Library subroutines Gl2 and G13: Runge--Kutta processes / 88 5-11 The independent variable / 88 5-12 Definition of the Runge--Kutta--Gill process / 89 5-13 Taylor-series method / 90 5-14 Interpretive subroutines / 90 5-15 Floating-point subroutines / 90 CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 6-1 Introduction / 92 6-2 Proofreading of programs / 93 6-3 Punching / 93 6-4 Locating mistakes in a program- / 94 6-5 Subroutines for checking programs / 96 6-6 The development of a program / 97 CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC / 99 EXAMPLE 1 Calculation of $e^-sin x$ / 99 EXAMPLE 2 The evaluation of a definite integral / 102 EXAMPLE 3 Integration of an ordinary differential equation / 108 EXAMPLE 4 Evaluation of a Fourier transform / 113 EXAMPLE 5 Evaluation of a definite integral / 118 CHAPTER 8. AUTOMATIC PROGRAMMING / 126 8-1 Introduction / 126 8-2 Conversion versus interpretation / 127 8-3 Assembly of a program / 127 8-4 Floating addresses / 129 8-5 Formula recognition / 136 Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES / 139 CATEGORY A. Subroutines to carry out floating-point arithmetic / 140 CATEGORY B. Subroutines to perform arithmetical operations on complex numbers / 142 CATEGORY C. Error-diagnosis subroutines / 144 CATEGORY D. Division subroutines / 146 CATEGORY E. Exponential subroutines / 148 CATEGORY F. General subroutines relating to functions / 148 CATEGORY G. Subroutines for the integration of differential equations / 150 CATEGORY L. Subroutines for evaluating logarithms / 153 CATEGORY M. Miscellaneous subroutines / 154 CATEGORY N. Operations on double-length numbers / 156 CATEGORY P. Print subroutines / 158 CATEGORY Q. Quadrature subroutines / 162 CATEGORY R. Input subroutines / 164 CATEGORY s. Subroutines for evaluating fractional powers / 168 CATEGORY T. Subroutines for calculating trigonometric functions / 169 CATEGORY Z. Post-mortem routines / 170 PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY SUBROUTINES / 173 APPENDIX 1. Input and output codes of the EDSAC / 212 APPENDIX 2. Order code and controls of the EDSAC / 214 APPENDIX 3. The initial input routine of the EDSAC / 218 APPENDIX 4. Control combinations / 221 APPENDIX 5. Specimen solutions to programming exercises / 223 BIBLIOGRAPHY / 233 INDEX / 237

rawTOC:
CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\ 1-1 Introduction / 1 \\ 1-2 Types of automatic computing machine / 1 \\ 1-3 The EDSAC / 3 \\ 1-4 Store / 5 \\ 1-5 Arithmetical unit / 5 \\ 1-6 Form of numbers in the machine / 5 \\ 1-7 Form of orders in the machine / 6 \\ 1-8 Storage of orders / 6 \\ 1-9 Written form of orders / 7 \\ 1-10 Some simple examples / 7 \\ Exercises A / 9 \\ 1-11 Jump orders / 9 \\ Exercises B / 11 \\ 1-12 Repeated groups of orders / 11 \\ 1-13 The use of the B-register / 15 \\ Exercises C / 18 \\ 1-14 Equivalence between orders and numbers; pseudo-orders / 18 \\ 1-15 Use of the arithmetical unit for constructing or modifying orders / 20 \\ 1-16 The mix order / 23 \\ Exercises D / 24 \\ CHAPTER 2. SUBROUTINES / 25 \\ 2-1 Introduction / 25 \\ 2-2 Relative numbering of addresses / 25 \\ 2-3 Internal and external forms of orders / 26 \\ 2-4 Reading of orders from the input tape / 28 \\ 2-5 Open and closed subroutines / 29 \\ 2-6 Entering and leaving a closed subroutine / 29 \\ 2-7 Closed B subroutines / 30 \\ 2-8 Closed A subroutines / 31 \\ 2-9 Use of library subroutines / 32 \\ Exercises E / 33 \\ 2-10 Long numbers / 35 \\ 2-11 Some further orders in the order code / 36 \\ 2-12 Scale factors / 38 \\ 2-13 Control combinations / 39 \\ Exercises F / 40 \\ 2-14 Relative addresses in control combinations / 41 \\ 2-15 Extension of the use of relative addresses / 41 \\ 2-16 Setting of the constants to be added by terminal code letters / 43 \\ 2-17 Complete table of terminal code letters / 44 \\ 2-18 Parameters / 45 \\ 2-19 Preset parameters / 46 \\ 2-20 Program parameters / 46 \\ 2-21 Standard procedure for setting preset parameters / 46 \\ 2-22 Interpretive subroutines / 47 \\ Exercises G / 49 \\ CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\ 3-1 Introduction / 51 \\ 3-2 Single-address codes / 52 \\ 3-3 Multi-address codes / 53 \\ 3-4 Multiplication and division / 56 \\ 3-5 Source-destination codes / 57 \\ 3-6 Representation of negative numbers / 59 \\ 3-7 Miscellaneous facilities / 60 \\ 3-8 Minimum-access coding / 61 \\ 3-9 The evaluation of an order code / 63 \\ 3-10 Use of an auxiliary store / 64 \\ CHAPTER 4. INPUT AND OUTPUT / 66 \\ 4-1 Introduction / 66 \\ 4-2 Input of numbers / 66 \\ 4-3 Output of numbers / 67 \\ 4-4 Input of orders / 69 \\ 4-5 Recognition of the code letter S / 72 \\ 4-6 Economy of input and output time / 72 \\ 4-7 Some features of input systems used with other machines / 73 \\ 4-8 Punched tape / 73 \\ 4-9 Punched cards / 75 \\ CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\ 5-1 Introduction / 80 \\ 5-2 Library catalog / 80 \\ 5-3 Input subroutines / 81 \\ 5-4 Output subroutines / 81 \\ 5-5 Division subroutines / 82 \\ 5-6 Trigonometric and other functions / 82 \\ 5-7 The economization of a power series by the use of Chebyshev polynomials / 83 \\ 5-8 Quadrature / 86 \\ 5-9 Integration of ordinary differential equations / 87 \\ 5-10 Library subroutines Gl2 and G13: Runge--Kutta processes / 88 \\ 5-11 The independent variable / 88 \\ 5-12 Definition of the Runge--Kutta--Gill process / 89 \\ 5-13 Taylor-series method / 90 \\ 5-14 Interpretive subroutines / 90 \\ 5-15 Floating-point subroutines / 90 \\ CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\ 6-1 Introduction / 92 \\ 6-2 Proofreading of programs / 93 \\ 6-3 Punching / 93 \\ 6-4 Locating mistakes in a program- / 94 \\ 6-5 Subroutines for checking programs / 96 \\ 6-6 The development of a program / 97 \\ CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC / 99 \\ EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\ EXAMPLE 2 The evaluation of a definite integral / 102 \\ EXAMPLE 3 Integration of an ordinary differential equation / 108 \\ EXAMPLE 4 Evaluation of a Fourier transform / 113 \\ EXAMPLE 5 Evaluation of a definite integral / 118 \\ CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\ 8-1 Introduction / 126 \\ 8-2 Conversion versus interpretation / 127 \\ 8-3 Assembly of a program / 127 \\ 8-4 Floating addresses / 129 \\ 8-5 Formula recognition / 136 \\ Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES / 139 \\ CATEGORY A. Subroutines to carry out floating-point arithmetic / 140 \\ CATEGORY B. Subroutines to perform arithmetical operations on complex numbers / 142 \\ CATEGORY C. Error-diagnosis subroutines / 144 \\ CATEGORY D. Division subroutines / 146 \\ CATEGORY E. Exponential subroutines / 148 \\ CATEGORY F. General subroutines relating to functions / 148 \\ CATEGORY G. Subroutines for the integration of differential equations / 150 \\ CATEGORY L. Subroutines for evaluating logarithms / 153 \\ CATEGORY M. Miscellaneous subroutines / 154 \\ CATEGORY N. Operations on double-length numbers / 156 \\ CATEGORY P. Print subroutines / 158 \\ CATEGORY Q. Quadrature subroutines / 162 \\ CATEGORY R. Input subroutines / 164 \\ CATEGORY s. Subroutines for evaluating fractional powers / 168 \\ CATEGORY T. Subroutines for calculating trigonometric functions / 169 \\ CATEGORY Z. Post-mortem routines / 170 \\ PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY SUBROUTINES / 173 \\ APPENDIX 1. Input and output codes of the EDSAC / 212 \\ APPENDIX 2. Order code and controls of the EDSAC / 214 \\ APPENDIX 3. The initial input routine of the EDSAC / 218 \\ APPENDIX 4. Control combinations / 221 \\ APPENDIX 5. Specimen solutions to programming exercises / 223 \\ BIBLIOGRAPHY / 233 \\ INDEX / 237

entry:
@Book{Wilkes:1957:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xiv + 238",
  year =         "1957",
  LCCN =         "QA76.5 .W52 1957",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also first edition \cite{Wilkes:1951:PPE}.",
  URL =          "https://b-ok.org/book/3668116/b363ff",
  acknowledgement = ack-nhfb,
  remark-1 =     "According to \cite{Anderson:2019:SAM}, this book
                 discusses the computation of integer population counts
                 on the Electronic Delay Storage Automatic Calculator
                 (EDSAC) computer using a recursive divide-and-conquer
                 algorithm. See also somewhat negative 1958 review by
                 Fernando J. Corbat{\'o}
                 \cite{https://doi.org/10.1063/1.3062687}.
                 Floating-point arithmetic is discussed on pages 60,
                 90--91, and 135--137.",
  remark-2 =     "From page 5: ``Each storage location in the EDSAC
                 holds 17 binary digits. In words representing numbers,
                 the binary point is regarded as being to the right of
                 the extreme left-hand digit; this digit (the most
                 significant digit) is used as a sign indicator and is
                 referred to as the sign digit. \ldots{} the capacity of
                 the accumulator is 70 digits; there is, therefore,
                 plenty of room to hold the full 33-digit product of two
                 17-digit numbers. \ldots{} A negative number $-x$
                 (where $O < x \leq 1$) is represented by a $1$ in the
                 sign-digit position, followed by the digits of $(1 -
                 x)$; for example, $1.1100\ldots{}$ represents $-(1 -
                 3/4) = -1/4$. \ldots{}. Another way of explaining the
                 representation of negative numbers is to regard the
                 sign digit as an ordinary numerical digit, and to say
                 that $-x$ is stored as the number $(2 - x)$. Note in
                 particular that $1.0000\ldots{}$ represents $-1$.''
                 [Page 59 calls this a {\em True complements}
                 representation, distinguished from one's complement.]",
  remark-3 =     "From page 35: ``The EDSAC has a facility which enables
                 an even-numbered storage location and the following
                 odd-numbered storage to be used as a single storage
                 location holding 35 binary digits.'' [This suggests the
                 word size in 18, not 17 as page 5 suggests. The
                 Wikipedia article on the EDSAC reports: ``The EDSAC's
                 main memory consisted of 1024 locations, though only
                 512 locations were initially installed. Each contained
                 18 bits, but the topmost bit was always unavailable due
                 to timing problems, so only 17 bits were used.'']",
  remark-4 =     "From page 36: ``The multiplier register of the
                 arithmetical unit is of sufficient capacity to hold a
                 long number, and the accumulator is of sufficient
                 capacity to hold the complete (69) binary digit
                 [including the sign bit] product of two long
                 numbers.''",
  remark-5 =     "From page 36: ``In some calculations, long numbers may
                 not provide sufficient precision. In such cases, the
                 programmer may make use of what is known as
                 double-length or double-precision working, in which two
                 long storage locations are used to hold the digits of a
                 single number.'' [this would be a quad-word number
                 holding 69 bits, including the sign bit.].",
  remark-6 =     "From page 60: ``\ldots{} two double-length numbers,
                 each stored in two locations, can be added and the
                 result put in two locations in the store, by means of
                 six orders''.",
  remark-7 =     "From page 90: ``Each number is expressed in the form
                 $a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
                 p < 63$ and is represented in the store by $a \cdot
                 2^{-11} + p \cdot 2^{-6}$.''",
  remark-8 =     "From page 91: ``Numbers are expressed in the form $a
                 \cdot 10^p$, where $a$ and $p$ are packed into a single
                 storage location. The number of digits defining $p$ may
                 be varied from 4 to 15 by means of a preset parameter,
                 so that a suitable value for the permissible range of
                 variation of numbers may be selected for a given
                 calculation.''",
  remark-9 =     "From page 91: ``Although the use of floating-point
                 operation can simplify the programmer's task by
                 relieving him of undue preoccupation with scaling, it
                 must not be thought that it solves all his
                 difficulties. In particular, the loss of significant
                 digits resulting from the subtraction of a number from
                 a nearly equal number can have serious consequences
                 unless proper precautions are taken.''",
  tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machine / 1 \\
                 1-3 The EDSAC / 3 \\
                 1-4 Store / 5 \\
                 1-5 Arithmetical unit / 5 \\
                 1-6 Form of numbers in the machine / 5 \\
                 1-7 Form of orders in the machine / 6 \\
                 1-8 Storage of orders / 6 \\
                 1-9 Written form of orders / 7 \\
                 1-10 Some simple examples / 7 \\
                 Exercises A / 9 \\
                 1-11 Jump orders / 9 \\
                 Exercises B / 11 \\
                 1-12 Repeated groups of orders / 11 \\
                 1-13 The use of the B-register / 15 \\
                 Exercises C / 18 \\
                 1-14 Equivalence between orders and numbers;
                 pseudo-orders / 18 \\
                 1-15 Use of the arithmetical unit for constructing or
                 modifying orders / 20 \\
                 1-16 The mix order / 23 \\
                 Exercises D / 24 \\
                 CHAPTER 2. SUBROUTINES / 25 \\
                 2-1 Introduction / 25 \\
                 2-2 Relative numbering of addresses / 25 \\
                 2-3 Internal and external forms of orders / 26 \\
                 2-4 Reading of orders from the input tape / 28 \\
                 2-5 Open and closed subroutines / 29 \\
                 2-6 Entering and leaving a closed subroutine / 29 \\
                 2-7 Closed B subroutines / 30 \\
                 2-8 Closed A subroutines / 31 \\
                 2-9 Use of library subroutines / 32 \\
                 Exercises E / 33 \\
                 2-10 Long numbers / 35 \\
                 2-11 Some further orders in the order code / 36 \\
                 2-12 Scale factors / 38 \\
                 2-13 Control combinations / 39 \\
                 Exercises F / 40 \\
                 2-14 Relative addresses in control combinations / 41
                 \\
                 2-15 Extension of the use of relative addresses / 41
                 \\
                 2-16 Setting of the constants to be added by terminal
                 code letters / 43 \\
                 2-17 Complete table of terminal code letters / 44 \\
                 2-18 Parameters / 45 \\
                 2-19 Preset parameters / 46 \\
                 2-20 Program parameters / 46 \\
                 2-21 Standard procedure for setting preset parameters /
                 46 \\
                 2-22 Interpretive subroutines / 47 \\
                 Exercises G / 49 \\
                 CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
                 3-1 Introduction / 51 \\
                 3-2 Single-address codes / 52 \\
                 3-3 Multi-address codes / 53 \\
                 3-4 Multiplication and division / 56 \\
                 3-5 Source-destination codes / 57 \\
                 3-6 Representation of negative numbers / 59 \\
                 3-7 Miscellaneous facilities / 60 \\
                 3-8 Minimum-access coding / 61 \\
                 3-9 The evaluation of an order code / 63 \\
                 3-10 Use of an auxiliary store / 64 \\
                 CHAPTER 4. INPUT AND OUTPUT / 66 \\
                 4-1 Introduction / 66 \\
                 4-2 Input of numbers / 66 \\
                 4-3 Output of numbers / 67 \\
                 4-4 Input of orders / 69 \\
                 4-5 Recognition of the code letter S / 72 \\
                 4-6 Economy of input and output time / 72 \\
                 4-7 Some features of input systems used with other
                 machines / 73 \\
                 4-8 Punched tape / 73 \\
                 4-9 Punched cards / 75 \\
                 CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
                 5-1 Introduction / 80 \\
                 5-2 Library catalog / 80 \\
                 5-3 Input subroutines / 81 \\
                 5-4 Output subroutines / 81 \\
                 5-5 Division subroutines / 82 \\
                 5-6 Trigonometric and other functions / 82 \\
                 5-7 The economization of a power series by the use of
                 Chebyshev polynomials / 83 \\
                 5-8 Quadrature / 86 \\
                 5-9 Integration of ordinary differential equations / 87
                 \\
                 5-10 Library subroutines Gl2 and G13: Runge--Kutta
                 processes / 88 \\
                 5-11 The independent variable / 88 \\
                 5-12 Definition of the Runge--Kutta--Gill process / 89
                 \\
                 5-13 Taylor-series method / 90 \\
                 5-14 Interpretive subroutines / 90 \\
                 5-15 Floating-point subroutines / 90 \\
                 CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
                 6-1 Introduction / 92 \\
                 6-2 Proofreading of programs / 93 \\
                 6-3 Punching / 93 \\
                 6-4 Locating mistakes in a program- / 94 \\
                 6-5 Subroutines for checking programs / 96 \\
                 6-6 The development of a program / 97 \\
                 CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
                 / 99 \\
                 EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
                 EXAMPLE 2 The evaluation of a definite integral / 102
                 \\
                 EXAMPLE 3 Integration of an ordinary differential
                 equation / 108 \\
                 EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
                 EXAMPLE 5 Evaluation of a definite integral / 118 \\
                 CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
                 8-1 Introduction / 126 \\
                 8-2 Conversion versus interpretation / 127 \\
                 8-3 Assembly of a program / 127 \\
                 8-4 Floating addresses / 129 \\
                 8-5 Formula recognition / 136 \\
                 Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
                 139 \\
                 CATEGORY A. Subroutines to carry out floating-point
                 arithmetic / 140 \\
                 CATEGORY B. Subroutines to perform arithmetical
                 operations on complex numbers / 142 \\
                 CATEGORY C. Error-diagnosis subroutines / 144 \\
                 CATEGORY D. Division subroutines / 146 \\
                 CATEGORY E. Exponential subroutines / 148 \\
                 CATEGORY F. General subroutines relating to functions /
                 148 \\
                 CATEGORY G. Subroutines for the integration of
                 differential equations / 150 \\
                 CATEGORY L. Subroutines for evaluating logarithms / 153
                 \\
                 CATEGORY M. Miscellaneous subroutines / 154 \\
                 CATEGORY N. Operations on double-length numbers / 156
                 \\
                 CATEGORY P. Print subroutines / 158 \\
                 CATEGORY Q. Quadrature subroutines / 162 \\
                 CATEGORY R. Input subroutines / 164 \\
                 CATEGORY s. Subroutines for evaluating fractional
                 powers / 168 \\
                 CATEGORY T. Subroutines for calculating trigonometric
                 functions / 169 \\
                 CATEGORY Z. Post-mortem routines / 170 \\
                 PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
                 SUBROUTINES / 173 \\
                 APPENDIX 1. Input and output codes of the EDSAC / 212
                 \\
                 APPENDIX 2. Order code and controls of the EDSAC / 214
                 \\
                 APPENDIX 3. The initial input routine of the EDSAC /
                 218 \\
                 APPENDIX 4. Control combinations / 221 \\
                 APPENDIX 5. Specimen solutions to programming exercises
                 / 223 \\
                 BIBLIOGRAPHY / 233 \\
                 INDEX / 237",
}


bibtype: article
filename: elefunt.bib
label: Beattie:1958:TFZ
author: Curtis L. Beattie
title: Table of First 700 Zeros of Bessel Functions --- $ J_l(x) $ and $ J^prime _l(x) $
journal: j-BELL-SYST-TECH-J
volume: 37
number: 3
pages: 689--697
month: may
monthnumber: 5
year: 1958
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
MRclass: 65.00
MRnumber: 0093928 (20 \#448)
MRreviewer: J. C. P. Miller
bibdate: Tue Nov 9 11:15:54 MST 2010
bibtimestamp: 2010.11.09 11:15:54 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol37/bstj37-3-689.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: Curtis L. Beattie
rawtitle: Table of First 700 Zeros of {Bessel} Functions --- {$ J_l(x) $} and {$ J^{\prime }_l(x) $}
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1958/BSTJ.1958.3703.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Beattie:1958:TFZ,
  author =       "Curtis L. Beattie",
  title =        "Table of First 700 Zeros of {Bessel} Functions --- {$
                 J_l(x) $} and {$ J^{\prime }_l(x) $}",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "37",
  number =       "3",
  pages =        "689--697",
  month =        may,
  year =         "1958",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "65.00",
  MRnumber =     "0093928 (20 \#448)",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1958/BSTJ.1958.3703.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol37/bstj37-3-689.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Belaga:1958:SPI
author: E. G. Belaga
title: Some problems involved in the calculation of polynomials
journal: j-DOKL-AKAD-NAUK
volume: 123
pages: 775--777
year: 1958
CODEN: DANKAS
ISSN: 0002-3264 OR 00023264
MRclass: 65.00
MRnumber: 105192
MRreviewer: John Todd
bibdate: Fri Oct 20 10:34:44 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 10:34:44 ???
fjournal: Doklady Akademii Nauk SSSR
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
journalURL: http://istina.msu.ru/journals/366838/
rawauthor: {\`E}. G. Belaga
rawtitle: Some problems involved in the calculation of polynomials
entry:
@Article{Belaga:1958:SPI,
  author =       "{\`E}. G. Belaga",
  title =        "Some problems involved in the calculation of
                 polynomials",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "123",
  pages =        "775--777",
  year =         "1958",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  MRclass =      "65.00",
  MRnumber =     "105192",
  MRreviewer =   "John Todd",
  bibdate =      "Fri Oct 20 10:34:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii Nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
  keywords =     "number of multiplications to evaluate a polynomial",
}


bibtype: book
filename: elefunt.bib
label: Bowman:1958:IBF
author: Frank Bowman
title: Introduction to Bessel Functions
publisher: pub-DOVER
address: pub-DOVER:adr
pages: x + 135
year: 1958
LCCN: QA408 .B68i 1958
bibdate: Sat Jan 15 17:24:26 MST 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2011.01.15 17:24:26 MST
remark: An unabridged and unaltered republication of the first edition.
subject: Bessel functions
acknowledgement: ack-nhfb
rawauthor: Frank Bowman
rawtitle: Introduction to {Bessel} Functions
entry:
@Book{Bowman:1958:IBF,
  author =       "Frank Bowman",
  title =        "Introduction to {Bessel} Functions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 135",
  year =         "1958",
  LCCN =         "QA408 .B68i 1958",
  bibdate =      "Sat Jan 15 17:24:26 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "An unabridged and unaltered republication of the first
                 edition.",
  subject =      "Bessel functions",
}


bibtype: article
filename: elefunt.bib
label: Dingle:1958:AEC
author: R. B. Dingle
journal: j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI
volume: 244
number: 1239
pages: 484--490
day: 22
month: apr
monthnumber: 4
year: 1958
CODEN: PRLAAZ
ISSN: 0080-4630 OR 00804630
bibdate: Mon Jun 18 07:22:24 MDT 2012
bibtimestamp: 2012.06.18 07:22:24 MDT
URL: http://www.jstor.org/stable/100264
fjournal: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
acknowledgement: ack-nhfb
journalURL: http://rspa.royalsocietypublishing.org/content/current
rawauthor: R. B. Dingle
title:
Asymptotic Expansions and Converging Factors. III. Gamma, Psi and Polygamma Functions, and Fermi--Dirac and Bose--Einstein Integrals

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

rawtitle:
Asymptotic Expansions and Converging Factors. {III}. Gamma, Psi and Polygamma Functions, and {Fermi--Dirac} and {Bose--Einstein} Integrals

entry:
@Article{Dingle:1958:AEC,
  author =       "R. B. Dingle",
  title =        "Asymptotic Expansions and Converging Factors. {III}.
                 Gamma, Psi and Polygamma Functions, and {Fermi--Dirac}
                 and {Bose--Einstein} Integrals",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "244",
  number =       "1239",
  pages =        "484--490",
  day =          "22",
  month =        apr,
  year =         "1958",
  CODEN =        "PRLAAZ",
  ISSN =         "0080-4630",
  bibdate =      "Mon Jun 18 07:22:24 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/100264",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
}


bibtype: article
filename: elefunt.bib
label: Goldstein:1958:BFL
author: M. Goldstein and R. M. Thaler
title: Bessel Functions for Large Arguments
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 12
number: 61
pages: 18--26
month: jan
monthnumber: 1
year: 1958
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1958-0102906-3
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. Goldstein and R. M. Thaler
rawtitle: {Bessel} Functions for Large Arguments
entry:
@Article{Goldstein:1958:BFL,
  author =       "M. Goldstein and R. M. Thaler",
  title =        "{Bessel} Functions for Large Arguments",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "12",
  number =       "61",
  pages =        "18--26",
  month =        jan,
  year =         "1958",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1958-0102906-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Kogbetliantz:1958:CANa
author: E. G. Kogbetliantz
title: Computation of Arctan N for $ - infty < N < + infty $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 2
number: 1
pages: 43--53
month: jan
monthnumber: 1
year: 1958
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.21.0043
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65.3X
MRnumber: 19,982e
bibdate: Wed Aug 31 13:40:00 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.31 13:40:00 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: C. B. Haselgrove
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of Arctan {N} for $ - \infty < {N} < + \infty $ Using an Electronic Computer
entry:
@Article{Kogbetliantz:1958:CANa,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arctan {N} for $ - \infty < {N} < +
                 \infty $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "1",
  pages =        "43--53",
  month =        jan,
  year =         "1958",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.21.0043",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.3X",
  MRnumber =     "19,982e",
  bibdate =      "Wed Aug 31 13:40:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "C. B. Haselgrove",
}


bibtype: article
filename: elefunt.bib
label: Kogbetliantz:1958:CANb
author: E. G. Kogbetliantz
title: Computation of Arcsin N for $ 0 < N < 1 $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 2
number: 3
pages: 218--222
month: jul
monthnumber: 7
year: 1958
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.23.0218
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65.3X
MRnumber: 19,1197c
bibdate: Wed Aug 31 13:41:37 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.08.31 13:41:37 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: C. B. Haselgrove
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of Arcsin {N} for $ 0 < {N} < 1 $ Using an Electronic Computer
entry:
@Article{Kogbetliantz:1958:CANb,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arcsin {N} for $ 0 < {N} < 1 $ Using an
                 Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "3",
  pages =        "218--222",
  month =        jul,
  year =         "1958",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.23.0218",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.3X",
  MRnumber =     "19,1197c",
  bibdate =      "Wed Aug 31 13:41:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "C. B. Haselgrove",
}


bibtype: book
filename: elefunt.bib
label: Lewin:1958:DAF
author: Leonard Lewin
title: Dilogarithms and Associated Functions
publisher: Macdonald
address: London, UK
pages: 353
year: 1958
LCCN: QA351 .L5
bibdate: Fri Jun 16 13:51:36 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2023.06.16 13:51:36 MDT
remark: Foreword by J. C. P. Miller
subject: Dilogarithms
acknowledgement: ack-nhfb
authordates: 22-Jul-1919--13-Aug-2007
rawauthor: Leonard Lewin
rawtitle: Dilogarithms and Associated Functions
entry:
@Book{Lewin:1958:DAF,
  author =       "Leonard Lewin",
  title =        "Dilogarithms and Associated Functions",
  publisher =    "Macdonald",
  address =      "London, UK",
  pages =        "353",
  year =         "1958",
  LCCN =         "QA351 .L5",
  bibdate =      "Fri Jun 16 13:51:36 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "22-Jul-1919--13-Aug-2007",
  author-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  remark =       "Foreword by J. C. P. Miller",
  subject =      "Dilogarithms",
}


bibtype: techreport
filename: elefunt.bib
label: Miller:1958:LNN
author: J. C. P. Miller
title: Lecture Notes on Numerical Analysis
type: Report
institution: Cambridge University
address: Cambridge, England
pages: 353
year: 1958
bibdate: Fri Sep 20 14:46:35 2024
bibtimestamp: 2024.09.20 14:46:35 ???
URL: https://www.youtube.com/watch?v=81YrRSeReKo
acknowledgement: ack-nhfb
rawauthor: J. C. P. Miller
rawtitle: Lecture Notes on Numerical Analysis
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Miller:1958:LNN,
  author =       "J. C. P. Miller",
  title =        "Lecture Notes on Numerical Analysis",
  type =         "Report",
  institution =  "Cambridge University",
  address =      "Cambridge, England",
  year =         "1958",
  bibdate =      "Fri Sep 20 14:46:35 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.youtube.com/watch?v=81YrRSeReKo",
  acknowledgement = ack-nhfb,
  remark-1 =     "Cited in \cite[Reference 21]{Agarwal:1986:NSV} in
                 elefunt.bib and fparith.bib.",
  remark-2 =     "Page 135 of the Agarwal paper says ``Kahan has also
                 informed us that Miller [21] wrote about the
                 extra-accurate table idea in 1958.'' William M. Kahan
                 spent 1958--1960 in Cambridge, as a pro-forma student
                 of J. C. P. Miller --- Kahan already had a Ph.D. from
                 the University of Toronto, but it was not recognized by
                 Cambridge University! See the video interview in the
                 URL.",
}


bibtype: article
filename: elefunt.bib
label: Sugai:1958:ERR
author: Iwao Sugai
title: Extraction of Roots by Repeated Subtractions for Digital Computers
journal: j-CACM
volume: 1
number: 12
pages: 6--8
month: dec
monthnumber: 12
year: 1958
CODEN: CACMA2
DOI: https://doi.org/10.1145/377924.377928
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:22 MDT 2004
bibtimestamp: 2004.07.14 15:48:22 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Iwao Sugai
rawtitle: Extraction of Roots by Repeated Subtractions for Digital Computers
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sugai58; https://www.math.utah.edu/pub/tex/bib/cacm1950.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Sugai:1958:ERR,
  author =       "Iwao Sugai",
  title =        "Extraction of Roots by Repeated Subtractions for
                 Digital Computers",
  journal =      j-CACM,
  volume =       "1",
  number =       "12",
  pages =        "6--8",
  month =        dec,
  year =         "1958",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/377924.377928",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sugai58;
                 https://www.math.utah.edu/pub/tex/bib/cacm1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Sugai58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sugai58",
}


bibtype: article
filename: elefunt.bib
label: Wadey:1958:TSR
author: W. G. Wadey
title: Two Square-Root Approximations
journal: j-CACM
volume: 1
number: 11
pages: 13--14
month: nov
monthnumber: 11
year: 1958
CODEN: CACMA2
DOI: https://doi.org/10.1145/368932.368936
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:22 MDT 2004
bibtimestamp: 2004.07.14 15:48:22 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. G. Wadey
rawtitle: Two Square-Root Approximations
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Wadey:1958:TSR,
  author =       "W. G. Wadey",
  title =        "Two Square-Root Approximations",
  journal =      j-CACM,
  volume =       "1",
  number =       "11",
  pages =        "13--14",
  month =        nov,
  year =         "1958",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368932.368936",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Wadey58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}


bibtype: article
filename: elefunt.bib
label: Corbato:1959:GSB
author: Fernando J. Corbato and Jack L. Uretsky
title: Generation of Spherical Bessel Functions in Digital Computers
journal: j-J-ACM
volume: 6
number: 3
pages: 366--375
month: jul
monthnumber: 7
year: 1959
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Mon Dec 05 20:07:17 1994
bibtimestamp: 1994.12.05 20:07:17 ???
fjournal: Journal of the Association for Computing Machinery
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: Fernando J. Corbat{\'o} and Jack L. Uretsky
rawtitle: Generation of Spherical {Bessel} Functions in Digital Computers
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib

entry:
@Article{Corbato:1959:GSB,
  author =       "Fernando J. Corbat{\'o} and Jack L. Uretsky",
  title =        "Generation of Spherical {Bessel} Functions in Digital
                 Computers",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "3",
  pages =        "366--375",
  month =        jul,
  year =         "1959",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Mon Dec 05 20:07:17 1994",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: article
filename: elefunt.bib
label: Davis:1959:LEI
author: Philip J. Davis
journal: j-AMER-MATH-MONTHLY
volume: 66
number: 10
pages: 849--869
month: dec
monthnumber: 12
year: 1959
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2309786
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 00 (33.00)
MRnumber: MR0106810 (21 #5540)
bibdate: Mon Jun 28 12:39:33 MDT 1999
bibtimestamp: 1999.06.28 12:39:33 MDT
URL: http://www.jstor.org/stable/2309786
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Philip J. Davis (2 January 1923--14 March 2018)
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Philip J. Davis
title:
Leonhard Euler's Integral: a Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz

bibsource:
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1950.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
{Leonhard Euler}'s Integral: a Historical Profile of the Gamma Function: In Memoriam: {Milton Abramowitz}

entry:
@Article{Davis:1959:LEI,
  author =       "Philip J. Davis",
  title =        "{Leonhard Euler}'s Integral: a Historical Profile of
                 the Gamma Function: In Memoriam: {Milton Abramowitz}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "66",
  number =       "10",
  pages =        "849--869",
  month =        dec,
  year =         "1959",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2309786",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "00 (33.00)",
  MRnumber =     "MR0106810 (21 #5540)",
  bibdate =      "Mon Jun 28 12:39:33 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2309786",
  acknowledgement = ack-nhfb,
  author-dates = "Philip J. Davis (2 January 1923--14 March 2018)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1959:NFC
author: A. R. DiDonato and A. V. Hershey
title: New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind
journal: j-J-ACM
volume: 6
number: 4
pages: 515--526
month: oct
monthnumber: 10
year: 1959
CODEN: JACOAH
DOI: https://doi.org/10.1145/320998.321005
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65.00
MRnumber: 0107353
MRreviewer: F. Stallmann
bibdate: Mon Dec 05 20:10:59 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.12.05 20:10:59 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: A. R. DiDonato and A. V. Hershey
rawtitle: New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind
entry:
@Article{DiDonato:1959:NFC,
  author =       "A. R. DiDonato and A. V. Hershey",
  title =        "New Formulas for Computing Incomplete Elliptic
                 Integrals of the First and Second Kind",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "4",
  pages =        "515--526",
  month =        oct,
  year =         "1959",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/320998.321005",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.00",
  MRnumber =     "0107353",
  MRreviewer =   "F. Stallmann",
  bibdate =      "Mon Dec 05 20:10:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: book
filename: elefunt.bib
label: Emde:1959:TEF
author: Fritz Emde
title: Tafeln Elementarer Funktionen (German) [Tables of Elementary Functions]
publisher: B. T. Teubner
address: Leipzig, Germany and Berlin, Germany
edition: Third
pages: xii + 181
year: 1959
LCCN: QA47 .E5
bibdate: Fri Jun 11 12:34:09 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.06.11 12:34:09 ???
URL: http://lccn.loc.gov/61020314
language: German
acknowledgement: ack-nhfb
authordates: 1873--1951
rawauthor: Fritz Emde
rawtitle: {Tafeln Elementarer Funktionen} ({German}) [Tables of Elementary Functions]
entry:
@Book{Emde:1959:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "B. T. Teubner",
  address =      "Leipzig, Germany and Berlin, Germany",
  edition =      "Third",
  pages =        "xii + 181",
  year =         "1959",
  LCCN =         "QA47 .E5",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://lccn.loc.gov/61020314",
  acknowledgement = ack-nhfb,
  author-dates = "1873--1951",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1959:EIL
author: W. Gautschi
title: Exponential integral $ int _1^infty e^-x t t^-n d t $ for large values of $n$
journal: j-J-RES-NATL-BUR-STAND-1934
volume: 62
number: 3
pages: 123--125
month: mar
monthnumber: 3
year: 1959
DOI: https://doi.org/10.6028/jres.062.022
ISSN: 0091-0635 OR 00910635
bibdate: Sat Feb 18 14:39:27 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 14:39:27 ???
fjournal: Journal of Research of the National Bureau of Standards (1934)
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: W. Gautschi
rawtitle: Exponential integral $ \int_1^\infty e^{-x t} t^{-n} \, d t $ for large values of $n$
entry:
@Article{Gautschi:1959:EIL,
  author =       "W. Gautschi",
  title =        "Exponential integral $ \int_1^\infty e^{-x t} t^{-n}
                 \, d t $ for large values of $n$",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "62",
  number =       "3",
  pages =        "123--125",
  month =        mar,
  year =         "1959",
  DOI =          "https://doi.org/10.6028/jres.062.022",
  ISSN =         "0091-0635",
  bibdate =      "Sat Feb 18 14:39:27 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
}


bibtype: article
filename: elefunt.bib
label: Goldstein:1959:RTC
author: M. Goldstein and R. M. Thaler
title: Recurrence Techniques for the Calculation of Bessel Functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 13
number: 66
pages: 102--108
month: apr
monthnumber: 4
year: 1959
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1959-0105794-5
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. Goldstein and R. M. Thaler
rawtitle: Recurrence Techniques for the Calculation of {Bessel} Functions
entry:
@Article{Goldstein:1959:RTC,
  author =       "M. Goldstein and R. M. Thaler",
  title =        "Recurrence Techniques for the Calculation of {Bessel}
                 Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "66",
  pages =        "102--108",
  month =        apr,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0105794-5",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Greenhill:1959:AEF
author: Alfred George Greenhill
title: The Applications of Elliptic Functions
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xi + 357
year: 1959
bibdate: Wed Mar 15 08:21:33 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 08:21:33 ???
note: See cite Greenhill:1892:AEF.
remark: Reprint of cite Greenhill:1892:AEF.
acknowledgement: ack-nhfb
authordates: 1847--1927
rawauthor: Alfred George Greenhill
rawnote: See \cite{Greenhill:1892:AEF}.
rawtitle: The Applications of Elliptic Functions
entry:
@Book{Greenhill:1959:AEF,
  author =       "Alfred George Greenhill",
  title =        "The Applications of Elliptic Functions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 357",
  year =         "1959",
  bibdate =      "Wed Mar 15 08:21:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Greenhill:1892:AEF}.",
  acknowledgement = ack-nhfb,
  author-dates = "1847--1927",
  remark =       "Reprint of \cite{Greenhill:1892:AEF}.",
}


bibtype: article
filename: elefunt.bib
label: Kogbetliantz:1959:CSC
author: E. G. Kogbetliantz
title: Computation of $ sin N $, $ cos N $, and $ M $ th Root of $ N $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 3
number: 2
pages: 147--152
month: apr
monthnumber: 4
year: 1959
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.32.0147
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65.00
MRnumber: 21 \#964
bibdate: Thu Sep 1 10:15:56 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:56 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: B. A. Chartres
rawauthor: E. G. Kogbetliantz
rawtitle:
Computation of $ \sin {N} $, $ \cos {N} $, and $ {M} $ th Root of $ {N} $ Using an Electronic Computer

entry:
@Article{Kogbetliantz:1959:CSC,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $ \sin {N} $, $ \cos {N} $, and $ {M} $
                 th Root of $ {N} $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "3",
  number =       "2",
  pages =        "147--152",
  month =        apr,
  year =         "1959",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.32.0147",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.00",
  MRnumber =     "21 \#964",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "B. A. Chartres",
}


bibtype: article
filename: elefunt.bib
label: Kreyszig:1959:RUE
author: Erwin Kreyszig and John Todd
title: The radius of univalence of the error function
journal: j-NUM-MATH
volume: 1
pages: 78--89
month: dec
monthnumber: 12
year: 1959
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 20:47:18 MDT 1999
bibtimestamp: 1999.10.17 20:47:18 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Erwin Kreyszig and John Todd
rawtitle: The radius of univalence of the error function
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib

entry:
@Article{Kreyszig:1959:RUE,
  author =       "Erwin Kreyszig and John Todd",
  title =        "The radius of univalence of the error function",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "78--89",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 20:47:18 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Longman:1959:STT
author: I. M. Longman
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 13
number: 68
pages: 306--311
month: oct
monthnumber: 10
year: 1959
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1959-0108892-5
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
remark: Fullerton: 6-digit values for $ n = 1, 2, ldots , 22 $ and for $ x = 1, 2, ldots , 10 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: I. M. Longman
title:
A Short Table of $ int ^infty _x J_0 (t)t^-n d t $ and $ int ^infty _x J_1 (t) t^-n d t $ (in Technical Notes and Short Papers)

rawtitle:
A Short Table of $ \int^\infty_x {J}_0 (t)t^{-n} d t $ and $ \int^\infty_x {J}_1 (t) t^{-n} d t $ (in {Technical Notes and Short Papers})

entry:
@Article{Longman:1959:STT,
  author =       "I. M. Longman",
  title =        "A Short Table of $ \int^\infty_x {J}_0 (t)t^{-n} d t $
                 and $ \int^\infty_x {J}_1 (t) t^{-n} d t $ (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "306--311",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0108892-5",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 6-digit values for $ n = 1, 2, \ldots {},
                 22 $ and for $ x = 1, 2, \ldots {}, 10 $.",
}


bibtype: article
filename: elefunt.bib
label: Luke:1959:ECH
author: Yudell L. Luke
title: Expansion of the Confluent Hypergeometric Function in Series of Bessel Functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 13
number: 68
pages: 261--271
month: oct
monthnumber: 10
year: 1959
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1959-0107027-2
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke
rawtitle: Expansion of the Confluent Hypergeometric Function in Series of {Bessel} Functions
entry:
@Article{Luke:1959:ECH,
  author =       "Yudell L. Luke",
  title =        "Expansion of the Confluent Hypergeometric Function in
                 Series of {Bessel} Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "261--271",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0107027-2",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Pan:1959:CSC
author: V. Ya. Pan
title: Certain schemes for the calculation of values of polynomials with real coefficients
journal: Problemy Kibernetiki
volume: 5
pages: 17--29
year: 1959
bibdate: Fri Oct 20 10:40:33 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 10:40:33 ???
note: Also available as English translation JPRS No. 11045.
keywords: number of multiplications to evaluate a polynomial
language: Russian
acknowledgement: ack-nhfb
ajournal: Probl. Kibernetiki
rawauthor: V. Ya. Pan
rawnote: Also available as English translation JPRS No. 11045.
rawtitle: Certain schemes for the calculation of values of polynomials with real coefficients
remark:
Check: MathSciNet does not cover this volume, or record this paper, and the year may be wrong (based on available volume/year list entries). Cited in cite [ref. 5, p. 178]Fike:1967:MEP.

entry:
@Article{Pan:1959:CSC,
  author =       "V. Ya. Pan",
  title =        "Certain schemes for the calculation of values of
                 polynomials with real coefficients",
  journal =      "Problemy Kibernetiki",
  volume =       "5",
  number =       "??",
  pages =        "17--29",
  month =        "????",
  year =         "1959",
  bibdate =      "Fri Oct 20 10:40:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Also available as English translation JPRS No.
                 11045.",
  acknowledgement = ack-nhfb,
  ajournal =     "Probl. Kibernetiki",
  keywords =     "number of multiplications to evaluate a polynomial",
  language =     "Russian",
  remark =       "Check: MathSciNet does not cover this volume, or
                 record this paper, and the year may be wrong (based on
                 available volume/year list entries). Cited in
                 \cite[ref. 5, p. 178]{Fike:1967:MEP}.",
}


bibtype: article
filename: elefunt.bib
label: Pan:1959:SCP
author: V. Ya. Pan
title: Schemes for the computation of polynomials with real coefficients
journal: j-DOKL-AKAD-NAUK
volume: 127
number: 2
pages: 266--269
year: 1959
CODEN: DANKAS
ISSN: 0002-3264 OR 00023264
bibdate: Fri Oct 20 10:38:12 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 10:38:12 ???
fjournal: Doklady Akademii nauk SSSR
keywords: number of multiplications to evaluate a polynomial
language: Russian
acknowledgement: ack-nhfb
journalURL: http://istina.msu.ru/journals/366838/
rawauthor: V. Ya. Pan
rawtitle: Schemes for the computation of polynomials with real coefficients
entry:
@Article{Pan:1959:SCP,
  author =       "V. Ya. Pan",
  title =        "Schemes for the computation of polynomials with real
                 coefficients",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "127",
  number =       "2",
  pages =        "266--269",
  month =        "????",
  year =         "1959",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  bibdate =      "Fri Oct 20 10:38:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
  keywords =     "number of multiplications to evaluate a polynomial",
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Sarafyan:1959:NMC
author: Diran Sarafyan
title: A New Method of Computation of Square Roots Without Using Division
journal: j-CACM
volume: 2
number: 11
pages: 23--24
month: nov
monthnumber: 11
year: 1959
CODEN: CACMA2
DOI: https://doi.org/10.1145/368481.368511
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:24 MDT 2004
bibtimestamp: 2004.07.14 15:48:24 MDT
note: See comments cite Traub:1960:CNM.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Diran Sarafyan
rawnote: See comments \cite{Traub:1960:CNM}.
rawtitle: A New Method of Computation of Square Roots Without Using Division
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Sarafyan:1959:NMC,
  author =       "Diran Sarafyan",
  title =        "A New Method of Computation of Square Roots Without
                 Using Division",
  journal =      j-CACM,
  volume =       "2",
  number =       "11",
  pages =        "23--24",
  month =        nov,
  year =         "1959",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368481.368511",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:24 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See comments \cite{Traub:1960:CNM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Sarafyan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}


bibtype: article
filename: elefunt.bib
label: Sherry:1959:CGF
author: M. E. Sherry and S. Fulda
title: Calculation of Gamma Functions to High Accuracy (in Technical Notes and Short Papers)
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 13
number: 68
pages: 314--315
month: oct
monthnumber: 10
year: 1959
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1959-0108891-3
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. E. Sherry and S. Fulda
rawtitle: Calculation of Gamma Functions to High Accuracy (in {Technical Notes and Short Papers})
entry:
@Article{Sherry:1959:CGF,
  author =       "M. E. Sherry and S. Fulda",
  title =        "Calculation of Gamma Functions to High Accuracy (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "314--315",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0108891-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Stiefel:1959:NMT
author: Eduard L. Stiefel
title: Numerical methods of Tchebycheff approximation
crossref: Langer:1959:NAP
pages: 217--232
year: 1959
MRclass: 65.00 (41.00)
MRnumber: 0107961
MRreviewer: M. R. Hestenes
bibdate: Wed Sep 2 16:23:13 2020
bibtimestamp: 2020.09.02 16:23:13 ???
acknowledgement: ack-nhfb
authordates: Eduard Stiefel (21 April 1909--25 November 1978)
rawauthor: Eduard L. Stiefel
rawtitle: Numerical methods of {Tchebycheff} approximation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Stiefel:1959:NMT,
  author =       "Eduard L. Stiefel",
  title =        "Numerical methods of {Tchebycheff} approximation",
  crossref =     "Langer:1959:NAP",
  pages =        "217--232",
  year =         "1959",
  MRclass =      "65.00 (41.00)",
  MRnumber =     "0107961",
  MRreviewer =   "M. R. Hestenes",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
}


bibtype: article
filename: elefunt.bib
label: Strachey:1959:TSR
author: C. Strachey
title: On taking the square root of a complex number
journal: j-COMP-J
volume: 2
number: 2
pages: 89--89
month: jul
monthnumber: 7
year: 1959
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/2.2.89
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:55:11 MDT 2000
bibtimestamp: 2000.09.29 08:55:11 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: C. Strachey
rawtitle: On taking the square root of a complex number
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/; https://www.math.utah.edu/pub/tex/bib/compj1950.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif

entry:
@Article{Strachey:1959:TSR,
  author =       "C. Strachey",
  title =        "On taking the square root of a complex number",
  journal =      j-COMP-J,
  volume =       "2",
  number =       "2",
  pages =        "89--89",
  month =        jul,
  year =         "1959",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/2.2.89",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: elefunt.bib
label: Volder:1959:CCT
author: Jack Volder
title: The CORDIC Computing Technique
journal: Proceedings of the Western Joint Computer Conference
pages: 257--261
year: 1959
DOI: https://doi.org/10.1145/1457838.1457886
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
keywords: elementary functions
acknowledgement: ack-nhfb
rawauthor: Jack Volder
rawtitle: The {CORDIC} Computing Technique
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Volder:1959:CCT,
  author =       "Jack Volder",
  title =        "The {CORDIC} Computing Technique",
  journal =      "Proceedings of the Western Joint Computer Conference",
  pages =        "257--261",
  year =         "1959",
  DOI =          "https://doi.org/10.1145/1457838.1457886",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}


bibtype: article
filename: elefunt.bib
label: Volder:1959:CTC
author: Jack E. Volder
title: The CORDIC Trigonometric Computing Technique
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 3
pages: 330--334
month: sep
monthnumber: 9
year: 1959
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1959.5222693
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:45 MDT 2011
bibtimestamp: 2011.07.14 15:56:45 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222693
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Jack E. Volder
rawtitle: The {CORDIC} Trigonometric Computing Technique
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Volder:1959:CTC,
  author =       "Jack E. Volder",
  title =        "The {CORDIC} Trigonometric Computing Technique",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "3",
  pages =        "330--334",
  month =        sep,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222693",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222693",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: book
filename: elefunt.bib
label: Anonymous:1960:BFP
author: Anonymous
title: Bessel Functions. Part III: Zeros and Associated Values
volume: 7
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: lx + 79
year: 1960
MRclass: 65.00
MRnumber: 119441
MRreviewer: L. Fox
bibdate: Tue Nov 14 17:19:58 2023
bibtimestamp: 2023.11.14 17:19:58 ???
note: Prepared under the direction of the Bessel Functions Panel of the Mathematical Tables Committee
series: Royal Society Mathematical Tables
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawnote: Prepared under the direction of the Bessel Functions Panel of the Mathematical Tables Committee
rawtitle: {Bessel} Functions. {Part III}: {Zeros} and Associated Values
entry:
@Book{Anonymous:1960:BFP,
  author =       "Anonymous",
  title =        "{Bessel} Functions. {Part III}: {Zeros} and Associated
                 Values",
  volume =       "7",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "lx + 79",
  year =         "1960",
  MRclass =      "65.00",
  MRnumber =     "119441",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Prepared under the direction of the Bessel Functions
                 Panel of the Mathematical Tables Committee",
  series =       "Royal Society Mathematical Tables",
  acknowledgement = ack-nhfb,
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1960:EFG
author: Anonymous
title: Errata to Fisher and Gupta
journal: j-TECHNOMETRICS
volume: 2
number: 4
pages: 523--524
month: nov
monthnumber: 11
year: 1960
CODEN: TCMTA2
DOI: https://doi.org/10.2307/1266462
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Sat Jun 21 13:17:29 MDT 2014
bibtimestamp: 2014.06.21 13:17:29 MDT
note: See cite Fisher:1960:PPD,Gupta:1960:OSG.
URL: http://www.jstor.org/stable/1266462
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00401706.html
subjectdates: Sir Ronald Aylmer Fisher (17 February 1890--29 July 1962)
rawauthor: Anonymous
rawnote: See \cite{Fisher:1960:PPD,Gupta:1960:OSG}.
rawtitle: Errata to {Fisher} and {Gupta}
bibsource:
http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254224; https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib

entry:
@Article{Anonymous:1960:EFG,
  author =       "Anonymous",
  title =        "Errata to {Fisher} and {Gupta}",
  journal =      j-TECHNOMETRICS,
  volume =       "2",
  number =       "4",
  pages =        "523--524",
  month =        nov,
  year =         "1960",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1266462",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:17:29 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254224;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  note =         "See \cite{Fisher:1960:PPD,Gupta:1960:OSG}.",
  URL =          "http://www.jstor.org/stable/1266462",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
  subject-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July
                 1962)",
}


bibtype: article
filename: elefunt.bib
label: Beam:1960:ACE
author: A. Beam
title: Algorithm 14: Complex exponential integral
journal: j-CACM
volume: 3
number: 7
pages: 406--406
month: jul
monthnumber: 7
year: 1960
CODEN: CACMA2
DOI: https://doi.org/10.1145/367349.367351
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:27 MST 2005
bibtimestamp: 2005.11.25 18:19:27 MST
fjournal: Communications of the ACM
keywords: $Ei (z)$; special functions
remark: Fullerton: 30-line Algol procedure incorrectly labelled algorithm 13.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: A. Beam
rawtitle: {Algorithm 14}: {Complex} exponential integral
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Beam:1960:ACE,
  author =       "A. Beam",
  title =        "{Algorithm 14}: {Complex} exponential integral",
  journal =      j-CACM,
  volume =       "3",
  number =       "7",
  pages =        "406--406",
  month =        jul,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367349.367351",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:27 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Ei(z)$; special functions",
  remark =       "Fullerton: 30-line Algol procedure incorrectly
                 labelled algorithm 13.",
}


bibtype: book
filename: elefunt.bib
label: Edmonds:1960:AMQ
author: A. R. (Alan Robert) Edmonds
title: Angular Momentum in Quantum Mechanics
volume: 4
publisher: pub-PRINCETON
address: pub-PRINCETON:adr
edition: Second
pages: viii + 146
year: 1960
ISSN: 0075-0220 OR 00750220
LCCN: QC174; QC793.3.A5 E36 1960
bibdate: Mon Aug 4 15:01:00 MDT 2025
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.08.04 15:01:00 MDT
series: Investigations in physics
acknowledgement: ack-nhfb
rawauthor: A. R. (Alan Robert) Edmonds
rawtitle: Angular Momentum in Quantum Mechanics
ISBN:
0-691-02589-4 (hardcover), 0-691-07912-9 (paperback), 1-4008-8418-7 (online) OR 0691025894 (hardcover), 0691079129 (paperback), 1400884187 (online)

ISBN13:
978-0-691-02589-6 (hardcover), 978-0-691-07912-7 (paperback), 978-1-4008-8418-6 (online) OR 9780691025896 (hardcover), 9780691079127 (paperback), 9781400884186 (online)

TOC:
GROUP THEORETICAL PRELIMINARIES / 3 Introduction Elementary theory of groups The Euler angles Representation theory THE QUANTIZATION OF ANGULAR MOMENTUM / 10 Definition of angular momentum in quantum mechanics Angular momentum of a system of particles Representation of the angular momentum operators The physical significance of the quantization of angular momentum The eigenvectors of the angular momentum operators [symbols] The spin eigenvectors Angular momentum eigenfunctions in the case of large $l$ Time reversal and the angular momentum operators THE COUPLING OF ANGULAR MOMENTUM VECTORS / 31 The addition of angular momenta Commutation relations between components of $J_1$, $J_2$, and $J$ Selection rules for the matrix elements of $J_1$ and $J_2$ The choice of the phases of the states [symbols] The vector coupling coefficients Computation of the vector coupling coefficients The Wigner 3-j symbol Tabulation of formulas and numerical values for vector-coupling coefficients Time reversal and the eigenvectors resulting from vector coupling THE REPRESENTATIONS OF FINITE ROTATIONS / 53 The transformations of the angular momentum eigenvectors under finite rotations The symmetries of the [symbols] Products of the [symbols] Recursion relations for the [symbols] Computation of the [symbols] Integrals involving the [symbols] The [symbols] as angular momentum eigenfunctions The symmetric top SPHERICAL TENSORS AND TENSOR OPERATORS / 68 Spherical tensors The tensor operators in quantum mechanics Factorization of the matrix elements of tensor operators (Wigner--Eckart theorem) The reduced matrix elements of a tensor operator Hermitian adjoint of tensor operators Electric quadrupole moment of proton or electron The gradient formula Expansion of a plane wave in spherical waves Vector spherical harmonics Spin spherical harmonics Emission and absorption of particles THE CONSTRUCTION OF INVARIANTS FROM THE VECTOR COUPLING COEFFICIENTS / 90 The recoupling of three angular momenta The properties of the 6-j symbol The 9-j symbol THE EVALUATION OF MATRIX ELEMENTS IN ACTUAL PROBLEMS / 109 Matrix elements of the tensor product of two tensor operators Selected examples for atomic, molecular and nuclear physics APPENDICES Appendix 1: Theorems used in chapter 3 / 121 Appendix 2: Approximate expressions for vector-coupling coefficients and 6-j symbols / 122 Tables 1--5 / 124 Cited References and Bibliography / 133 Index / 141

shortTOC:
Group theoretical preliminaries / 3 The quantization of angular momentum / 10 The coupling of angular momentum vectors / 31 The representations of finite rotations / 53 Spherical tensors and tensor operators / 68 The construction of invariants from the vector-coupling coefficients / 90 The evaluation of matrix elements in actual problems / 109 Appendix 2: Approximate expressions for vector-coupling coefficients and 6-j symbols / 122 Tables 1--5 / 124 Cited References and Bibliography / 133 Index / 141

rawshortTOC:
Group theoretical preliminaries / 3 \\ The quantization of angular momentum / 10 \\ The coupling of angular momentum vectors / 31 \\ The representations of finite rotations / 53 \\ Spherical tensors and tensor operators / 68 \\ The construction of invariants from the vector-coupling coefficients / 90 \\ The evaluation of matrix elements in actual problems / 109 \\ Appendix 2: Approximate expressions for vector-coupling coefficients and 6-j symbols / 122 \\ Tables 1--5 / 124 \\ Cited References and Bibliography / 133 \\ Index / 141

rawTOC:
GROUP THEORETICAL PRELIMINARIES / 3 \\ Introduction \\ Elementary theory of groups \\ The Euler angles \\ Representation theory \\ THE QUANTIZATION OF ANGULAR MOMENTUM / 10 \\ Definition of angular momentum in quantum mechanics \\ Angular momentum of a system of particles \\ Representation of the angular momentum operators \\ The physical significance of the quantization of angular momentum \\ The eigenvectors of the angular momentum operators [symbols] \\ The spin eigenvectors \\ Angular momentum eigenfunctions in the case of large $l$ \\ Time reversal and the angular momentum operators \\ THE COUPLING OF ANGULAR MOMENTUM VECTORS / 31\\ The addition of angular momenta \\ Commutation relations between components of $J_1$, $J_2$, and $J$ \\ Selection rules for the matrix elements of $J_1$ and $J_2$ \\ The choice of the phases of the states [symbols] \\ The vector coupling coefficients \\ Computation of the vector coupling coefficients \\ The Wigner 3-j symbol \\ Tabulation of formulas and numerical values for vector-coupling coefficients \\ Time reversal and the eigenvectors resulting from vector coupling \\ THE REPRESENTATIONS OF FINITE ROTATIONS / 53 \\ The transformations of the angular momentum eigenvectors under finite rotations \\ The symmetries of the [symbols] \\ Products of the [symbols] \\ Recursion relations for the [symbols] \\ Computation of the [symbols] \\ Integrals involving the [symbols] \\ The [symbols] as angular momentum eigenfunctions \\ The symmetric top \\ SPHERICAL TENSORS AND TENSOR OPERATORS / 68 \\ Spherical tensors \\ The tensor operators in quantum mechanics \\ Factorization of the matrix elements of tensor operators (Wigner--Eckart theorem) \\ The reduced matrix elements of a tensor operator \\ Hermitian adjoint of tensor operators \\ Electric quadrupole moment of proton or electron \\ The gradient formula \\ Expansion of a plane wave in spherical waves \\ Vector spherical harmonics \\ Spin spherical harmonics \\ Emission and absorption of particles \\ THE CONSTRUCTION OF INVARIANTS FROM THE VECTOR COUPLING COEFFICIENTS / 90 \\ The recoupling of three angular momenta \\ The properties of the 6-j symbol \\ The 9-j symbol \\ THE EVALUATION OF MATRIX ELEMENTS IN ACTUAL PROBLEMS / 109 \\ Matrix elements of the tensor product of two tensor operators \\ Selected examples for atomic, molecular and nuclear physics \\ APPENDICES \\ Appendix 1: Theorems used in chapter 3 / 121 \\ Appendix 2: Approximate expressions for vector-coupling coefficients and 6-j symbols / 122 \\ Tables 1--5 / 124 \\ Cited References and Bibliography / 133 \\ Index / 141

entry:
@Book{Edmonds:1960:AMQ,
  author =       "A. R. (Alan Robert) Edmonds",
  title =        "Angular Momentum in Quantum Mechanics",
  volume =       "4",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  edition =      "Second",
  pages =        "viii + 146",
  year =         "1960",
  ISBN =         "0-691-02589-4 (hardcover), 0-691-07912-9 (paperback),
                 1-4008-8418-7 (online)",
  ISBN-13 =      "978-0-691-02589-6 (hardcover), 978-0-691-07912-7
                 (paperback), 978-1-4008-8418-6 (online)",
  ISSN =         "0075-0220",
  LCCN =         "QC174; QC793.3.A5 E36 1960",
  bibdate =      "Mon Aug 4 15:01:00 MDT 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Investigations in physics",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Group theoretical preliminaries / 3 \\
                 The quantization of angular momentum / 10 \\
                 The coupling of angular momentum vectors / 31 \\
                 The representations of finite rotations / 53 \\
                 Spherical tensors and tensor operators / 68 \\
                 The construction of invariants from the vector-coupling
                 coefficients / 90 \\
                 The evaluation of matrix elements in actual problems /
                 109 \\
                 Appendix 2: Approximate expressions for vector-coupling
                 coefficients and 6-j symbols / 122 \\
                 Tables 1--5 / 124 \\
                 Cited References and Bibliography / 133 \\
                 Index / 141",
  tableofcontents = "GROUP THEORETICAL PRELIMINARIES / 3 \\
                 Introduction \\
                 Elementary theory of groups \\
                 The Euler angles \\
                 Representation theory \\
                 THE QUANTIZATION OF ANGULAR MOMENTUM / 10 \\
                 Definition of angular momentum in quantum mechanics \\
                 Angular momentum of a system of particles \\
                 Representation of the angular momentum operators \\
                 The physical significance of the quantization of angular
                 momentum \\
                 The eigenvectors of the angular momentum operators
                 [symbols] \\
                 The spin eigenvectors \\
                 Angular momentum eigenfunctions in the case of large
                 $l$ \\
                 Time reversal and the angular momentum operators \\
                 THE COUPLING OF ANGULAR MOMENTUM VECTORS / 31\\
                 The addition of angular momenta \\
                 Commutation relations between components of $J_1$,
                 $J_2$, and $J$ \\
                 Selection rules for the matrix elements of $J_1$ and
                 $J_2$ \\
                 The choice of the phases of the states [symbols] \\
                 The vector coupling coefficients \\
                 Computation of the vector coupling coefficients \\
                 The Wigner 3-j symbol \\
                 Tabulation of formulas and numerical values for
                 vector-coupling coefficients \\
                 Time reversal and the eigenvectors resulting from
                 vector coupling \\
                 THE REPRESENTATIONS OF FINITE ROTATIONS / 53 \\
                 The transformations of the angular momentum
                 eigenvectors under finite rotations \\
                 The symmetries of the [symbols] \\
                 Products of the [symbols] \\
                 Recursion relations for the [symbols] \\
                 Computation of the [symbols] \\
                 Integrals involving the [symbols] \\
                 The [symbols] as angular momentum eigenfunctions \\
                 The symmetric top \\
                 SPHERICAL TENSORS AND TENSOR OPERATORS / 68 \\
                 Spherical tensors \\
                 The tensor operators in quantum mechanics \\
                 Factorization of the matrix elements of tensor
                 operators (Wigner--Eckart theorem) \\
                 The reduced matrix elements of a tensor operator \\
                 Hermitian adjoint of tensor operators \\
                 Electric quadrupole moment of proton or electron \\
                 The gradient formula \\
                 Expansion of a plane wave in spherical waves \\
                 Vector spherical harmonics \\
                 Spin spherical harmonics \\
                 Emission and absorption of particles \\
                 THE CONSTRUCTION OF INVARIANTS FROM THE VECTOR COUPLING
                 COEFFICIENTS / 90 \\
                 The recoupling of three angular momenta \\
                 The properties of the 6-j symbol \\
                 The 9-j symbol \\
                 THE EVALUATION OF MATRIX ELEMENTS IN ACTUAL PROBLEMS /
                 109 \\
                 Matrix elements of the tensor product of two tensor
                 operators \\
                 Selected examples for atomic, molecular and nuclear
                 physics \\
                 APPENDICES \\
                 Appendix 1: Theorems used in chapter 3 / 121 \\
                 Appendix 2: Approximate expressions for vector-coupling
                 coefficients and 6-j symbols / 122 \\
                 Tables 1--5 / 124 \\
                 Cited References and Bibliography / 133 \\
                 Index / 141",
}


bibtype: article
filename: elefunt.bib
label: Fisher:1960:PPD
author: Ronald A. Fisher and E. A. Cornish
title: The Percentile Points of Distributions Having Known Cumulants
journal: j-TECHNOMETRICS
volume: 2
number: 2
pages: 209--225
month: may
monthnumber: 5
year: 1960
CODEN: TCMTA2
DOI: https://doi.org/10.2307/1266546
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Sat Jun 21 13:17:27 MDT 2014
bibtimestamp: 2014.06.21 13:17:27 MDT
note: See errata cite Anonymous:1960:EFG.
URL: http://www.jstor.org/stable/1266546
fjournal: Technometrics
acknowledgement: ack-nhfb
authordates: Sir Ronald Aylmer Fisher (17 February 1890--29 July 1962)
journalURL: http://www.jstor.org/journals/00401706.html
rawauthor: Ronald A. Fisher and E. A. Cornish
rawnote: See errata \cite{Anonymous:1960:EFG}.
rawtitle: The Percentile Points of Distributions Having Known Cumulants
bibsource:
http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254222; https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib

entry:
@Article{Fisher:1960:PPD,
  author =       "Ronald A. Fisher and E. A. Cornish",
  title =        "The Percentile Points of Distributions Having Known
                 Cumulants",
  journal =      j-TECHNOMETRICS,
  volume =       "2",
  number =       "2",
  pages =        "209--225",
  month =        may,
  year =         "1960",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1266546",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:17:27 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254222;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  note =         "See errata \cite{Anonymous:1960:EFG}.",
  URL =          "http://www.jstor.org/stable/1266546",
  acknowledgement = ack-nhfb,
  author-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July
                 1962)",
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}


bibtype: book
filename: elefunt.bib
label: Fox:1960:TWP
author: L. Fox
title: Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments
volume: 4
publisher: pub-HMSO
address: pub-HMSO:adr
pages: iii + 40
year: 1960
MRclass: 65.00 (33.00)
MRnumber: 120778
MRreviewer: L. J. Slater
bibdate: Mon Nov 13 14:02:18 2023
bibtimestamp: 2023.11.13 14:02:18 ???
note: Department of Scientific and Industrial Research
series: National Physical Laboratory Mathematical Tables
acknowledgement: ack-nhfb
authordates: Leslie Fox (30 September 1918--1 August 1992)
rawauthor: L. Fox
rawnote: Department of Scientific and Industrial Research
rawtitle: Tables of {Weber} Parabolic Cylinder Functions and Other Functions for Large Arguments
entry:
@Book{Fox:1960:TWP,
  author =       "L. Fox",
  title =        "Tables of {Weber} Parabolic Cylinder Functions and
                 Other Functions for Large Arguments",
  volume =       "4",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "iii + 40",
  year =         "1960",
  MRclass =      "65.00 (33.00)",
  MRnumber =     "120778",
  MRreviewer =   "L. J. Slater",
  bibdate =      "Mon Nov 13 14:02:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Department of Scientific and Industrial Research",
  series =       "National Physical Laboratory Mathematical Tables",
  acknowledgement = ack-nhfb,
  author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: article
filename: elefunt.bib
label: Gupta:1960:OSG
author: Shanti S. Gupta
title: Order Statistics from the Gamma Distribution
journal: j-TECHNOMETRICS
volume: 2
number: 2
pages: 243--262
month: may
monthnumber: 5
year: 1960
CODEN: TCMTA2
DOI: https://doi.org/10.2307/1266548
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
MRclass: 62.00
MRnumber: 0112225 (22 \#3079)
MRreviewer: S. S. Wilks
bibdate: Sat Jun 21 13:17:27 MDT 2014
bibtimestamp: 2014.06.21 13:17:27 MDT
note: See errata cite Anonymous:1960:EFG.
URL: http://www.jstor.org/stable/1266548
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00401706.html
rawauthor: Shanti S. Gupta
rawnote: See errata \cite{Anonymous:1960:EFG}.
rawtitle: Order Statistics from the Gamma Distribution
bibsource:
http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254222; https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib

entry:
@Article{Gupta:1960:OSG,
  author =       "Shanti S. Gupta",
  title =        "Order Statistics from the Gamma Distribution",
  journal =      j-TECHNOMETRICS,
  volume =       "2",
  number =       "2",
  pages =        "243--262",
  month =        may,
  year =         "1960",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1266548",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  MRclass =      "62.00",
  MRnumber =     "0112225 (22 \#3079)",
  MRreviewer =   "S. S. Wilks",
  bibdate =      "Sat Jun 21 13:17:27 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254222;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  note =         "See errata \cite{Anonymous:1960:EFG}.",
  URL =          "http://www.jstor.org/stable/1266548",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}


bibtype: article
filename: elefunt.bib
label: Haimovici:1960:MRE
author: Corina Haimovici
title: A method of representing elementary functions in algebras of finite order. (Romanian)
journal: An. Sti. Univ. ``Al. I. Cuza'' Iasi Sect I. (N.S.)
volume: 6
pages: 507--515
year: 1960
MRclass: 26.00
MRnumber: 24 \#A1342
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Corina Haimovici
rawtitle: A method of representing elementary functions in algebras of finite order. ({Romanian})
entry:
@Article{Haimovici:1960:MRE,
  author =       "Corina Haimovici",
  title =        "A method of representing elementary functions in
                 algebras of finite order. ({Romanian})",
  journal =      "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
                 Sec{\c{t}} I. (N.S.)",
  volume =       "6",
  pages =        "507--515",
  year =         "1960",
  MRclass =      "26.00",
  MRnumber =     "24 \#A1342",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Harumi:1960:VTN
author: Kasaburo Harumi and Shigetoshi Katsura and John W. Wrench, Jr.
journal: j-MATH-COMPUT
volume: 14
number: 72
pages: 379--379
month: oct
monthnumber: 10
year: 1960
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1960-0122010-7
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: 10-digit table for $ n = 1, 2, ldots , 30 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Kasabur{\^o} Harumi and Shigetoshi Katsura and John W. {Wrench, Jr.}
title:
Values of $ frac 2pi int ^infty _0 Big (frac sin tt Big )^n d t $ (in Technical Notes and Short Papers)

rawtitle:
Values of {$ \frac {2}{\pi } \int^\infty_0 \Big (\frac {\sin t}{t} \Big)^n d t $} (in {Technical Notes and Short Papers})

entry:
@Article{Harumi:1960:VTN,
  author =       "Kasabur{\^o} Harumi and Shigetoshi Katsura and John W.
                 {Wrench, Jr.}",
  title =        "Values of {$ \frac {2}{\pi } \int^\infty_0 \Big (\frac
                 {\sin t}{t} \Big)^n d t $} (in {Technical Notes and
                 Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "72",
  pages =        "379--379",
  month =        oct,
  year =         "1960",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1960-0122010-7",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 10-digit table for $ n = 1, 2, \ldots {},
                 30 $.",
}


bibtype: incollection
filename: elefunt.bib
label: Kogbetliantz:1960:GEF
author: E. G. Kogbetliantz
title: Generation of elementary functions
crossref: Ralston:1960:MMD
pages: 7--35
year: 1960
MRclass: 68.00 (65.00)
MRnumber: 22 \#8681
MRreviewer: J. C. P. Miller
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: E. G. Kogbetliantz
rawtitle: Generation of elementary functions
entry:
@InCollection{Kogbetliantz:1960:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of elementary functions",
  crossref =     "Ralston:1960:MMD",
  pages =        "7--35",
  year =         "1960",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "22 \#8681",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Lang:1960:ECC
author: H. A. Lang
title: On the Evaluation of Certain Complex Elliptic Integrals (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 14
number: 70
pages: 195--199
month: apr
monthnumber: 4
year: 1960
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1960-0112241-4
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. A. Lang
rawtitle: On the Evaluation of Certain Complex Elliptic Integrals (in {Technical Notes and Short Papers})
entry:
@Article{Lang:1960:ECC,
  author =       "H. A. Lang",
  title =        "On the Evaluation of Certain Complex Elliptic
                 Integrals (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "70",
  pages =        "195--199",
  month =        apr,
  year =         "1960",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1960-0112241-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Lebedev:1960:GMT
title: A Guide to Mathematical Tables
publisher: pub-PERGAMON
address: pub-PERGAMON:adr
pages: xlvi + 586
year: 1960
LCCN: Z6654.T3 L42
bibdate: Mon Feb 13 17:12:14 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.02.13 17:12:14 MST
note: English edition prepared by D. G. Fry from the Russian original.
subject: Mathematics; Tables; Indexes
acknowledgement: ack-nhfb
rawnote: English edition prepared by D. G. Fry from the Russian original.
rawtitle: A Guide to Mathematical Tables
author:
A. V. (Aleksandr Vasil'evich) Lebedev and R. M. (Rimma Maksimova) Fedorova and Nina Mikhollovna Burunova

TOC:
Front Cover A Guide to Mathematical Tables Copyright Page Translator's Preface Preface Index to the Section Headings in the Table of Contents of the Guide and the Supplement Table of Contents Part One: Description of the Tables 1. Powers, Rational and Algebraic Functions Positive Whole Powers Fractional Positive Powers Reciprocals (Negative Whole and Fractional Powers) Rational Functions Algebraic Functions Complex Numbers and Their Powers 2. Trigonometric Functions. Various Values Connected With the Circle and the Sphere Natural Values of Trigonometric Functions Various Expressions Containing Trigonometric Functions Derivatives and Powers of Trigonometric Functions Reciprocal Trigonometric Functions of A Complex Variable Geometric Quantities Tables For Converting From One Angular Measure to Another 3. Exponential and Hyperbolic Functions Exponential Functions Hyperbolic Functions Expressions Containing Trigonometric and Hyperbolic Functions Inverse Hyperbolic Functions 4. Logarithms Common Logarithms and Antilogarithms Natural Logarithms Logarithms to Base 2 5. Factorials, Euler Integrals and Related Functions Factorials the Gamma Function the Psi Function and Its Derivatives the Beta Function Certain Constants 6. Sine and Cosine Integrals, Exponential and Logarithmic Integrals and Related Functions Sine and Cosine Integrals Hyperbolic Sine and Cosine Integrals Exponential Integral Logarithmic Integral Generalised and Composite Integral Functions Integral Functions of Complex Argument 7. Probability Integrals and Related Functions Functions of the Distribution of Probability and Related Functions Probability Integrals and Expressions Containing Probability Integrals Tables in Which the Integral Serves As the Argument Probability Integrals of Complex Argument Derivatives of Various Orders of Probability Distribution Functions Zeros of Probability Integrals Logarithms of Probability Integrals Fresnel Integrals and Related Functions 8. Elliptic Integrals and Elliptic Functions Moduli of the Integrals Complete Elliptic Integrals Incomplete Elliptic Integrals Elliptic Functions Theta Functions 9. Legendre Functions and Polynomials Legendre Polynomials and Legendre Functions of the First Kind Associated Legendre Functions of the First Kind Roots of Legendre Functions Various Expressions Containing Legendre Functions 10. Cylinder Functions Cylinder Functions of the First and Second Kinds of Real Argument Riccati--Bessel Functions Lommel Functions of Two Real Variables Cylinder Functions of the Third Kind (Hankel Functions) Cylinder Functions of the First and Second Kinds of Imaginary Argument Lommel Functions of Two Imaginary Variables Cylinder Functions of Complex Argument Thomson Functions

rawauthor:
A. V. (Aleksandr Vasil'evich) Lebedev and R. M. (Rimma Maksimova) Fedorova and Nina Mikhollovna Burunova

rawTOC:
Front Cover \\ A Guide to Mathematical Tables \\ Copyright Page \\ Translator's Preface \\ Preface \\ Index to the Section Headings in the Table of Contents of the Guide and the Supplement \\ Table of Contents \\ Part One: Description of the Tables \\ 1. Powers, Rational and Algebraic Functions \\ Positive Whole Powers \\ Fractional Positive Powers \\ Reciprocals (Negative Whole and Fractional Powers) \\ Rational Functions \\ Algebraic Functions \\ Complex Numbers and Their Powers \\ 2. Trigonometric Functions. Various Values Connected With the Circle and the Sphere \\ Natural Values of Trigonometric Functions \\ Various Expressions Containing Trigonometric Functions \\ Derivatives and Powers of Trigonometric Functions \\ Reciprocal Trigonometric Functions of A Complex Variable \\ Geometric Quantities \\ Tables For Converting From One Angular Measure to Another \\ 3. Exponential and Hyperbolic Functions \\ Exponential Functions \\ Hyperbolic Functions \\ Expressions Containing Trigonometric and Hyperbolic Functions \\ Inverse Hyperbolic Functions \\ 4. Logarithms \\ Common Logarithms and Antilogarithms \\ Natural Logarithms \\ Logarithms to Base 2 \\ 5. Factorials, Euler Integrals and Related Functions \\ Factorials \\ the Gamma Function \\ the Psi Function and Its Derivatives \\ the Beta Function \\ Certain Constants \\ 6. Sine and Cosine Integrals, Exponential and Logarithmic Integrals and Related Functions \\ Sine and Cosine Integrals \\ Hyperbolic Sine and Cosine Integrals \\ Exponential Integral \\ Logarithmic Integral \\ Generalised and Composite Integral Functions \\ Integral Functions of Complex Argument \\ 7. Probability Integrals and Related Functions \\ Functions of the Distribution of Probability and Related Functions \\ Probability Integrals and Expressions Containing Probability Integrals \\ Tables in Which the Integral Serves As the Argument \\ Probability Integrals of Complex Argument \\ Derivatives of Various Orders of Probability Distribution Functions \\ Zeros of Probability Integrals \\ Logarithms of Probability Integrals \\ Fresnel Integrals and Related Functions \\ 8. Elliptic Integrals and Elliptic Functions \\ Moduli of the Integrals \\ Complete Elliptic Integrals \\ Incomplete Elliptic Integrals \\ Elliptic Functions \\ Theta Functions \\ 9. Legendre Functions and Polynomials \\ Legendre Polynomials and Legendre Functions of the First Kind \\ Associated Legendre Functions of the First Kind \\ Roots of Legendre Functions \\ Various Expressions Containing Legendre Functions \\ 10. Cylinder Functions \\ Cylinder Functions of the First and Second Kinds of Real Argument \\ Riccati--Bessel Functions \\ Lommel Functions of Two Real Variables \\ Cylinder Functions of the Third Kind (Hankel Functions) \\ Cylinder Functions of the First and Second Kinds of Imaginary Argument \\ Lommel Functions of Two Imaginary Variables \\ Cylinder Functions of Complex Argument \\ Thomson Functions

entry:
@Book{Lebedev:1960:GMT,
  author =       "A. V. (Aleksandr Vasil'evich) Lebedev and R. M. (Rimma
                 Maksimova) Fedorova and Nina Mikhollovna Burunova",
  title =        "A Guide to Mathematical Tables",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xlvi + 586",
  year =         "1960",
  LCCN =         "Z6654.T3 L42",
  bibdate =      "Mon Feb 13 17:12:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "English edition prepared by D. G. Fry from the Russian
                 original.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Tables; Indexes",
  tableofcontents = "Front Cover \\
                 A Guide to Mathematical Tables \\
                 Copyright Page \\
                 Translator's Preface \\
                 Preface \\
                 Index to the Section Headings in the Table of Contents
                 of the Guide and the Supplement \\
                 Table of Contents \\
                 Part One: Description of the Tables \\
                 1. Powers, Rational and Algebraic Functions \\
                 Positive Whole Powers \\
                 Fractional Positive Powers \\
                 Reciprocals (Negative Whole and Fractional Powers) \\
                 Rational Functions \\
                 Algebraic Functions \\
                 Complex Numbers and Their Powers \\
                 2. Trigonometric Functions. Various Values Connected
                 With the Circle and the Sphere \\
                 Natural Values of Trigonometric Functions \\
                 Various Expressions Containing Trigonometric Functions
                 \\
                 Derivatives and Powers of Trigonometric Functions \\
                 Reciprocal Trigonometric Functions of A Complex
                 Variable \\
                 Geometric Quantities \\
                 Tables For Converting From One Angular Measure to
                 Another \\
                 3. Exponential and Hyperbolic Functions \\
                 Exponential Functions \\
                 Hyperbolic Functions \\
                 Expressions Containing Trigonometric and Hyperbolic
                 Functions \\
                 Inverse Hyperbolic Functions \\
                 4. Logarithms \\
                 Common Logarithms and Antilogarithms \\
                 Natural Logarithms \\
                 Logarithms to Base 2 \\
                 5. Factorials, Euler Integrals and Related Functions
                 \\
                 Factorials \\
                 the Gamma Function \\
                 the Psi Function and Its Derivatives \\
                 the Beta Function \\
                 Certain Constants \\
                 6. Sine and Cosine Integrals, Exponential and
                 Logarithmic Integrals and Related Functions \\
                 Sine and Cosine Integrals \\
                 Hyperbolic Sine and Cosine Integrals \\
                 Exponential Integral \\
                 Logarithmic Integral \\
                 Generalised and Composite Integral Functions \\
                 Integral Functions of Complex Argument \\
                 7. Probability Integrals and Related Functions \\
                 Functions of the Distribution of Probability and
                 Related Functions \\
                 Probability Integrals and Expressions Containing
                 Probability Integrals \\
                 Tables in Which the Integral Serves As the Argument \\
                 Probability Integrals of Complex Argument \\
                 Derivatives of Various Orders of Probability
                 Distribution Functions \\
                 Zeros of Probability Integrals \\
                 Logarithms of Probability Integrals \\
                 Fresnel Integrals and Related Functions \\
                 8. Elliptic Integrals and Elliptic Functions \\
                 Moduli of the Integrals \\
                 Complete Elliptic Integrals \\
                 Incomplete Elliptic Integrals \\
                 Elliptic Functions \\
                 Theta Functions \\
                 9. Legendre Functions and Polynomials \\
                 Legendre Polynomials and Legendre Functions of the
                 First Kind \\
                 Associated Legendre Functions of the First Kind \\
                 Roots of Legendre Functions \\
                 Various Expressions Containing Legendre Functions \\
                 10. Cylinder Functions \\
                 Cylinder Functions of the First and Second Kinds of
                 Real Argument \\
                 Riccati--Bessel Functions \\
                 Lommel Functions of Two Real Variables \\
                 Cylinder Functions of the Third Kind (Hankel Functions)
                 \\
                 Cylinder Functions of the First and Second Kinds of
                 Imaginary Argument \\
                 Lommel Functions of Two Imaginary Variables \\
                 Cylinder Functions of Complex Argument \\
                 Thomson Functions",
}


bibtype: manual
filename: elefunt.bib
label: Maehly:1960:ACD
author: Hans J. Maehly
title: Approximations for the Control Data 1604
organization: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
pages: ii + 44
day: 15
month: jan
monthnumber: 1
year: 1960
bibdate: Tue Nov 06 00:39:07 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.11.06 00:39:07 ???
URL: http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf
keywords: $arctan (x)$; $cos (x)$; $exp (x)$; $log (x)$; $sin (x)$; $sqrt (x)$; $tan (x)$; CDC 1604
acknowledgement: ack-nhfb
rawauthor: Hans J. Maehly
rawtitle: Approximations for the {Control Data 1604}
entry:
@Manual{Maehly:1960:ACD,
  author =       "Hans J. Maehly",
  title =        "Approximations for the {Control Data 1604}",
  organization = inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "ii + 44",
  day =          "15",
  month =        jan,
  year =         "1960",
  bibdate =      "Tue Nov 06 00:39:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$;
                 $\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604",
}


bibtype: article
filename: elefunt.bib
label: Philip:1960:FI
author: J. R. Philip
title: The function $ operatorname inverfc theta $
journal: j-AUSTRALIAN-J-PHYS
volume: 13
number: 1
pages: 13--20
month: mar
monthnumber: 3
year: 1960
CODEN: AUJPAS
DOI: https://doi.org/10.1071/PH600013
ISSN: 0004-9506 (print), 1446-5582 (electronic) OR 00049506 (print), 14465582 (electronic)
ISSNL: 0004-9506 OR 00049506
MRnumber: 22 9626
bibdate: Tue Sep 11 20:53:59 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.09.11 20:53:59 ???
fjournal: Australian Journal of Physics
ZMnumber: 135.28302
acknowledgement: ack-nhfb
journalURL: http://www.publish.csiro.au/ph/content/allissues
rawauthor: J. R. Philip
rawtitle: The function $ \operatorname {inverfc} \theta $
abstract:
The function inverfc $ theta $ arises in certain differential equations when concentration is taken as an independent variable. It enters into a general method of exact solution of the concentration-dependent diffusion equation. An account is given of the properties of this function, and of its derivatives and integrals. The functionpar $$ B(theta ) = (2 / pi ^1 / 2) exp [ - (operatorname inverfc theta )^2] $$ noindent is intimately connected with the first integral of inverfc $ theta $ and with its derivatives. Tables of $ operatorname inverfc theta $ and $ B(theta ) $ are given.

rawabstract:
The function inverfc $ \theta $ arises in certain differential equations when concentration is taken as an independent variable. It enters into a general method of exact solution of the concentration-dependent diffusion equation. An account is given of the properties of this function, and of its derivatives and integrals. The function\par $$ B(\theta) = (2 / \pi^{1 / 2}) \exp [ - (\operatorname {inverfc} \theta)^2] $$ \noindent is intimately connected with the first integral of inverfc $ \theta $ and with its derivatives. Tables of $ \operatorname {inverfc} \theta $ and $ B(\theta) $ are given.

entry:
@Article{Philip:1960:FI,
  author =       "J. R. Philip",
  title =        "The function $ \operatorname {inverfc} \theta $",
  journal =      j-AUSTRALIAN-J-PHYS,
  volume =       "13",
  number =       "1",
  pages =        "13--20",
  month =        mar,
  year =         "1960",
  CODEN =        "AUJPAS",
  DOI =          "https://doi.org/10.1071/PH600013",
  ISSN =         "0004-9506 (print), 1446-5582 (electronic)",
  ISSN-L =       "0004-9506",
  MRnumber =     "22 9626",
  bibdate =      "Tue Sep 11 20:53:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "135.28302",
  abstract =     "The function inverfc $ \theta $ arises in certain
                 differential equations when concentration is taken as
                 an independent variable. It enters into a general
                 method of exact solution of the concentration-dependent
                 diffusion equation. An account is given of the
                 properties of this function, and of its derivatives and
                 integrals. The function\par

                  $$ B(\theta) = (2 / \pi^{1 / 2}) \exp [ - (\operatorname {inverfc} \theta)^2] $$

                 \noindent is intimately connected with the first
                 integral of inverfc $ \theta $ and with its
                 derivatives. Tables of $ \operatorname {inverfc} \theta
                 $ and $ B(\theta) $ are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Journal of Physics",
  journal-URL =  "http://www.publish.csiro.au/ph/content/allissues",
}


bibtype: book
filename: elefunt.bib
label: Rainville:1960:SF
author: Earl David Rainville
title: Special Functions
publisher: pub-MACMILLAN
address: pub-MACMILLAN:adr
pages: xii + 365
year: 1960
ISBN: 0-8284-0258-2 OR 0828402582
ISBN13: 978-0-8284-0258-3 OR 9780828402583
LCCN: QA331 R15; QA351 .R3 1971
bibdate: Mon Sep 3 16:04:28 MDT 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.09.03 16:04:28 MDT
note: Reprinted in 1971.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: Earl David Rainville
rawnote: Reprinted in 1971.
rawtitle: Special Functions
remark:
Based upon the lectures on special functions which ldots [the author has] been giving at the University of Michigan since 1946. Fullerton: All traditional functions and polynomials are discussed in some detail.

TOC:
1: Infinite Products 1. Introduction / 1 2. Definition of an infinite product / 1 3. A necessary condition for convergence . / 2 4. The associated series of logarithms / 2 5. Absolute convergence / 3 6. Uniform convergence / 5 2: The Gamma and Beta Functions 7. The Euler or Mascheroni constant $gamma $ / 8 8. The Gamma function / 9 9. A series for $Gamma '(z) / Gamma (z)$ / 10 10. Evaluation of $Gamma (1)$ and $Gamma '(1)$ / 10 11. The Euler product for $Gamma (z)$ / 11 12. The difference equation $Gamma (z + 1) = z Gamma (z)$ / 12 13. The order symbols $o$ and $O$ / 12 14. Evaluation of certain infinite products / 13 15. Euler's integral for $Gamma (z)$ / 15 16. The Beta function / 18 17. The value of $Gamma (z) Gamma (1 - z)$ / 19 18. The factorial function / 22 19. Legendre's duplication formula / 23 20. Gauss' multiplication theorem / 24 21. A summation formula due to Euler / 26 22. The behavior of $log Gamma (z)$ for large $|z|$ / 29 3: Asymptotic Series 23. Definition of an asymptotic expansion / 33 24. Asymptotic expansions about infinity / 36 25. Algebraic properties / 38 26. Term-by-term integration / 39 27. Uniqueness / 40 28. Watson's lemma / 41 4: The Hypergeometric Function 29. The function $F(a, b; c; z)$ / 45 30. A simple integral form / 47 31. $F(a, b; c; 1)$ as a function of the parameters / 48 32. Evaluation of $F(a, b; c; 1)$ / 48 33. The contiguous function relations / 50 34. The hypergeometric differential equation / 53 35. Logarithmic solutions of the hypergeometric equation / 54 36. $F(a, b; c; 2)$ as a function of its parameters / 55 37. Elementary series manipulations / 56 38. Simple transformations / 58 39. Relation between functions of $z$ and $1 - z$ / 61 40. A quadratic transformation / 63 41. Other quadratic transformations / 65 42. A theorem due to Kummer / 68 43. Additional properties / 68 5: Generalized Hypergeometric Functions 44. The function $_pF_q$ / 73 45. The exponential and binomial functions / 74 46. A differential equation / 74 47. Other solutions of the differential equation / 76 48. The contiguous function relations / 80 49. A simple integral / 85 50. The $_pF_q$ with unit argument / 85 51. Saalschutz' theorem / 86 52. Whipple's theorem / 88 53. Dixon's theorem / 92 54. Contour integrals of Barnes' type / 94 55. The Barnes integrals and the function $_pF_q$ / 98 56. A useful integral / 102 6: Bessel Functions 57. Remarks / 108 58. Definition of $J_n(z)$ / 108 59. Bessel's differential equation / 109 60. Differential recurrence relations / 110 61. A pure recurrence relation / 111 62. A generating function / 112 63. Bessel's integral / 114 64. Index half an odd integer 114 , 65. Modified Bessel functions / 116 66. Neumann polynomials / 116 67. Neumann series / 119 7: The Confluent Hypergeometric Function 68. Basic properties of the $_1F_1$ / 123 69. Kummer's first formula / 124 70. Kummer's second formula / 125 8: Generating Functions 71. The generating function concept / 129 72. Generating functions of the form $G(2 x t - t^2)$ / 131 73. Sets generated by $e^t psi (x t)$ / 132 74. The generating functions $A(t) exp [-x t / (1 - t)]$ / 135 75. Another class of generating functions / 137 76. Boas and Buck generating functions / 140 77. An extension / 143 9: Orthogonal Polynomials 78. Simple sets of polynomials / 147 79. Orthogonality / 147 80. An equivalent condition for orthogonality / 148 81. Zeros of orthogonal polynomials / 149 82. Expansion of polynomials / 150 83. The three-term recurrence relation / 151 84. The Christoffel--Darboux formula / 153 85. Normalization; Bessel's inequality / 155 10: Legendre Polynomials 86. A generating function / 157 87. Differential recurrence relations / 158 88. The pure recurrence relation / 159 89. Legendre's differential equation / 160 90. The Rodrigues formula / 161 91. Bateman's generating function / 162 92. Additional generating functions / 163 93. Hypergeometric forms of $P_n(x)$ / 163 94. Brafman's generating functions / 167 95. Special properties of $P_n(x)$ / 168 96. More generating functions / 169 97. Laplace's first integral form / 171 98. Some bounds on $P_n(z)$ / 172 99. Orthogonality / 173 100. An expansion theorem / 176 101. Expansion of $x^n$ / 179 102. Expansion of analytic functions / 181 11: Hermite Polynomials 103. Definition of $H_n(x)$ / 187 104. Recurrence relations / 188 105. The Rodrigues formula / 189 106. Other generating functions / 190 107. Integrals / 190 108. The Hermite polynomial as a $_2F_0$ / 191 109. Orthogonality / 191 110. Expansion of polynomials / 193 111. More generating functions / 196 12: Laguerre Polynomials 112. The polynomial $L_n^(alpha )(x)$ / 200 113. Generating functions / 201 114. Recurrence relations / 202 115. The Rodrigues formula / 203 116. The differential equation / 204 117. Orthogonality / 204 118. Expansion of polynomials / 206 119. Special properties / 209 120. Other generating functions / 211 121. The simple Laguerre polynomials / 213 13: The Sheffer Classification and Related Topics 122. Differential operators and polynomial sets / 218 123. Sheffer's $A$-type classification / 221 124. Polynomials of Sheffer $A$-type zero / 222 195. An extension of Sheffer's classification / 226 126. Polynomials of $sigma $-type zero / 228 14: Pure Recurrence Relations 127. Sister Celine's technique / 233 128. A mild extension / 240 15: Symbolic Relations 129. Notation / 246 130. Symbolic relations among classical polynomials / 247 131. Polynomials of symbolic form $L_n(y(x))$ / 249 16: Jacobi Polynomials 132. The Jacobi polynomials / 254 133. Bateman's generating function / 256 134. The Rodrigues formula / 257 135. Orthogonality / 258 136. Differential recurrence relations / 261 137. The pure recurrence relation / 263 138. Mixed relations / 263 139. Appell's functions of two variables / 265 140. An elementary generating function / 269 141. Brafman's generating functions / 271 142. Expansion in series of polynomials / 272 17: Ultraspherical and Gegenbauer Polynomials 143. Definitions / 276 144. The Gegenbauer polynomials / 277 145. The ultraspherical polynomials / 283 18: Other Polynomial Sets 146. Bateman's $Z_n(x)$ / 285 147. Rice's $H_n(zeta , p, v)$ / 287 148. Bateman's $F_n(z)$ / 289 149. Sister Celine's polynomials / 290 150. Bessel polynomials / 293 151. Bedient's polynomials / 297 152. Shively's pseudo-Laguerre and other polynomials / 298 153. Bernoulli polynomials / 299 154. Euler polynomials / 300 155. Tchebicheff polynomials / 301 19: Elliptic Functions 156. Doubly periodic functions / 305 157. Elliptic functions / 306 158. Elementary properties / 306 159. Order of an elliptic function / 308 160. The Weierstrass function $P(z)$ / 309 161. Other elliptic functions / 311 162. A differential equation for $P(z)$ / 311 163. Connection with elliptic integrals / 313 20: Theta Functions 164. Definitions / 314 165. Elementary properties / 315 166. The basic property table / 316 167. Location of zeros / 319 168. Relations among squares of theta functions / 322 169. Pseudo addition theorems / 325 170. Relation to the heat equation / 328 171. The relation $theta _1' = theta _2 theta _3 theta _4$ / 329 172. Infinite products / 332 173. The value of $G$ / 334 21: Jacobian Elliptic Functions 174. A differential equation involving theta functions / 339 175. The function $sn (u)$ / 342 176. The functions $cn (u)$ and $dn (u)$ / 343 177. Relations involving squares / 344 178. Relations involving derivatives / 345 179. Addition theorems / 347 Bibliography / 349 Index / 359

shortTOC:
1: Infinite Products 2: The Gamma and Beta Functions 3: Asymptotic Series 4: The Hypergeometric Function 5: Generalized Hypergeometric Functions 6: Bessel Functions 7: The Confluent Hypergeometric Function 8: Generating Functions 9: Orthogonal Polynomials 10: Legendre Polynomials 11: Hermite Polynomials 12: Laguerre Polynomials 13: The Sheffer Classification and Related Topics 14: Pure Recurrence Relations 15: Symbolic Relations 16: Jacobi Polynomials 17: Ultraspherical and Gegenbauer Polynomials 18: Other Polynomial Sets 19: Elliptic Functions 20: Theta Functions 21: Jacobian Elliptic Functions Bibliography Index

rawshortTOC:
1: Infinite Products \\ 2: The Gamma and Beta Functions \\ 3: Asymptotic Series \\ 4: The Hypergeometric Function \\ 5: Generalized Hypergeometric Functions \\ 6: Bessel Functions \\ 7: The Confluent Hypergeometric Function \\ 8: Generating Functions \\ 9: Orthogonal Polynomials \\ 10: Legendre Polynomials \\ 11: Hermite Polynomials \\ 12: Laguerre Polynomials \\ 13: The Sheffer Classification and Related Topics \\ 14: Pure Recurrence Relations \\ 15: Symbolic Relations \\ 16: Jacobi Polynomials \\ 17: Ultraspherical and Gegenbauer Polynomials \\ 18: Other Polynomial Sets \\ 19: Elliptic Functions \\ 20: Theta Functions \\ 21: Jacobian Elliptic Functions \\ Bibliography \\ Index

rawTOC:
1: Infinite Products \\ 1. Introduction / 1 \\ 2. Definition of an infinite product / 1 \\ 3. A necessary condition for convergence . / 2 \\ 4. The associated series of logarithms / 2 \\ 5. Absolute convergence / 3 \\ 6. Uniform convergence / 5 \\ \\ 2: The Gamma and Beta Functions \\ 7. The Euler or Mascheroni constant $\gamma$ / 8 \\ 8. The Gamma function / 9 \\ 9. A series for $\Gamma'(z) / \Gamma(z)$ / 10 \\ 10. Evaluation of $\Gamma(1)$ and $\Gamma'(1)$ / 10 \\ 11. The Euler product for $\Gamma(z)$ / 11 \\ 12. The difference equation $\Gamma(z + 1) = z \Gamma(z)$ / 12 \\ 13. The order symbols $o$ and $O$ / 12 \\ 14. Evaluation of certain infinite products / 13 \\ 15. Euler's integral for $\Gamma(z)$ / 15 \\ 16. The Beta function / 18 \\ 17. The value of $\Gamma(z) \Gamma(1 - z)$ / 19 \\ 18. The factorial function / 22 \\ 19. Legendre's duplication formula / 23 \\ 20. Gauss' multiplication theorem / 24 \\ 21. A summation formula due to Euler / 26 \\ 22. The behavior of $\log \Gamma(z)$ for large $|z|$ / 29 \\ \\ 3: Asymptotic Series \\ 23. Definition of an asymptotic expansion / 33 \\ 24. Asymptotic expansions about infinity / 36 \\ 25. Algebraic properties / 38 \\ 26. Term-by-term integration / 39 \\ 27. Uniqueness / 40 \\ 28. Watson's lemma / 41 \\ \\ 4: The Hypergeometric Function \\ 29. The function $F(a, b; c; z)$ / 45 \\ 30. A simple integral form / 47 \\ 31. $F(a, b; c; 1)$ as a function of the parameters / 48 \\ 32. Evaluation of $F(a, b; c; 1)$ / 48 \\ 33. The contiguous function relations / 50 \\ 34. The hypergeometric differential equation / 53 \\ 35. Logarithmic solutions of the hypergeometric equation / 54 \\ 36. $F(a, b; c; 2)$ as a function of its parameters / 55 \\ 37. Elementary series manipulations / 56 \\ 38. Simple transformations / 58 \\ 39. Relation between functions of $z$ and $1 - z$ / 61 \\ 40. A quadratic transformation / 63 \\ 41. Other quadratic transformations / 65 \\ 42. A theorem due to Kummer / 68 \\ 43. Additional properties / 68 \\ \\ 5: Generalized Hypergeometric Functions \\ 44. The function $_pF_q$ / 73 \\ 45. The exponential and binomial functions / 74 \\ 46. A differential equation / 74 \\ 47. Other solutions of the differential equation / 76 \\ 48. The contiguous function relations / 80 \\ 49. A simple integral / 85 \\ 50. The $_pF_q$ with unit argument / 85 \\ 51. Saalsch{\"u}tz' theorem / 86 \\ 52. Whipple's theorem / 88 \\ 53. Dixon's theorem / 92 \\ 54. Contour integrals of Barnes' type / 94 \\ 55. The Barnes integrals and the function $_pF_q$ / 98 \\ 56. A useful integral / 102 \\ \\ 6: Bessel Functions \\ 57. Remarks / 108 \\ 58. Definition of $J_n(z)$ / 108 \\ 59. Bessel's differential equation / 109 \\ 60. Differential recurrence relations / 110 \\ 61. A pure recurrence relation / 111 \\ 62. A generating function / 112 \\ 63. Bessel's integral / 114 \\ 64. Index half an odd integer 114 , \\ 65. Modified Bessel functions / 116 \\ 66. Neumann polynomials / 116 \\ 67. Neumann series / 119 \\ \\ 7: The Confluent Hypergeometric Function \\ 68. Basic properties of the $_1F_1$ / 123 \\ 69. Kummer's first formula / 124 \\ 70. Kummer's second formula / 125 \\ \\ 8: Generating Functions \\ 71. The generating function concept / 129 \\ 72. Generating functions of the form $G(2 x t - t^2)$ / 131 \\ 73. Sets generated by $e^t \psi(x t)$ / 132 \\ 74. The generating functions $A(t) \exp[-x t / (1 - t)]$ / 135 \\ 75. Another class of generating functions / 137 \\ 76. Boas and Buck generating functions / 140 \\ 77. An extension / 143 \\ \\ 9: Orthogonal Polynomials \\ 78. Simple sets of polynomials / 147 \\ 79. Orthogonality / 147 \\ 80. An equivalent condition for orthogonality / 148 \\ 81. Zeros of orthogonal polynomials / 149 \\ 82. Expansion of polynomials / 150 \\ 83. The three-term recurrence relation / 151 \\ 84. The Christoffel--Darboux formula / 153 \\ 85. Normalization; Bessel's inequality / 155 \\ \\ 10: Legendre Polynomials \\ 86. A generating function / 157 \\ 87. Differential recurrence relations / 158 \\ 88. The pure recurrence relation / 159 \\ 89. Legendre's differential equation / 160 \\ 90. The Rodrigues formula / 161 \\ 91. Bateman's generating function / 162 \\ 92. Additional generating functions / 163 \\ 93. Hypergeometric forms of $P_n(x)$ / 163 \\ 94. Brafman's generating functions / 167 \\ 95. Special properties of $P_n(x)$ / 168 \\ 96. More generating functions / 169 \\ 97. Laplace's first integral form / 171 \\ 98. Some bounds on $P_n(z)$ / 172 \\ 99. Orthogonality / 173 \\ 100. An expansion theorem / 176 \\ 101. Expansion of $x^n$ / 179 \\ 102. Expansion of analytic functions / 181 \\ \\ 11: Hermite Polynomials \\ 103. Definition of $H_n(x)$ / 187 \\ 104. Recurrence relations / 188 \\ 105. The Rodrigues formula / 189 \\ 106. Other generating functions / 190 \\ 107. Integrals / 190 \\ 108. The Hermite polynomial as a $_2F_0$ / 191 \\ 109. Orthogonality / 191 \\ 110. Expansion of polynomials / 193 \\ 111. More generating functions / 196 \\ \\ 12: Laguerre Polynomials \\ 112. The polynomial $L_n^{(\alpha)}(x)$ / 200 \\ 113. Generating functions / 201 \\ 114. Recurrence relations / 202 \\ 115. The Rodrigues formula / 203 \\ 116. The differential equation / 204 \\ 117. Orthogonality / 204 \\ 118. Expansion of polynomials / 206 \\ 119. Special properties / 209 \\ 120. Other generating functions / 211 \\ 121. The simple Laguerre polynomials / 213 \\ \\ 13: The Sheffer Classification and Related Topics \\ 122. Differential operators and polynomial sets / 218 \\ 123. Sheffer's $A$-type classification / 221 \\ 124. Polynomials of Sheffer $A$-type zero / 222 \\ 195. An extension of Sheffer's classification / 226 \\ 126. Polynomials of $\sigma$-type zero / 228 \\ \\ 14: Pure Recurrence Relations \\ 127. Sister Celine's technique / 233 \\ 128. A mild extension / 240 \\ \\ 15: Symbolic Relations \\ 129. Notation / 246 \\ 130. Symbolic relations among classical polynomials / 247 \\ 131. Polynomials of symbolic form $L_n(y(x))$ / 249 \\ \\ 16: Jacobi Polynomials \\ 132. The Jacobi polynomials / 254 \\ 133. Bateman's generating function / 256 \\ 134. The Rodrigues formula / 257 \\ 135. Orthogonality / 258 \\ 136. Differential recurrence relations / 261 \\ 137. The pure recurrence relation / 263 \\ 138. Mixed relations / 263 \\ 139. Appell's functions of two variables / 265 \\ 140. An elementary generating function / 269 \\ 141. Brafman's generating functions / 271 \\ 142. Expansion in series of polynomials / 272 \\ \\ 17: Ultraspherical and Gegenbauer Polynomials \\ 143. Definitions / 276 \\ 144. The Gegenbauer polynomials / 277 \\ 145. The ultraspherical polynomials / 283 \\ \\ 18: Other Polynomial Sets \\ 146. Bateman's $Z_n(x)$ / 285 \\ 147. Rice's $H_n(\zeta, p, v)$ / 287 \\ 148. Bateman's $F_n(z)$ / 289 \\ 149. Sister Celine's polynomials / 290 \\ 150. Bessel polynomials / 293 \\ 151. Bedient's polynomials / 297 \\ 152. Shively's pseudo-Laguerre and other polynomials / 298 \\ 153. Bernoulli polynomials / 299 \\ 154. Euler polynomials / 300 \\ 155. Tchebicheff polynomials / 301 \\ \\ 19: Elliptic Functions \\ 156. Doubly periodic functions / 305 \\ 157. Elliptic functions / 306 \\ 158. Elementary properties / 306 \\ 159. Order of an elliptic function / 308 \\ 160. The Weierstrass function $P(z)$ / 309 \\ 161. Other elliptic functions / 311 \\ 162. A differential equation for $P(z)$ / 311 \\ 163. Connection with elliptic integrals / 313 \\ \\ 20: Theta Functions \\ 164. Definitions / 314 \\ 165. Elementary properties / 315 \\ 166. The basic property table / 316 \\ 167. Location of zeros / 319 \\ 168. Relations among squares of theta functions / 322 \\ 169. Pseudo addition theorems / 325 \\ 170. Relation to the heat equation / 328 \\ 171. The relation $\theta_1' = \theta_2 \theta_3 \theta_4$ / 329 \\ 172. Infinite products / 332 \\ 173. The value of $G$ / 334 \\ \\ 21: Jacobian Elliptic Functions \\ 174. A differential equation involving theta functions / 339 \\ 175. The function $\sn(u)$ / 342 \\ 176. The functions $\cn(u)$ and $\dn(u)$ / 343 \\ 177. Relations involving squares / 344 \\ 178. Relations involving derivatives / 345 \\ 179. Addition theorems / 347 \\ \\ Bibliography / 349 \\ \\ Index / 359

entry:
@Book{Rainville:1960:SF,
  author =       "Earl David Rainville",
  title =        "Special Functions",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  pages =        "xii + 365",
  year =         "1960",
  ISBN =         "0-8284-0258-2",
  ISBN-13 =      "978-0-8284-0258-3",
  LCCN =         "QA331 R15; QA351 .R3 1971",
  bibdate =      "Mon Sep 3 16:04:28 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Reprinted in 1971.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Based upon the lectures on special functions which
                 \ldots{} [the author has] been giving at the University
                 of Michigan since 1946. Fullerton: All traditional
                 functions and polynomials are discussed in some
                 detail.",
  shorttableofcontents = "1: Infinite Products \\
                 2: The Gamma and Beta Functions \\
                 3: Asymptotic Series \\
                 4: The Hypergeometric Function \\
                 5: Generalized Hypergeometric Functions \\
                 6: Bessel Functions \\
                 7: The Confluent Hypergeometric Function \\
                 8: Generating Functions \\
                 9: Orthogonal Polynomials \\
                 10: Legendre Polynomials \\
                 11: Hermite Polynomials \\
                 12: Laguerre Polynomials \\
                 13: The Sheffer Classification and Related Topics \\
                 14: Pure Recurrence Relations \\
                 15: Symbolic Relations \\
                 16: Jacobi Polynomials \\
                 17: Ultraspherical and Gegenbauer Polynomials \\
                 18: Other Polynomial Sets \\
                 19: Elliptic Functions \\
                 20: Theta Functions \\
                 21: Jacobian Elliptic Functions \\
                 Bibliography \\
                 Index",
  subject =      "Functions, Special",
  tableofcontents = "1: Infinite Products \\
                 1. Introduction / 1 \\
                 2. Definition of an infinite product / 1 \\
                 3. A necessary condition for convergence . / 2 \\
                 4. The associated series of logarithms / 2 \\
                 5. Absolute convergence / 3 \\
                 6. Uniform convergence / 5 \\
                 \\
                 2: The Gamma and Beta Functions \\
                 7. The Euler or Mascheroni constant $\gamma$ / 8 \\
                 8. The Gamma function / 9 \\
                 9. A series for $\Gamma'(z) / \Gamma(z)$ / 10 \\
                 10. Evaluation of $\Gamma(1)$ and $\Gamma'(1)$ / 10 \\
                 11. The Euler product for $\Gamma(z)$ / 11 \\
                 12. The difference equation $\Gamma(z + 1) = z
                 \Gamma(z)$ / 12 \\
                 13. The order symbols $o$ and $O$ / 12 \\
                 14. Evaluation of certain infinite products / 13 \\
                 15. Euler's integral for $\Gamma(z)$ / 15 \\
                 16. The Beta function / 18 \\
                 17. The value of $\Gamma(z) \Gamma(1 - z)$ / 19 \\
                 18. The factorial function / 22 \\
                 19. Legendre's duplication formula / 23 \\
                 20. Gauss' multiplication theorem / 24 \\
                 21. A summation formula due to Euler / 26 \\
                 22. The behavior of $\log \Gamma(z)$ for large $|z|$ /
                 29 \\
                 \\
                 3: Asymptotic Series \\
                 23. Definition of an asymptotic expansion / 33 \\
                 24. Asymptotic expansions about infinity / 36 \\
                 25. Algebraic properties / 38 \\
                 26. Term-by-term integration / 39 \\
                 27. Uniqueness / 40 \\
                 28. Watson's lemma / 41 \\
                 \\
                 4: The Hypergeometric Function \\
                 29. The function $F(a, b; c; z)$ / 45 \\
                 30. A simple integral form / 47 \\
                 31. $F(a, b; c; 1)$ as a function of the parameters /
                 48 \\
                 32. Evaluation of $F(a, b; c; 1)$ / 48 \\
                 33. The contiguous function relations / 50 \\
                 34. The hypergeometric differential equation / 53 \\
                 35. Logarithmic solutions of the hypergeometric
                 equation / 54 \\
                 36. $F(a, b; c; 2)$ as a function of its parameters /
                 55 \\
                 37. Elementary series manipulations / 56 \\
                 38. Simple transformations / 58 \\
                 39. Relation between functions of $z$ and $1 - z$ / 61
                 \\
                 40. A quadratic transformation / 63 \\
                 41. Other quadratic transformations / 65 \\
                 42. A theorem due to Kummer / 68 \\
                 43. Additional properties / 68 \\
                 \\
                 5: Generalized Hypergeometric Functions \\
                 44. The function $_pF_q$ / 73 \\
                 45. The exponential and binomial functions / 74 \\
                 46. A differential equation / 74 \\
                 47. Other solutions of the differential equation / 76
                 \\
                 48. The contiguous function relations / 80 \\
                 49. A simple integral / 85 \\
                 50. The $_pF_q$ with unit argument / 85 \\
                 51. Saalsch{\"u}tz' theorem / 86 \\
                 52. Whipple's theorem / 88 \\
                 53. Dixon's theorem / 92 \\
                 54. Contour integrals of Barnes' type / 94 \\
                 55. The Barnes integrals and the function $_pF_q$ / 98
                 \\
                 56. A useful integral / 102 \\
                 \\
                 6: Bessel Functions \\
                 57. Remarks / 108 \\
                 58. Definition of $J_n(z)$ / 108 \\
                 59. Bessel's differential equation / 109 \\
                 60. Differential recurrence relations / 110 \\
                 61. A pure recurrence relation / 111 \\
                 62. A generating function / 112 \\
                 63. Bessel's integral / 114 \\
                 64. Index half an odd integer 114 , \\
                 65. Modified Bessel functions / 116 \\
                 66. Neumann polynomials / 116 \\
                 67. Neumann series / 119 \\
                 \\
                 7: The Confluent Hypergeometric Function \\
                 68. Basic properties of the $_1F_1$ / 123 \\
                 69. Kummer's first formula / 124 \\
                 70. Kummer's second formula / 125 \\
                 \\
                 8: Generating Functions \\
                 71. The generating function concept / 129 \\
                 72. Generating functions of the form $G(2 x t - t^2)$ /
                 131 \\
                 73. Sets generated by $e^t \psi(x t)$ / 132 \\
                 74. The generating functions $A(t) \exp[-x t / (1 -
                 t)]$ / 135 \\
                 75. Another class of generating functions / 137 \\
                 76. Boas and Buck generating functions / 140 \\
                 77. An extension / 143 \\
                 \\
                 9: Orthogonal Polynomials \\
                 78. Simple sets of polynomials / 147 \\
                 79. Orthogonality / 147 \\
                 80. An equivalent condition for orthogonality / 148 \\
                 81. Zeros of orthogonal polynomials / 149 \\
                 82. Expansion of polynomials / 150 \\
                 83. The three-term recurrence relation / 151 \\
                 84. The Christoffel--Darboux formula / 153 \\
                 85. Normalization; Bessel's inequality / 155 \\
                 \\
                 10: Legendre Polynomials \\
                 86. A generating function / 157 \\
                 87. Differential recurrence relations / 158 \\
                 88. The pure recurrence relation / 159 \\
                 89. Legendre's differential equation / 160 \\
                 90. The Rodrigues formula / 161 \\
                 91. Bateman's generating function / 162 \\
                 92. Additional generating functions / 163 \\
                 93. Hypergeometric forms of $P_n(x)$ / 163 \\
                 94. Brafman's generating functions / 167 \\
                 95. Special properties of $P_n(x)$ / 168 \\
                 96. More generating functions / 169 \\
                 97. Laplace's first integral form / 171 \\
                 98. Some bounds on $P_n(z)$ / 172 \\
                 99. Orthogonality / 173 \\
                 100. An expansion theorem / 176 \\
                 101. Expansion of $x^n$ / 179 \\
                 102. Expansion of analytic functions / 181 \\
                 \\
                 11: Hermite Polynomials \\
                 103. Definition of $H_n(x)$ / 187 \\
                 104. Recurrence relations / 188 \\
                 105. The Rodrigues formula / 189 \\
                 106. Other generating functions / 190 \\
                 107. Integrals / 190 \\
                 108. The Hermite polynomial as a $_2F_0$ / 191 \\
                 109. Orthogonality / 191 \\
                 110. Expansion of polynomials / 193 \\
                 111. More generating functions / 196 \\
                 \\
                 12: Laguerre Polynomials \\
                 112. The polynomial $L_n^{(\alpha)}(x)$ / 200 \\
                 113. Generating functions / 201 \\
                 114. Recurrence relations / 202 \\
                 115. The Rodrigues formula / 203 \\
                 116. The differential equation / 204 \\
                 117. Orthogonality / 204 \\
                 118. Expansion of polynomials / 206 \\
                 119. Special properties / 209 \\
                 120. Other generating functions / 211 \\
                 121. The simple Laguerre polynomials / 213 \\
                 \\
                 13: The Sheffer Classification and Related Topics \\
                 122. Differential operators and polynomial sets / 218
                 \\
                 123. Sheffer's $A$-type classification / 221 \\
                 124. Polynomials of Sheffer $A$-type zero / 222 \\
                 195. An extension of Sheffer's classification / 226 \\
                 126. Polynomials of $\sigma$-type zero / 228 \\
                 \\
                 14: Pure Recurrence Relations \\
                 127. Sister Celine's technique / 233 \\
                 128. A mild extension / 240 \\
                 \\
                 15: Symbolic Relations \\
                 129. Notation / 246 \\
                 130. Symbolic relations among classical polynomials /
                 247 \\
                 131. Polynomials of symbolic form $L_n(y(x))$ / 249 \\
                 \\
                 16: Jacobi Polynomials \\
                 132. The Jacobi polynomials / 254 \\
                 133. Bateman's generating function / 256 \\
                 134. The Rodrigues formula / 257 \\
                 135. Orthogonality / 258 \\
                 136. Differential recurrence relations / 261 \\
                 137. The pure recurrence relation / 263 \\
                 138. Mixed relations / 263 \\
                 139. Appell's functions of two variables / 265 \\
                 140. An elementary generating function / 269 \\
                 141. Brafman's generating functions / 271 \\
                 142. Expansion in series of polynomials / 272 \\
                 \\
                 17: Ultraspherical and Gegenbauer Polynomials \\
                 143. Definitions / 276 \\
                 144. The Gegenbauer polynomials / 277 \\
                 145. The ultraspherical polynomials / 283 \\
                 \\
                 18: Other Polynomial Sets \\
                 146. Bateman's $Z_n(x)$ / 285 \\
                 147. Rice's $H_n(\zeta, p, v)$ / 287 \\
                 148. Bateman's $F_n(z)$ / 289 \\
                 149. Sister Celine's polynomials / 290 \\
                 150. Bessel polynomials / 293 \\
                 151. Bedient's polynomials / 297 \\
                 152. Shively's pseudo-Laguerre and other polynomials /
                 298 \\
                 153. Bernoulli polynomials / 299 \\
                 154. Euler polynomials / 300 \\
                 155. Tchebicheff polynomials / 301 \\
                 \\
                 19: Elliptic Functions \\
                 156. Doubly periodic functions / 305 \\
                 157. Elliptic functions / 306 \\
                 158. Elementary properties / 306 \\
                 159. Order of an elliptic function / 308 \\
                 160. The Weierstrass function $P(z)$ / 309 \\
                 161. Other elliptic functions / 311 \\
                 162. A differential equation for $P(z)$ / 311 \\
                 163. Connection with elliptic integrals / 313 \\
                 \\
                 20: Theta Functions \\
                 164. Definitions / 314 \\
                 165. Elementary properties / 315 \\
                 166. The basic property table / 316 \\
                 167. Location of zeros / 319 \\
                 168. Relations among squares of theta functions / 322
                 \\
                 169. Pseudo addition theorems / 325 \\
                 170. Relation to the heat equation / 328 \\
                 171. The relation $\theta_1' = \theta_2 \theta_3
                 \theta_4$ / 329 \\
                 172. Infinite products / 332 \\
                 173. The value of $G$ / 334 \\
                 \\
                 21: Jacobian Elliptic Functions \\
                 174. A differential equation involving theta functions
                 / 339 \\
                 175. The function $\sn(u)$ / 342 \\
                 176. The functions $\cn(u)$ and $\dn(u)$ / 343 \\
                 177. Relations involving squares / 344 \\
                 178. Relations involving derivatives / 345 \\
                 179. Addition theorems / 347 \\
                 \\
                 Bibliography / 349 \\
                 \\
                 Index / 359",
}


