%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "3.13", %%% date = "16 July 2008", %%% time = "11:52:15 MDT", %%% filename = "elefunt.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "42035 18080 79592 757556", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "BibTeX, bibliography, elementary functions", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications about %%% the computation of the elementary functions %%% (square root, exponential, logarithm, %%% trigonometric, inverse trigonometric, %%% hyperbolic, inverse hyperbolic, ...) in %%% computer programming languages. %%% %%% At version 3.13, the year coverage looked %%% like this: %%% %%% 1925 ( 1) 1953 ( 1) 1981 ( 15) %%% 1926 ( 0) 1954 ( 2) 1982 ( 27) %%% 1927 ( 0) 1955 ( 0) 1983 ( 19) %%% 1928 ( 0) 1956 ( 0) 1984 ( 13) %%% 1929 ( 0) 1957 ( 4) 1985 ( 15) %%% 1930 ( 0) 1958 ( 4) 1986 ( 17) %%% 1931 ( 0) 1959 ( 5) 1987 ( 24) %%% 1932 ( 0) 1960 ( 9) 1988 ( 35) %%% 1933 ( 0) 1961 ( 5) 1989 ( 62) %%% 1934 ( 0) 1962 ( 0) 1990 ( 16) %%% 1935 ( 0) 1963 ( 5) 1991 ( 27) %%% 1936 ( 0) 1964 ( 4) 1992 ( 17) %%% 1937 ( 0) 1965 ( 4) 1993 ( 21) %%% 1938 ( 0) 1966 ( 7) 1994 ( 24) %%% 1939 ( 0) 1967 ( 3) 1995 ( 21) %%% 1940 ( 0) 1968 ( 7) 1996 ( 10) %%% 1941 ( 0) 1969 ( 7) 1997 ( 16) %%% 1942 ( 0) 1970 ( 5) 1998 ( 7) %%% 1943 ( 1) 1971 ( 15) 1999 ( 30) %%% 1944 ( 2) 1972 ( 15) 2000 ( 22) %%% 1945 ( 2) 1973 ( 9) 2001 ( 16) %%% 1946 ( 1) 1974 ( 8) 2002 ( 8) %%% 1947 ( 0) 1975 ( 10) 2003 ( 11) %%% 1948 ( 1) 1976 ( 10) 2004 ( 16) %%% 1949 ( 0) 1977 ( 6) 2005 ( 13) %%% 1950 ( 0) 1978 ( 13) 2006 ( 7) %%% 1951 ( 3) 1979 ( 12) 2007 ( 4) %%% 1952 ( 3) 1980 ( 10) 2008 ( 1) %%% %%% Article: 440 %%% Book: 32 %%% InBook: 1 %%% InCollection: 19 %%% InProceedings: 117 %%% Manual: 1 %%% MastersThesis: 3 %%% Misc: 3 %%% PhdThesis: 12 %%% Proceedings: 42 %%% TechReport: 38 %%% %%% Total entries: 708 %%% %%% This bibliography has been collected from %%% bibliographies in the author's personal %%% files, from the OCLC WorldCat and %%% Contents1st databases, from the American %%% Mathematical Society MathSciNet database, %%% from the ACM Computing Archive CD-ROM, %%% and from the computer science bibliography %%% collection on ftp.ira.uka.de in %%% /pub/bibliography to which many people of %%% have contributed. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% BibTeX citation tags are uniformly chosen as %%% name:year:abbrev, where name is the family %%% name of the first author or editor, year is a %%% 4-digit number, and abbrev is a 3-letter %%% condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% This bibliography is sorted by year, and %%% within each year, by author and title key, %%% using ``bibsort -byyear''. Cross-referenced %%% proceedings entries appear at the end, %%% because of a restriction in the current %%% BibTeX. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== %%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here. %%% The more conventional undelimited form \toenglish{...} has braces %%% that prevent BibTeX's downcasing operation, and the alternate form %%% {\toenglish{...}} is considered a `special character' by BibTeX, %%% and all of {...} gets downcased. We avoid the name \english to %%% prevent conflicts with language options in packages like Babel. %%% %%% To suppress output of English translations of non-English titles, %%% use %%% "\def \toenglish #1\endtoenglish{\unskip}" %%% instead. %%% %%% Alternative Cyrillic definitions are supplied in the event that %%% cyracc.def is not loaded. @Preamble{"\input bibnames.sty" # "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " # "\ifx \undefined \cyr \let \cyr = \relax \fi " # "\ifx \undefined \cdprime \def \cdprime{''} \fi " # "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" # "\hyphenation{ Rich-ard }" } %%% ==================================================================== %%% Acknowledgement abbreviations: @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, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} @String{ack-nj = "Norbert Juffa, 2445 Mission College Blvd., Santa Clara, CA 95054, USA, e-mail: \path|norbert@@iit.com|"} @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="} %%% ==================================================================== %%% Institution abbreviations: @String{inst-ANL = "Argonne National Laboratory"} @String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL 60439-4801, USA"} @String{inst-CPAM-UCB = "Center for Pure and Applied Mathematics, University of California, Berkeley"} @String{inst-CPAM-UCB:adr = "Berkeley, CA, USA"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ACTA-INFO = "Acta Informatica"} @String{j-ADV-APPL-MATH = "Advances in Applied Mathematics"} @String{j-AM-J-MATH = "American Journal of Mathematics"} @String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"} @String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial Intelligence"} @String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"} @String{j-AUSTRALIAN-J-PHYS = "Australian Journal of Physics"} @String{j-AUTOMATICA = "Automatica: the journal of IFAC, the International Federation of Automatic Control"} @String{j-BIT = "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"} @String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare des sciences"} @String{j-CACM = "Communications of the ACM"} @String{j-CCCUJ = "C/C++ Users Journal"} @String{j-COMP-MATH-APPL-B = "Computers and Mathematics with Applications. Part B"} @String{j-COMP-J = "The Computer Journal"} @String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"} @String{j-COMPUTER = "Computer"} @String{j-COMPUTING = "Computing: Archiv fur informatik und numerik"} @String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"} @String{j-CONST-APPROX = "Constructive Approximation"} @String{j-DDJ = "Dr. Dobb's Journal of Software Tools"} @String{j-ELECT-LETTERS = "Electronics Letters"} @String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"} @String{j-IBM-JRD = "IBM Journal of Research and Development"} @String{j-IBM-SYS-J = "IBM Systems Journal"} @String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital Techniques"} @String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"} @String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE signal processing letters"} @String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and systems. 2, Analog and digital signal processing"} @String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"} @String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"} @String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"} @String{j-IJSAHPC = "The International Journal of Supercomputer Applications and High Performance Computing"} @String{j-INFO-PROC-LETT = "Information Processing Letters"} @String{j-INT-J-COMPUT-INF-SCI = "International Journal of Computer and Information Sciences"} @String{j-INT-J-MATH-EDU-SCI-TECH = "International journal of mathematical education in science and technology"} @String{j-INT-J-MATH-MATH-SCI = "International Journal of Mathematics and Mathematical Sciences"} @String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"} @String{j-INTEL-TECH-J = "Intel Technology Journal"} @String{j-INTERVAL-COMP = "Interval Computations = Interval'nye vychisleniia"} @String{j-J-ACM = "Journal of the Association for Computing Machinery"} @String{j-J-ALG = "Journal of Algorithms"} @String{j-J-APPROX-THEORY = "Journal of Approximation Theory"} @String{j-J-COMP-APPL-MATH = "Journal of Computational and Applied Mathematics"} @String{j-J-COMPLEXITY = "Journal of complexity"} @String{j-J-MULTIVAR-ANAL = "Journal of multivariate analysis"} @String{j-J-PAR-DIST-COMP = "Journal of Parallel and Distributed Computing"} @String{j-J-PHYS-A = "Journal of Physics A (Mathematical and General)"} @String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and Simulation"} @String{j-J-STAT-SOFT = "Journal of Statistical Software"} @String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"} @String{j-J-SYMBOLIC-LOGIC = "Journal of Symbolic Logic"} @String{j-J-UCS = "J.UCS: The Journal of Universal Computer Science"} @String{j-J-VLSI-SIGNAL-PROC = "Journal of VLSI Signal Processing"} @String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"} @String{j-LIN-MULT-ALGEBRA = "Linear and Multilinear Algebra"} @String{j-LOGIN = ";login: the USENIX Association newsletter"} @String{j-MATH-COMP = "Mathematics of Computation"} @String{j-MATH-COMP-SIM = "Mathematics and Computers in Simulation"} @String{j-MATH-COMPUT = "Mathematics of Computation"} @String{j-MATH-MODEL-NUM-ANA = "Mathematical modelling and numerical analysis = Modelisation math{\'e}matique et analyse num{\'e}rique: $M^2AN$"} @String{j-MATH-OP-RES = "Mathematics of Operations Research"} @String{j-MATH-PROG = "Mathematical Programming"} @String{j-MATH-TABLES-AIDS-COMPUT = "Mathematical Tables and Aids to Computation"} @String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids to Computation"} @String{j-MICROPROC-MICROPROG = "Microprocessing and Microprogramming"} @String{j-MICROPROC-MICROSYS = "Microprocessors and Microsystems"} @String{j-NACH-ELEK = "Nachrichtentechnik Elektronik"} @String{j-NEURAL-COMP = "Neural Computation"} @String{j-NEURAL-NETWORKS = "Neural Networks"} @String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for informationsbehandling"} @String{j-NUM-MATH = "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS = "Numerical Algorithms"} @String{j-OPER-RES = "Operations Research"} @String{j-PAC-J-MATH = "Pacific Journal of Mathematics"} @String{j-PARALLEL-COMPUTING = "Parallel Computing"} @String{j-PHYS-TODAY = "Physics Today"} @String{j-PHYSICA-D = "Physica D"} @String{j-PROC-AM-MATH-SOC = "Proceedings of the American Mathematical Society"} @String{j-PROGRAMMIROVANIE = "Programmirovanie"} @String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-CONTROL-OPTIM = "SIAM Journal on Control and Optimization"} @String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-MATH-ANA = "SIAM journal on mathematical analysis"} @String{j-SIAM-REVIEW = "SIAM Review"} @String{j-SIGADA-LETTERS = "ACM SIGADA Ada Letters"} @String{j-SIGNUM = "ACM SIGNUM Newsletter"} @String{j-SIGPLAN = "ACM SIGPLAN Notices"} @String{j-TECHNIQUE-SCI-INFORMATIQUES = "Technique et Science Informatiques"} @String{j-THEOR-COMP-SCI = "Theoretical Computer Science"} @String{j-TOKYO-J-MATH = "Tokyo journal of mathematics"} @String{j-TOMS = "ACM Transactions on Mathematical Software"} @String{j-TRANS-AM-MATH-SOC = "Transactions of the American Mathematical Society"} @String{j-TRANS-SOC-COMP-SIM = "Transactions of the Society for Computer Simulation"} @String{j-Z-ANAL-ANWEND = "Zeitschrift f{\"u}r Analysis und ihre Anwendungen"} @String{j-Z-MATH-LOGIK-GRUNDL-MATH = "Zeitschrift f{\\\"u}r mathematische Logik und Grundlagen der Mathematik"} %%% ==================================================================== %%% Publishers and their addresses: @String{pub-ACM = "ACM Press"} @String{pub-ACM:adr = "New York, NY 10036, USA"} @String{pub-AFIPS = "AFIPS Press"} @String{pub-AFIPS:adr = "Montvale, NJ, USA"} @String{pub-AMS = "American Mathematical Society"} @String{pub-AMS:adr = "Providence, RI, USA"} @String{pub-AP = "Academic Press"} @String{pub-AP:adr = "New York, NY, USA"} @String{pub-BIRKHAUSER = "Birkh{\"a}user"} @String{pub-BIRKHAUSER:adr = "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-CHAPMAN-HALL = "Chapman and Hall, Ltd."} @String{pub-CHAPMAN-HALL:adr = "London, UK"} @String{pub-CLARENDON-PRESS = "Clarendon Press"} @String{pub-CLARENDON-PRESS:adr = "Oxford, UK"} @String{pub-CRC = "CRC Press"} @String{pub-CRC:adr = "2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-ELLIS-HORWOOD = "Ellis Horwood"} @String{pub-ELLIS-HORWOOD:adr = "New York, NY, USA"} @String{pub-ENH = "Elsevier North-Holland, Inc."} @String{pub-ENH:adr = "New York, NY, USA"} @String{pub-IBM = "IBM Corporation"} @String{pub-IBM:adr = "San Jose, CA, USA"} @String{pub-IEEE = "IEEE Computer Society Press"} @String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-MCGRAW-HILL = "Mc{\-}Graw-Hill"} @String{pub-MCGRAW-HILL:adr = "New York, NY, USA"} @String{pub-NIST = "National Institute for Standards and Technology"} @String{pub-NIST:adr = "Gaithersburg, MD, USA"} @String{pub-NORTH-HOLLAND = "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr = "Amsterdam, The Netherlands"} @String{pub-OXFORD = "Oxford University Press"} @String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PERGAMON = "Pergamon Press"} @String{pub-PERGAMON:adr = "New York, NY, USA"} @String{pub-PH = "Pren{\-}tice-Hall"} @String{pub-PH:adr = "Englewood Cliffs, NJ 07632, USA"} @String{pub-REK = "Robert E. Krieger Publishing Company"} @String{pub-REK:adr = "Huntington, NY, USA"} @String{pub-SIAM = "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr = "Philadelphia, PA, USA"} @String{pub-SPIE = "Society of Photo-optical Instrumentation Engineers (SPIE)"} @String{pub-SPIE:adr = "Bellingham, WA, USA"} @String{pub-SV = "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-TEUBNER = "Teubner"} @String{pub-TEUBNER:adr = "Stuttgart, Leipzig"} @String{pub-USENIX = "USENIX"} @String{pub-USENIX:adr = "San Francisco, CA, USA"} @String{pub-WCB = "William C. Brown Company Publishers"} @String{pub-WCB:adr = "Dubuque, IA, USA"} @String{pub-WILEY = "Wiley"} @String{pub-WILEY:adr = "New York, NY, USA"} @String{pub-WORLD-SCI = "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road, Singapore 9128"} %%% ==================================================================== %%% Series abbreviations: @String{ser-LNCS = "Lecture Notes in Computer Science"} %%% ==================================================================== %%% Bibliography entries, sorted by year and citation label: @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", ISSN = "0002-9947", MRclass = "30A05 (33B10)", MRnumber = "MR1501299", bibdate = "Wed Apr 13 06:46:35 2005", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", } @Article{RCA:1943:TTF, author = "{R. C. A.}", 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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", note = "Original journal has only `R. C. A.' as author: possibly R. C. Archibald.", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", MRclass = "", MRnumber = "6,132b", MRreviewer = "G. Szeg{\"o}", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{DHL:1944:NCB, author = "{D. H. L.}", 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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", note = "Original journal has only `D. H. L.' as author: probably D. H. Lehmer.", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", MRclass = "65.0X", MRnumber = "6,132c", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", note = "Original edition published in 1940.", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", acknowledgement = ack-nhfb, } @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\=at{\c{n}}u Akad. V\=estis", 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", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", acknowledgement = ack-nhfb, } @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", acknowledgement = ack-nhfb, } @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", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Clenshaw:1954:PAE, author = "C. W. Clenshaw", title = "Polynomial approximations to elementary functions", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "8", pages = "143--147", year = "1954", ISSN = "0891-6837", MRclass = "41.1X", MRnumber = "16,128f", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", ISSN = "0018-8646", MRclass = "68.0X", MRnumber = "19,775d", bibdate = "Tue Sep 06 20:55:54 1994", acknowledgement = ack-nhfb, reviewer = "W. F. Freiberger", } @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", acknowledgement = ack-nhfb, } @Article{Luke:1957:C, author = "Yudell L. Luke", title = "On the Computation of $\log {Z}$ and ${\rm arc} \tan {Z}$", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "11", number = "57", pages = "16--18", month = jan, year = "1957", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", ISSN = "0018-8646", MRclass = "65.3X", MRnumber = "19,982e", bibdate = "Wed Aug 31 13:40:00 1994", acknowledgement = ack-nhfb, reviewer = "C. B. Haselgrove", } @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", ISSN = "0018-8646", MRclass = "65.3X", MRnumber = "19,1197c", bibdate = "Wed Aug 31 13:41:37 1994", acknowledgement = ack-nhfb, reviewer = "C. B. Haselgrove", } @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", ISSN = "0001-0782", bibdate = "Wed Jul 14 15:48:22 MDT 2004", bibsource = "http://portal.acm.org/; http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58", acknowledgement = ack-nhfb, oldlabel = "Wadey58", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58", } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", ISSN = "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", acknowledgement = ack-nhfb, reviewer = "B. A. Chartres", } @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", ISSN = "0001-0782", bibdate = "Wed Jul 14 15:48:24 MDT 2004", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59; http://portal.acm.org/", note = "See comments \cite{Traub:1960:CNM}.", acknowledgement = ack-nhfb, oldlabel = "Sarafyan59", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59", } @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", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @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", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz", acknowledgement = ack-nhfb, keywords = "elementary functions", } @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", acknowledgement = ack-nhfb, } @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", acknowledgement = ack-nhfb, } @Manual{Maehly:1960:ACD, author = "Hans J. Maehly", title = "Approximations for the {Control Data 1604}", organization = "Institute for Advanced Study", address = "Princeton, NJ", pages = "ii + 44", day = "15", month = jan, year = "1960", bibdate = "Tue Nov 06 00:39:07 2007", 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", } @Article{Philip:1960:FI, author = "J. R. Philip", title = "The function inverfc $\theta$", journal = j-AUSTRALIAN-J-PHYS, volume = "13", number = "1", pages = "13--20", month = mar, year = "1960", CODEN = "AUJPAS", ISSN = "0004-9506", MRnumber = "22 \9626", bibdate = "Tue Sep 11 20:53:59 2007", 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 $$B(\theta) = (2/\pi^{1/2}) \exp[-({\rm inverfc} \theta)^2]$$ \noindent is intimately connected with the first integral of inverfc $\theta$ and with its derivatives. Tables of inverfc $\theta$ and $B(\theta)$ are given.", acknowledgement = ack-nhfb, ZMnumber = "135.28302", } @Article{Sarafyan:1960:DCS, author = "Diran Sarafyan", title = "Divisionless computation of square roots through continued squaring", journal = j-CACM, volume = "3", number = "5", pages = "319--321", month = may, year = "1960", CODEN = "CACMA2", ISSN = "0001-0782", MRclass = "65.00", MRnumber = "22\#8639", bibdate = "Fri Nov 25 18:19:26 MST 2005", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.acm.org/pubs/contents/journals/cacm/", acknowledgement = ack-nhfb, keywords = "$\sqrt(x)$; elementary functions", ZMreviewer = "M. Lotkin", } @Article{Sholander:1960:AEE, author = "Marlow Sholander", title = "Analytical expressions and elementary functions", journal = j-AMER-MATH-MONTHLY, volume = "67", pages = "213--214", year = "1960", CODEN = "AMMYAE", ISSN = "0002-9890", MRclass = "26.00", MRnumber = "22 \#9553", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Traub:1960:CNM, author = "J. F. Traub", title = "Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]", journal = j-CACM, volume = "3", number = "2", pages = "86--86", month = feb, year = "1960", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Nov 25 18:19:25 MST 2005", bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/cacm1960.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/", note = "See \cite{Sarafyan:1959:NMC}.", acknowledgement = ack-nhfb, oldlabel = "Traub60", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60", } @Book{Warmus:1960:TEF, author = "Mieczys{\l}aw Warmus", title = "Tables of elementary functions", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "vii + 567", year = "1960", LCCN = "QA55 .W3 1960", MRclass = "65.05", MRnumber = "23 \#B1141", MRreviewer = "J. C. P. Miller", bibdate = "Sat Jan 11 17:44:01 MST 1997", note = "Pa\'nstwowe Wydawnictwo Naukowe, Warsaw. Separately bound table of proportional parts, 30 pp.", acknowledgement = ack-nhfb, } @Article{Barakat:1961:EIG, author = "Richard Barakat", title = "Evaluation of the Incomplete Gamma Function of Imaginary Argument by {Chebyshev} Polynomials", journal = j-MATH-COMPUT, volume = "15", number = "73", pages = "7--11", month = jan, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Froberg:1961:RCA, author = "Carl-Erik Fr{\"o}berg", title = "Rational {Chebyshev} Approximations of Elementary Functions", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "1", number = "4", pages = "256--262", month = dec, year = "1961", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933243", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 18:52:07 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4", note = "See erratum \cite{Froberg:1963:ERC}.", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Article{Spielberg:1961:ECF, author = "Kurt Spielberg", title = "Efficient Continued Fraction Approximations To Elementary Functions", journal = j-MATH-COMP, volume = "15", number = "76", pages = "409--417", month = oct, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65.20", MRnumber = "MR0134842 (24 \#B894)", MRreviewer = "M. E. Rose", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj # " and " # ack-nhfb, } @Article{Thacher:1961:ISR, author = "Henry C. {Thacher, Jr.}", title = "Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine", journal = j-MATH-COMPUT, volume = "15", number = "76", pages = "399--403", month = oct, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Werner:1961:CAG, author = "Helmut Werner and Robert Collinge", title = "{Chebyshev} Approximations to the Gamma Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "15", number = "74", pages = "195--197", month = apr, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Carlitz:1963:IEF, author = "L. Carlitz", title = "The Inverse of the Error Function", journal = j-PAC-J-MATH, volume = "13", number = "2", pages = "459--470", year = "1963", CODEN = "PJMAAI", ISSN = "0030-8730", bibdate = "Thu Sep 13 21:30:05 2007", URL = "http://pjm.math.berkeley.edu/pjm; http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1", acknowledgement = ack-nhfb, } @Article{Froberg:1963:ERC, author = "C.-E. Fr{\"o}berg", title = "Erratum: {``Rational Chebyshev Approximations of Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261, line 12]}", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "3", number = "1", pages = "68--68", month = mar, year = "1963", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01963538", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 18:52:07 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1", note = "See \cite{Froberg:1961:RCA}.", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68", acknowledgement = ack-nhfb, keywords = "elementary functions", } @Book{Ljusternik:1963:MVF, author = "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R. Janpol'ski{{\u{\i}}}", title = "{\cyr Matematicheski{\u{\i}}analiz. Vychislenie {\`e}lementarnykh funktsi{\u{\i}}}. [Mathematical analysis. Computation of the elementary functions]", publisher = "Gosudarstv. Izdat. Fiz-Mat. Lit.", address = "Moscow, USSR", pages = "247", year = "1963", MRclass = "65.25", MRnumber = "28 \#1733", MRreviewer = "John Todd", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Peuizulaev:1963:AEF, author = "{\v{S}}. I. Pe{\u{\i}}zulaev", title = "An approximation by elementary functions. ({Russian})", journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.", volume = "3", pages = "769--770", year = "1963", MRclass = "41.30", MRnumber = "28 \#398", MRreviewer = "D. D. Stancu", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Whittlesey:1963:IGF, author = "John R. B. Whittlesey", title = "Incomplete Gamma Functions for Evaluating {Erlang} Process Probabilities", journal = j-MATH-COMPUT, volume = "17", number = "81", pages = "11--17", month = jan, year = "1963", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Burgoyne:1964:GTF, author = "F. D. Burgoyne", title = "Generalized Trigonometric Functions (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "18", number = "86", pages = "314--316", month = apr, year = "1964", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Morelock:1964:AAE, author = "J. C. Morelock", title = "{ACM} Algorithm 229: Elementary Functions by Continued Fractions", journal = j-CACM, volume = "7", number = "5", pages = "296", month = may, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:32:21 1994", acknowledgement = ack-nhfb, } @Article{Simauti:1964:AFS, author = "Takakazu Simauti", title = "Approximation formulas for some elementary functions", journal = "Comment. Math. Univ. St. Paul.", volume = "12", pages = "23--35", year = "1964", CODEN = "COMAAC", ISSN = "0010-258X", MRclass = "65.25", MRnumber = "28 \#5552", MRreviewer = "John Todd", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Wengert:1964:SAD, author = "R. E. Wengert", title = "A simple automatic derivative evaluation program", journal = j-CACM, volume = "7", number = "8", pages = "463--464", year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz", abstract = "A procedure for automatic evaluation of total and partial derivatives of arbitrary algebraic functions is presented. The numerical values of derivatives are computed without developing analytic expressions for the derivatives. The function is decomposed into a sequence of elementary expressions A library is provided for differentiating of elementary functions.", acknowledgement = ack-nhfb, keywords = "point algorithm; differentiation arithmetic; computer program.", referred = "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a]; [Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a]; [Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a]; [Wilk64a].", } @Article{Kazangapov:1965:REF, author = "A. N. Kazangapov", title = "Representation of elementary function in the system of residual classes. ({Russian})", journal = "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk", volume = "3", pages = "79--84", year = "1965", MRclass = "65.25", MRnumber = "33 \#5090", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Book{Lyusternik:1965:HCE, author = "L. A. Lyusternik and O. A. Chervonenkis and A. R. Yanpol'skii", title = "Handbook for Computing Elementary Functions", volume = "76", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "xiii + 251", year = "1965", LCCN = "QA221.L513", MRclass = "65.25", MRnumber = "32 \#584", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", note = "Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.", series = "International series of monographs on pure and applied mathematics", acknowledgement = ack-nhfb, } @Article{Maklovic:1965:IIC, author = "S. T. Maklovi{\v{c}}", title = "Investigation of integrals containing {Bessel} and elementary functions. ({Russian})", journal = "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.", volume = "82", pages = "75--81", year = "1965", MRclass = "33.25", MRnumber = "34 \#387", MRreviewer = "H. A. Lauwerier", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Medhurst:1965:EI, author = "R. G. Medhurst and J. H. Roberts", title = "Evaluation of the Integral ${I}_n(b) = \frac{2}{\pi} \int^\infty_0 \bigg(\frac{\sin x}{x}\bigg)^n \cos (bx) dx$", journal = j-MATH-COMPUT, volume = "19", number = "89", pages = "113--117", month = apr, year = "1965", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Filippi:1966:BEE, author = "S. Filippi", title = "{Die Berechnung einiger elementarer transzendenter Funktionen mit Hilfe des Richardson-Algorithmus} \toenglish {The Computation of Some Elementary Transcendental Functions by Means of the {Richardson} Algorithm} \endtoenglish", journal = j-COMPUTING, volume = "1", number = "??", pages = "127--132", month = "????", year = "1966", CODEN = "CMPTA2", ISSN = "0010-485X", bibdate = "Fri Sep 16 16:30:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Glasser:1966:ESI, author = "M. L. Glasser", title = "Evaluation of Some Integrals Involving the $\psi$-Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "94", pages = "332--333", month = apr, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Jurimae:1966:KFT, author = "E. J{\"u}rim{\"a}e", title = "Kompleksmuutuja funktsioonide teooria. {I}: Elementaarsed funktsioonid. ({Estonian}) [Theory of functions of a complex variable. {I}: Elementary functions]", publisher = "Tartu Riiklik {\"U}likool", address = "Tartu, Estonia", pages = "131", year = "1966", MRclass = "30.00", MRnumber = "40 \#5827a", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Kogbetliantz:1966:GEF, author = "E. G. Kogbetliantz", title = "Generation of Elementary Functions", crossref = "Ralston:1960:MMD", pages = "7--35", year = "1966", bibdate = "Sat Dec 09 14:09:27 1995", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @TechReport{Kuki:1966:CAE, author = "H. Kuki", title = "Comments on the {ANL} Evaluation of the {OS\slash 360 FORTRAN} Math Function Library", type = "????", number = "SSD 169, C4773", institution = "SHARE Secretary Distribution", address = "????", pages = "47--53", year = "1966", bibdate = "Wed Feb 14 19:13:50 2007", acknowledgement = ack-nhfb, } @Article{Takenaga:1966:EIG, author = "Roy Takenaga", title = "On the Evaluation of the Incomplete Gamma Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "96", pages = "606--610", month = oct, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Thompson:1966:ESI, author = "Rory Thompson", title = "Evaluation of ${I}_n(b) = 2\pi^{-1} \int^\infty_0 \big(\frac{sin x}{x}\big) ^n \cos (bx) dx$ and of Similar Integrals (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "94", pages = "330--332", month = apr, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Cody:1967:CAN, author = "W. J. Cody and K. E. Hillstrom", title = "{Chebyshev} Approximations for the Natural Logarithm of the Gamma Function", journal = j-MATH-COMPUT, volume = "21", number = "98", pages = "198--203", month = apr, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Fettis:1967:MCI, author = "Henry E. Fettis", title = "More on the Calculation of the Integral ${I}_n(b) = \frac{2}{\pi}\int^\infty_0\big(\frac{\sin x}{x}\big)^n \cos bx dx$ (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "21", number = "100", pages = "727--730", month = oct, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Moody:1967:ADF, author = "William T. Moody", title = "Approximations for the Psi (Digamma) Function (in Technical Notes and Short Notices)", journal = j-MATH-COMPUT, volume = "21", number = "97", pages = "112--112", month = jan, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Fike:1968:CEM, author = "C. T. Fike", title = "Computer Evaluation of Mathematical Functions", publisher = pub-PH, address = pub-PH:adr, pages = "xii + 227", year = "1968", LCCN = "QA297 .F5", bibdate = "Thu Sep 1 10:12:51 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", acknowledgement = ack-nj, } @Article{Galant:1968:HAG, author = "D. C. Galant and P. F. Byrd", title = "High Accuracy Gamma Function Values for Some Rational Arguments (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "22", number = "104", pages = "885--887", month = oct, year = "1968", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Book{Hart:1968:CAa, author = "John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall", title = "Computer Approximations", publisher = pub-REK, address = pub-REK:adr, pages = "x + 343", year = "1968", ISBN = "0-88275-642-7", ISBN-13 = "978-0-88275-642-4", LCCN = "QA 297 C64 1978", bibdate = "Tue Dec 14 22:55:11 1993", note = "Reprinted 1978 with corrections.", acknowledgement = ack-nhfb, } @Book{Hart:1968:CAb, author = "John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall", title = "Computer Approximations", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "x + 343", year = "1968", ISBN = "0-471-35630-1", ISBN-13 = "978-0-471-35630-1", LCCN = "????", bibdate = "Sat Jan 14 14:53:06 2006", acknowledgement = ack-nhfb, } @Article{Nagashima:1968:EFN, author = "Takashi Nagashima", title = "On elementary functions of natural numbers", journal = "Hitotsubashi J. Arts Sci.", volume = "9", pages = "50--58", year = "1968", ISSN = "0073-2788", MRclass = "02.72", MRnumber = "MR0232678 (38 \#1001)", MRreviewer = "R. L. Goodstein", fjournal = "Hitotsubashi Journal of Arts \& Sciences", } @Article{Richardson:1968:SUP, author = "Daniel Richardson", title = "Some Undecidable Problems Involving Elementary Functions of a Real Variable", journal = j-J-SYMBOLIC-LOGIC, volume = "33", number = "4", pages = "514--520", month = dec, year = "1968", CODEN = "JSYLA6", ISSN = "0022-4812", MRclass = "02.75", MRnumber = "39 #1330", bibdate = "Mon May 19 13:04:20 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz", acknowledgement = ack-nhfb, } @Article{Wrench:1968:CTS, author = "John W. {Wrench, Jr.}", title = "Concerning Two Series for the Gamma Function", journal = j-MATH-COMPUT, volume = "22", number = "103", pages = "617--626", month = jul, year = "1968", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Carlson:1969:CBE, author = "B. C. Carlson", title = "A connection between elementary functions and higher transcendental functions", journal = j-SIAM-J-APPL-MATH, volume = "17", pages = "116--148", year = "1969", CODEN = "SMJMAP", ISSN = "0036-1399", MRclass = "33.20 (30.00)", MRnumber = "40 \#408", MRreviewer = "S. K. Bose", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Clark:1969:SCE, author = "N. W. Clark and W. J. Cody", title = "Self-contained exponentiation", crossref = "AFIPS:1969:ACPb", pages = "701--706", year = "1969", bibdate = "Wed Sep 07 10:49:33 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt, ftp://ftp.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib", acknowledgement = ack-nj, } @Article{Herman:1969:NHE, author = "G. T. Herman", title = "A new hierarchy of elementary functions", journal = j-PROC-AM-MATH-SOC, volume = "20", pages = "557--562", year = "1969", CODEN = "PAMYAR", ISSN = "0002-9939", MRclass = "02.77", MRnumber = "40 \#4110", MRreviewer = "G. E. Sacks", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Lewis:1969:FII, author = "Richard L. Lewis", title = "On Finite Integrals Involving Trigonometric, {Bessel}, and {Legendre} Functions", journal = j-MATH-COMPUT, volume = "23", number = "106", pages = "259--273", month = apr, year = "1969", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InProceedings{Tesler:1969:AEF, author = "G. S. Tesler", booktitle = "Mathematical provisioning of electronic digital computers and effective organization of the computing process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2", title = "The approximation of elementary functions by means of polynomials of degree zero and one. ({Russian})", publisher = "Akad. Nauk Ukrain. SSR", address = "Kiev, USSR", pages = "75--88", year = "1969", MRclass = "65D15", MRnumber = "45 \#4600", MRreviewer = "I. Selihova", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Turner:1969:DSC, author = "L. R. Turner", title = "Difficulty in {\tt sin}/{\tt cos} Routine", journal = j-SIGNUM, volume = "4", number = "3", pages = "13--13", year = "1969", CODEN = "SNEWD6", ISSN = "0163-5778", bibdate = "Thu Feb 15 15:23:23 2007", acknowledgement = ack-nhfb, } @TechReport{DeLugish:1970:CAA, author = "Bruce Gene DeLugish", title = "A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer", number = "399", institution = "Department of Computer Science, University of Illinois at Urbana-Champaign", address = "Urbana, Illinois", pages = "191", year = "1970", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz", acknowledgement = ack-nhfb, } @Article{Kolbig:1970:CZI, author = "K. S. Kolbig", title = "Complex Zeros of an Incomplete {Riemann} Zeta Function and of the Incomplete Gamma Function", journal = j-MATH-COMPUT, volume = "24", number = "111", pages = "679--696", month = jul, year = "1970", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @TechReport{Lugish:1970:CAA, author = "B. G. de Lugish", title = "A Class of Algorithms for Automatic Evaluation of Certain Elementary Function in a Binary Computer", type = "Report", number = "399", institution = "Department of Computer Science, University of Illinois", pages = "????", month = jun, year = "1970", bibdate = "Fri Sep 02 22:49:20 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Ninomiya:1970:BRS, author = "Ichizo Ninomiya", title = "Best Rational Starting Approximations and Improved {Newton} Iteration for the Square Root", journal = j-MATH-COMPUT, volume = "24", number = "110", pages = "391--404", month = apr, year = "1970", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb # " and " # ack-nj, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Nagoya Univ., Chikua ku, Japan", keywords = "computing procedure; function approximation; iterative methods; Newton iteration; rational approximation; square root", treatment = "T Theoretical or Mathematical", } @TechReport{Rothmaier:1970:DSB, author = "B. Rothmaier", title = "{Dokumentation der Standardfunktionen des Betriebssystems {Hydra X8}} \toenglish {Documentation} of the Elementary Functions of the Operating System {Hydra X8} \endtoenglish", type = "Interner {Bericht}", number = "Nr. 70/8", institution = "Institut f{\"u}r Informatik, Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1970", bibdate = "Fri Jun 11 12:37:53 1999", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Bohan:1971:ADC, author = "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov", title = "The analytic definition of certain elementary functions. ({Russian}) Questions of modern mathematics and methods of teaching it at institutions of higher learning", journal = "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.", volume = "404", pages = "59--78", year = "1971", MRclass = "26A09", MRnumber = "55 \#10612", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InCollection{Cody:1971:SEF, author = "W. J. Cody", title = "Software for the Elementary Functions", crossref = "Rice:1971:MS", pages = "171--186", year = "1971", bibdate = "Thu Sep 15 18:56:47 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Herman:1971:EDH, author = "G. T. Herman", title = "The equivalence of different hierarchies of elementary functions", journal = "Z. Math. Logik Grundlagen Math.", volume = "17", pages = "219--224", year = "1971", MRclass = "02.77 (68.00)", MRnumber = "44 \#6494", MRreviewer = "D. A. Clarke", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Kuki:1971:FEP, author = "H. Kuki and J. Ascoly", title = "{FORTRAN} extended-precision library", journal = j-IBM-SYS-J, volume = "10", number = "1", pages = "39--61", year = "1971", coden = "IBMSA7", ISSN = "0018-8670", bibdate = "Thu Sep 15 18:51:32 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt, ftp://ftp.math.utah.edu/pub/tex/bib/ibmsysj.bib, ftp://ftp.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nj, xxmonth = "(none)", } @InCollection{Kuki:1971:MFS, author = "H. Kuki", title = "Mathematical Function Subprograms for Basic System Libraries{}\emdash Objectives, Constraints, and Trade-Off", crossref = "Rice:1971:MS", pages = "187--199", year = "1971", bibdate = "Fri Sep 16 16:27:40 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", acknowledgement = ack-nj, } @Article{Liron:1971:ISR, author = "N. Liron", title = "Infinite Sums of Roots for a Class of Transcendental Equations and {Bessel} Functions of Order One-Half", journal = j-MATH-COMPUT, volume = "25", number = "116", pages = "769--781", month = oct, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Luke:1971:MTBa, author = "Yudell L. Luke", title = "Miniaturized Tables of {Bessel} Functions", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "323--330", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Luke:1971:MTBb, author = "Yudell L. Luke", title = "Miniaturized Tables of {Bessel} Functions, {II}", journal = j-MATH-COMPUT, volume = "25", number = "116", pages = "789--795", month = oct, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @Article{Matta:1971:UCE, author = "F. Matta and A. Reichel", title = "Uniform Computation of the Error Function and Other Related Functions", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "339--344", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @PhdThesis{Rothmaier:1971:BEF, author = "B. Rothmaier", title = "{Die Berechnung der elementaren Funktionen mit beliebiger Genauigkeit} \toenglish {The Computation of Elementary Functions with Arbitrary Accuracy} \endtoenglish", type = "Dissertation", school = "Universit{\"a}t Karlsruhe", address = "Karlsruhe, Germany", pages = "????", year = "1971", bibdate = "Fri Sep 16 16:30:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Spellucci:1971:DPA, author = "P. Spellucci", title = "Double precision approximations to the elementary functions using {Jacobi-fractions}", journal = j-NUM-MATH, volume = "18", pages = "127--143", year = "1971/1972", CODEN = "NUMMA7", ISSN = "0029-599X", MRclass = "65D20", MRnumber = "45 \#7938", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Spira:1971:CGF, author = "Robert Spira", title = "Calculation of the Gamma Function by {Stirling}'s Formula", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "317--322", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, } @InProceedings{Walther:1971:UAE, author = "J. S. Walther", title = "A unified algorithm for elementary functions", crossref = "AFIPS:1971:ACP", volume = "38", pages = "379--385", year = "1971", bibdate = "Thu Sep 1 10:15:31 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Book{Bark:1972:MTF, author = "L. S. Bark", title = "{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh funktsi{\u{\i}}} (${\rm sin} x$, ${\rm cos} x$, $e^{x}$ {\cyr i} $e^{-x}$). ({Russian}) [Multiplace tables of the elementary functions (${\rm sin}\ x$, ${\rm cos}\ x$, $e^{x}$ and $e^{-x}$)]", publisher = "Vy{\v{c}}isl. Centr Akad. Nauk SSSR", address = "Moscow, USSR", edition = "Second, unrevised", pages = "134", year = "1972", MRclass = "65A05", MRnumber = "50 \#6100", bibdate = "Sat Jan 11 17:44:01 MST 1997", note = "Tables processed and text translated from the English by L. S. Bark. Library of Mathematical Tables, No. 9. 1972", acknowledgement = ack-nhfb, } @Article{Carlson:1972:ACL, author = "B. C. Carlson", title = "An algorithm for computing logarithms and arctangents", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "543--549", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Iowa State Univ., Ames, IA, USA", keywords = "acceleration; arctangents; auxiliary; Borchardt's algorithm; convergence; fast; function approximation; functions; inverse circular functions; inverse hyperbolic; iterative algorithm; logarithms; numerical methods; rational operations; recurrence relation; square roots", treatment = "T Theoretical or Mathematical", } @Article{Chen:1972:ACE, author = "Tien Chi Chen", title = "Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots", journal = j-IBM-JRD, volume = "16", number = "4", pages = "380--388", month = jul, year = "1972", CODEN = "IBMJAE", ISSN = "0018-8646", MRclass = "65D20", MRnumber = "49 \#1738", bibdate = "Tue Mar 25 14:26:59 MST 1997", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip", URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf", abstract = "It is shown how a relatively simple device can evaluate exponentials, logarithms, ratios and square roots for fraction arguments, employing only shifts, adds, high-speed table lookups, and bit counting. The scheme is based on the cotransformation of a number pair $(x, y)$ such that the $F(x, y) = f(x_0)$ is invariant; when $x$ is driven towards a known value $x_w$, $y$ is driven towards the result. For an $N$-bit fraction about $N / 4$ iterations are required, each involving two or three adds; then a termination algorithm, based on an add and an abbreviated multiply, completes the process, for a total cost of about one conventional multiply time. Convergence, errors and simulation using APL are discussed.", acknowledgement = ack-nhfb # " and " # ack-nj, classcodes = "C5230 (Digital arithmetic methods)", corpsource = "IBM, San Jose, CA, USA", keywords = "adds; APL; bit counting; convergence; cotransformation; digital arithmetic; errors; exponentials; high speed table; iteration; logarithms; lookups; ratios; shifts; simulation; square roots; termination algorithm", reviewer = "F. Gotze", treatment = "P Practical", } @TechReport{Ercegovac:1972:RES, author = "Milos D. Ercegovac", title = "Radix 16 Evaluation of Some Elementary Functions", number = "540", institution = "Department of Computer Science, University of Illinois at Urbana-Champaign", address = "Urbana, Illinois", pages = "30", year = "1972", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz", acknowledgement = ack-nhfb, } @Article{Hunter:1972:NEC, author = "D. B. Hunter and T. Regan", title = "A note on the evaluation of the complementary error function", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "539--541", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4160 (Numerical integration and differentiation)", corpsource = "Univ. Bradford, UK", keywords = "complementary error function; complex variable; evaluation; integration; method of Matta and Reichel; modification; numerical; stability", treatment = "T Theoretical or Mathematical", } @Article{Kolbig:1972:ZIG, author = "K. S. Kolbig", title = "On the Zeros of the Incomplete Gamma Function", journal = j-MATH-COMPUT, volume = "26", number = "119", pages = "751--755", month = jul, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "CERN, Geneva, Switzerland", keywords = "asymptotic formulae; complex w plane; function approximation; incomplete gamma function; poles and zeros; zeros", treatment = "T Theoretical or Mathematical", } @Article{Ling:1972:EM, author = "Chih-Bing Ling and Jung Lin", title = "On Evaluation of Moments of ${K}_\nu(t)/{I}_\nu(t)$", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "529--537", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4190 (Other numerical methods)", corpsource = "Virginia Politech. Inst., Blacksburg, VA, USA", keywords = "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t); numerical methods; Watson's method", treatment = "T Theoretical or Mathematical", } @Article{Linz:1972:MCB, author = "Peter Linz", title = "A Method for Computing {Bessel} Function Integrals", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "509--513", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4160 (Numerical integration and differentiation)", corpsource = "Univ. California, Davis, CA, USA", keywords = "Abel; Bessel function integrals; Fourier integrals; infinite integrals; integration; numerical computation; transform", treatment = "T Theoretical or Mathematical", } @Article{Luke:1972:MTB, author = "Yudell L. Luke", title = "Miniaturized Tables of {Bessel} Functions. {III}", journal = j-MATH-COMPUT, volume = "26", number = "117", pages = "237--240", month = jan, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4190 (Other numerical methods)", corpsource = "Univ. Missouri, Kansas City, KS, USA", keywords = "Bessel functions; miniaturized tables; numerical methods", treatment = "T Theoretical or Mathematical", } @Article{MacKinnon:1972:AEH, author = "Robert F. MacKinnon", title = "The asymptotic expansions of {Hankel} transforms and related integrals", journal = j-MATH-COMPUT, volume = "26", number = "118", pages = "515--527", month = apr, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0230 (Integral transforms); C1130 (Integral transforms)", corpsource = "Defence Res. Establ., Pacific, Victoria, BC, Canada", keywords = "asymptotic expansions; Bessel; functions; Hankel transforms; integrals; transforms", treatment = "T Theoretical or Mathematical", } @TechReport{Manos:1972:CCA, author = "Paul Manos and L. Richard Turner", title = "Constrained {Chebyshev} approximations to some elementary functions suitable for evaluation with floating-point arithmetic", type = "{NASA} Technical Note", number = "TN D-6698", institution = "NASA", address = "Washington, DC, USA", pages = "iii + 68", month = mar, year = "1972", bibdate = "Mon May 22 11:27:24 2006", URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf", acknowledgement = ack-nhfb, } @Article{Marino:1972:NAA, author = "D. Marino", title = "New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions", journal = j-IEEE-TRANS-COMPUT, volume = "21", number = "12", pages = "1416--1421", month = dec, year = "1972", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Thu Sep 08 08:05:51 1994", acknowledgement = ack-nj, } @Article{Olver:1972:NBR, author = "F. W. J. Olver and D. J. Sookne", title = "Note on Backward Recurrence Algorithms", journal = j-MATH-COMPUT, volume = "26", number = "120", pages = "941--947", month = oct, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290Z (Other numerical methods); C4190 (Other numerical methods)", corpsource = "Univ. Maryland, College Park, MD, USA", keywords = "backward recurrence algorithms; Bessel; Bessel functions; difference equations; functions; recessive solution; second order linear difference equation", treatment = "T Theoretical or Mathematical", } @Article{Parnes:1972:CZM, author = "R. Parnes", title = "Complex zeros of the modified {Bessel} function {$K_n(Z)$}", journal = j-MATH-COMPUT, volume = "26", number = "120", pages = "949--953", month = oct, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "City Univ., New York, NY, USA", keywords = "and zeros; Bessel functions; complex zeros; interpolation; interpolation scheme; iterative; iterative methods; modified Bessel function; poles", treatment = "T Theoretical or Mathematical", } @Article{Turunov:1972:EFD, author = "M. Turunov", title = "Elementary functions of a discrete real and complex argument. ({Russian})", journal = "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy", volume = "418 Voprosy Mat.", pages = "263--271, 386", year = "1972", MRclass = "30A95", MRnumber = "50 \#13556", MRreviewer = "G. Berzsenyi", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Baker:1973:PAS, author = "P. W. Baker", title = "Predictive algorithms for some elementary functions in radix $2$", journal = j-ELECT-LETTERS, volume = "9", pages = "493--494", year = "1973", CODEN = "ELLEAK", ISBN = "0013-5194", ISBN-13 = "0013-5194", ISSN = "0013-5194", MRclass = "68A10", MRnumber = "57 \#18203", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Cody:1973:CAP, author = "W. J. Cody and Anthony J. Strecok and Henry C. {Thacher, Jr.}", title = "{Chebyshev} Approximations for the Psi Function", journal = j-MATH-COMPUT, volume = "27", number = "121", pages = "123--127", month = jan, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", MRclass = "65-06 (68-06)", MRnumber = "50 6095", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Argonne Nat. Lab., IL, USA", keywords = "Chebyshev approximation; Chebyshev approximations; digamma function; psi function", treatment = "T Theoretical or Mathematical", } @Article{Ercegovac:1973:REC, author = "M. D. Ercegovac", title = "Radix-16 Evaluation of Certain Elementary Functions", journal = j-IEEE-TRANS-COMPUT, volume = "C-22", number = "6", pages = "561--566", month = jun, year = "1973", CODEN = "ITCOB4", ISSN = "0018-9340", bibdate = "Thu Sep 1 10:15:39 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Fettis:1973:CZE, author = "Henry E. Fettis and James C. Caslin and Kenneth R. Cramer", title = "Complex zeros of the error function and of the complementary error function", journal = j-MATH-COMPUT, volume = "27", number = "122", pages = "401--407", month = apr, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Wright-Patterson Air Force Base, OH, USA", keywords = "asymptotic formula; complementary error function; complex zeros; error function; errors; first one hundred zeros; function evaluation; poles and zeros", treatment = "T Theoretical or Mathematical", } @Article{Fettis:1973:SPC, author = "Henry E. Fettis and James C. Caslin and Kenneth R. Cramer", title = "Saddle Points of the Complementary Error Function", journal = j-MATH-COMPUT, volume = "27", number = "122", pages = "409--412", month = apr, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Sandia Labs., Albuquerque, NM, USA", keywords = "asymptotic; complementary error function; errors; formula; function evaluation; poles and zeros; saddle points", treatment = "T Theoretical or Mathematical", } @TechReport{Hemker:1973:SDL, author = "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen} and H. L. Oudshoorn and D. T. Winter", title = "Single- and double-length computation of elementary functions", number = "NW 7", institution = "Mathematical Centre", address = "Amsterdam", year = "1973", bibdate = "Mon May 19 13:30:58 1997", bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib", acknowledgement = ack-nhfb, } @Article{Linz:1973:NCI, author = "Peter Linz and T. E. Kropp", title = "A note on the computation of integrals involving products of trigonometric and {Bessel} functions", journal = j-MATH-COMPUT, volume = "27", number = "124", pages = "871--872", month = oct, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Univ. California, Davies, CA, USA", keywords = "Bessel functions; computation; integration; numerical; numerical methods; products; trigonometric", treatment = "T Theoretical or Mathematical", } @Article{Lozier:1973:BCP, author = "D. W. Lozier and L. C. Maximon and W. L. Sadowski", title = "A bit comparison program for algorithm testing", journal = j-COMP-J, volume = "16", number = "2", pages = "111--117", month = may, year = "1973", CODEN = "CMPJA6", ISSN = "0010-4620", bibdate = "Fri Sep 29 08:52:11 MDT 2000", bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif", acknowledgement = ack-nhfb, classcodes = "C6150G (Diagnostic, testing, debugging and evaluating systems)", corpsource = "Nat. Bur. Stand., Washington, DC, USA", keywords = "accuracy; algorithm testing; bit comparison program; computer algorithms; program debugging", treatment = "P Practical", } @Article{McNolty:1973:SPD, author = "Frank McNolty", title = "Some probability density functions and their characteristic functions", journal = j-MATH-COMPUT, volume = "27", number = "123", pages = "495--504", month = jul, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0240 (Probability and statistics); C1140 (Probability and statistics)", corpsource = "Lockheed Palo Alto Res. Lab., CA, USA", keywords = "Bessel function; characteristic functions; functions; hypergeometric function; probability; probability density functions", treatment = "T Theoretical or Mathematical", } @Article{Amos:1974:CMB, author = "D. E. Amos", title = "Computation of modified {Bessel} functions and their ratios", journal = j-MATH-COMPUT, volume = "28", number = "125", pages = "239--251", month = jan, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Sandia Labs., Albuquerque, NM, USA", keywords = "Bessel functions; computation; low order Bessel functions; modified Bessel functions; monotonicity; properties; ratios; recursion; relation", treatment = "T Theoretical or Mathematical", } @Article{Blair:1974:RCA, author = "J. M. Blair", title = "Rational {Chebyshev} approximations for the modified {Bessel} functions {$I_0(x)$} and {$I_1(x)$}", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "581--583", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Atomic Energy Canada Ltd., Chalk River, Ont., Canada", keywords = "Chebyshev approximation; functions; modified Bessel; nearly best rational approximations; rational Chebyshev approximations; series (mathematics)", treatment = "T Theoretical or Mathematical", } @Article{Buschman:1974:FSR, author = "R. G. Buschman", title = "Finite sum representations for partial derivatives of special functions with respect to parameters", journal = j-MATH-COMPUT, volume = "28", number = "127", pages = "817--824", month = jul, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Univ. Wyoming, Laramie, WY, USA", keywords = "Bessel functions; differentiation; finite sum representations; finite sums; functions; G function; Gegenbauer functions; hypergeometric; Legendre; Mellin transformation; partial derivatives; special functions; Whittaker functions", treatment = "T Theoretical or Mathematical", } @Article{Fettis:1974:SAC, author = "Henry E. Fettis", title = "A stable algorithm for computing the inverse error function in the `tail-end' region", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "585--587", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Wright-Patterson Air Force Base, OH, USA", keywords = "function evaluation; inverse error function; iterative algorithm; stability; stable algorithm; tail end region", treatment = "T Theoretical or Mathematical", } @Article{Glasser:1974:SDI, author = "M. L. Glasser", title = "Some definite integrals of the product of two {Bessel} functions of the second kind: (order zero)", journal = j-MATH-COMPUT, volume = "28", number = "126", pages = "613--615", month = apr, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Battelle Memorial Inst., Columbus, OH, USA", keywords = "Bessel functions; definite integrals; evaluate; function evaluation; integral representation; order; second kind; zero", treatment = "T Theoretical or Mathematical", } @Article{Nasell:1974:IMB, author = "Ingemar Nasell", title = "Inequalities for Modified {Bessel} Functions", journal = j-MATH-COMPUT, volume = "28", number = "125", pages = "253--256", month = jan, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290D (Functional analysis); C4120 (Functional analysis)", corpsource = "Bell Labs., Holmdel, NJ, USA", keywords = "Bessel functions; inequalities; modified Bessel functions; sharp versions", treatment = "T Theoretical or Mathematical", } @Article{Pisarskii:1974:QCD, author = "A. V. Pisarski{{\u{\i}}} and A. F. Kurgaev and A. V. Palagin", title = "On the question of the convergence of the {``digit by digit''} methods of computing the elementary functions", journal = "Kibernetika (Kiev)", volume = "4", pages = "147--149", year = "1974", CODEN = "KBRNA5", ISSN = "0023-1274", MRclass = "65D20", MRnumber = "53 \#1915", MRreviewer = "V. V. Ivanov", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Wang:1974:UEZ, author = "Paul S. Wang", title = "The Undecidability of the Existence of Zeros of Real Elementary Functions", journal = j-J-ACM, volume = "21", number = "4", pages = "586--589", month = oct, year = "1974", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database, ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib", abstract = "From Richardson's undecidability results, it is shown that the predicate ``there exists a real number such that G(r) equals 0'' is recursively undecidable for G(x) in a class of functions which involves polynomials and the sine function. The deduction follows that the convergence of a class of improper integrals is recursively undecidable.", acknowledgement = ack-nhfb, classification = "921", journalabr = "J Assoc Comput Mach", keywords = "mathematical techniques", } @Article{Baker:1975:MER, author = "P. W. Baker", title = "More efficient radix-$2$ algorithms for some elementary functions", journal = j-IEEE-TRANS-COMPUT, volume = "C-24", number = "11", pages = "1049--1054", month = nov, year = "1975", CODEN = "ITCOB4", ISSN = "0018-9340", MRclass = "68A10", MRnumber = "52 \#7193", MRreviewer = "I. Kaufmann", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb, } @TechReport{Brent:1975:MZM, author = "R. P. (Richard P.) Brent", title = "Multiple-precision zero-finding methods and the complexity of elementary function evaluation", institution = "Department of Computer Science, Carnegie-Mellon University", address = "Pittsburgh, PA, USA", pages = "26", year = "1975", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, keywords = "Iterative methods (Mathematics)", searchkey = "ti:elementary n1 function", } @Article{Carta:1975:LOA, author = "David G. Carta", title = "Low-Order Approximations for the Normal Probability Integral and the Error Function", journal = j-MATH-COMPUT, volume = "29", number = "131", pages = "856--862", month = jul, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0260 (Optimisation techniques); B0290R (Integral equations); C1180 (Optimisation techniques); C4180 (Integral equations)", corpsource = "Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA", keywords = "error function; fraction; integral equations; linear minimax problems; linear programming; low; normal probability integral; order approximations; polynomials; rational", treatment = "T Theoretical or Mathematical", } @PhdThesis{Epstein:1975:AET, author = "Harvey Irwin Epstein", title = "Algorithms for elementary transcendental function arithmetic", school = "University of Wisconsin", address = "Madison, WI, USA", pages = "409", year = "1975", bibdate = "Sat Jan 11 10:14:06 MST 1997", acknowledgement = ack-nhfb, annote = "Typescript. Vita. Thesis (Ph. D.)--University of Wisconsin--Madison, 1975.", keywords = "Functions, Transcendental.; Algorithms.; Functions -- Data processing.", searchkey = "ti:elementary n1 function", } @Article{Headley:1975:DZG, author = "V. B. Headley and V. K. Barwell", title = "On the distribution of the zeros of generalized {Airy} functions", journal = j-MATH-COMPUT, volume = "29", number = "131", pages = "863--877", month = jul, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290P (Differential equations); C4170 (Differential equations)", corpsource = "Dept. of Math., Brock Univ., St. Catherines, Ont., Canada", keywords = "Bessel functions; boundary rays; differential equations; generalized Airy functions; nonreal zeros; zeros distribution", treatment = "T Theoretical or Mathematical", } @InProceedings{Hitotumatu:1975:SRU, author = "Sin Hitotumatu", title = "Some remarks on the unified treatment of elementary functions by microprogramming", crossref = "Miller:1975:TNA", pages = "51--56 (vol. 2)", year = "1975", MRclass = "65D15", MRnumber = "54 \#11733", MRreviewer = "Luciano Biasini", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Ikebe:1975:ZRC, author = "Yasuhiko Ikebe", title = "The Zeros of Regular {Coulomb} Wave Functions and of Their Derivatives", journal = j-MATH-COMPUT, volume = "29", number = "131", pages = "878--887", month = jul, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Centre Numerical Analysis, Univ. of Texas, Austin, TX, USA", keywords = "Bessel function; compact matrix; eigenvalues; eigenvalues and eigenfunctions; function zeros characterisation; matrix algebra; methods; numerical; operators; regular Coulomb wave functions; wave functions; zeros", treatment = "T Theoretical or Mathematical", } @Article{Temme:1975:UAE, author = "N. M. Temme", title = "Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function", journal = j-MATH-COMPUT, volume = "29", number = "132", pages = "1109--1114", month = oct, year = "1975", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Appl. Math., Amsterdam, Netherlands", keywords = "asymptotic expansions; asymptotic series; complementary error function; function approximation; incomplete beta function; incomplete gamma functions; uniform", treatment = "T Theoretical or Mathematical", } @TechReport{Warner:1975:PDG, author = "D. D. Warner", title = "A partial derivative generator", type = "Computing Science Technical Report", number = "28", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", year = "1975", bibdate = "Mon May 19 13:30:58 1997", bibsource = "Theory/auto.diff.bib", abstract = "A precompiler is described which takes a specification of a function as input and produces a Fortran subroutine which will evaluate the component functions and the corresponding Jacobian. Many of the Fortran elementary functions are provided, as well as a facility which allows the user to specify their own differentiation rules.", acknowledgement = ack-nhfb, keywords = "differentiation arithmetic; precompiler.", referred = "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].", } @Article{Blair:1976:RCA, author = "J. M. Blair and C. A. Edwards and J. H. Johnson", title = "Rational {Chebyshev} approximations for the inverse of the error function", journal = j-MATH-COMPUT, volume = "30", number = "136", pages = "827--830", month = oct, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", corpsource = "Atomic Energy of Canada Ltd., Chalk River Nuclear Lab., Chalk River, Ont., Canada", keywords = "Chebyshev approximation; Chebyshev approximations; error function; inverse; rational", treatment = "T Theoretical or Mathematical", } @Article{Brent:1976:FMP, author = "Richard P. Brent", title = "Fast Multiple-Precision Evaluation of Elementary Functions", journal = j-J-ACM, volume = "23", number = "2", pages = "242--251", month = apr, year = "1976", CODEN = "JACOAH", DOI = "http://doi.acm.org/10.1145/321941.321944", ISSN = "0004-5411", MRclass = "68A20 (68A10)", MRnumber = "52 \#16111", MRreviewer = "Amnon Barak", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", abstract = "Let $f(x)$ be one of the usual elementary functions ($\exp$, $\log$, $\artan$, $\sin$, $\cosh$, etc.), and let $M(n)$ be the number of single-precision operations required to multiply $n$-bit integers. It is shown that $f(x)$ can be evaluated, with relative error $O(2-n)$, in $O(M(n)log (n))$ operations as $n \rightarrow \infty$, for any floating-point number $x$ (with an $n$-bit fraction) in a suitable finite interval. From the Sch{\"o}nhage--Strassen bound on $M(n)$, it follows that an $n$-bit approximation to $f(x)$ may be evaluated in $O(n \log_(n) \log \log(n))$ operations. Special cases include the evaluation of constants such as $\pi$ $e$, and $e^\pi$. The algorithms depend on the theory of elliptic integrals, using the arithmetic-geometric mean iteration and ascending Landen transformations.", acknowledgement = ack-nhfb, classification = "723", journalabr = "J Assoc Comput Mach", keywords = "computational complexity; computer arithmetic; computer programming", } @InProceedings{Brent:1976:MPZ, author = "Richard P. Brent", title = "Multiple-precision zero-finding methods and the complexity of elementary function evaluation", crossref = "Traub:1976:ACC", pages = "151--176", year = "1976", MRclass = "68A20", MRnumber = "54 \#11843", MRreviewer = "Claus-Peter Schnorr", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Buschman:1976:IHF, author = "R. G. Buschman", title = "Inequalities for Hypergeometric Functions", journal = j-MATH-COMPUT, volume = "30", number = "134", pages = "303--305", month = apr, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", corpsource = "Dept. of Math. and Statistics, Univ. of Guelph, Guelph, Ont., Canada", keywords = "Bessel functions; classical orthogonal polynomials; confluence; dominant diagonal matrix; function; functions; Gauss' hypergeometric; hypergeometric functions; Kummer's hypergeometric function; modified Bessel function; principle", treatment = "T Theoretical or Mathematical", } @Article{Fettis:1976:CR, author = "Henry E. Fettis", title = "Complex Roots of $\sin z = az, \cos z = az$, and $\cosh z = az$", journal = j-MATH-COMPUT, volume = "30", number = "135", pages = "541--545", month = jul, year = "1976", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0220 (Mathematical analysis); C1120 (Mathematical analysis)", keywords = "complex roots; cos z=az; cosh z=az; functional equations; sin z=az", treatment = "T Theoretical or Mathematical", } @Article{Kononova:1976:CEF, author = "N. F. Kononova", title = "The computation of elementary functions by means of polynomial approximations by the method of {V. K. Dzjadik}. ({Russian})", journal = "Vy{\v{c}}isl. Prikl. Mat. (Kiev)", volume = "29", pages = "27--39", year = "1976", ISSN = "0321-4117", MRclass = "151. 65D15", MRnumber = "57 \#18026", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Paul:1976:SEF, author = "George Paul and M. Wayne Wilson", title = "Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?", journal = j-TOMS, volume = "2", number = "2", pages = "132--142", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", acknowledgement = ack-nhfb, } @InCollection{Salimov:1976:OCE, author = "F. I. Salimov", booktitle = "Probabilistic methods and cybernetics", title = "The organization of calculations of elementary functions into tables. ({Russian})", volume = "12--13", publisher = "Kazan. Univ.,", address = "Kazan, USSR", pages = "77--90", year = "1976", MRclass = "65A05", MRnumber = "58 \#31706", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Siemieniuch:1976:PCR, author = "J. L. Siemieniuch", title = "Properties of certain rational approximations to $e^{-z}$", journal = j-BIT, volume = "16", number = "2", pages = "172--191", month = jun, year = "1976", CODEN = "BITTEL, NBITAB", DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01931369", ISSN = "0006-3835 (print), 1572-9125 (electronic)", bibdate = "Wed Jan 4 18:52:14 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172", acknowledgement = ack-nhfb, keywords = "elefunt; elementary functions", } @Article{Danilcenko:1977:ETC, author = "L. S. Danil'{\v{c}}enko", title = "An efficient technique for the construction of rational approximations of elementary functions. ({Russian}) Optimization of computations (approximation and minimization of functions)", journal = "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint", volume = "18", pages = "17--21", year = "1977", MRclass = "65D15", MRnumber = "80b:65016", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{Dzjadyk:1977:TPA, author = "V. K. Dzjadyk and S. F. Karpenko", title = "Tables of polynomials for the approximate solution of elementary functions. ({Russian})", number = "28", institution = "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint", pages = "28", year = "1977", MRclass = "65A05 (65D20)", MRnumber = "58 \#19016", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @TechReport{Dzyadyk:1977:OPM, author = "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko and N. F. Kononova", title = "{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami {\`e}lementarnykh funktsi{\u{\i}}.} ({Russian}) [Efficient approximation by polynomials of elementary functions]", type = "Preprint", number = "IM-77-21", institution = "Akad. Nauk Ukrain. SSR Inst. Mat.", address = "Kiev, USSR", pages = "42", year = "1977", MRclass = "65L99", MRnumber = "57 \#11075", MRreviewer = "B. D. Donevski", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @Article{Gautschi:1977:ACC, author = "Walter Gautschi", title = "Anomalous convergence of a continued fraction for ratios of {Kummer} functions", journal = j-MATH-COMPUT, volume = "31", number = "140", pages = "994--999", month = oct, year = "1977", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Mathematical analysis); C4170 (Differential equations)", corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA", keywords = "apparent; Bessel functions; continued fraction; convergence; differential equations; gamma functions; Kummer functions; wrong limit", treatment = "T Theoretical or Mathematical", } @Article{McCarthy:1977:OAE, author = "D. P. McCarthy", title = "The optimal algorithm to evaluate $x^n$ using elementary multiplication methods", journal = j-MATH-COMP, volume = "31", number = "137", pages = "251--256", month = jan, year = "1977", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4120 (Functional analysis); C4240 (Programming and algorithm theory)", keywords = "computational complexity; function evaluation; optimal multiplication chains; symbolic algebraic manipulation", treatment = "T Theoretical or Mathematical", } @Article{Pexton:1977:RTTa, author = "Robert L. Pexton and Arno D. Steiger", title = "Roots of two transcendental equations involving spherical {Bessel} functions", journal = j-MATH-COMPUT, volume = "31", number = "139", pages = "752--753", month = jul, year = "1977", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra)", corpsource = "Univ. of California, Livermore, CA, USA", keywords = "Bessel functions; root; spherical Bessel functions; transcendental equations", treatment = "T Theoretical or Mathematical", } @Article{Andrews:1978:UEF, author = "M. Andrews and T. Mraz", title = "Unified elementary function generator", journal = j-MICROPROC-MICROSYS, volume = "2", number = "5", pages = "270--273", month = oct, year = "1978", CODEN = "MIMID5", ISSN = "0141-9331", bibdate = "Thu Sep 1 10:15:39 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Benton:1978:CZT, author = "T. C. Benton and H. D. Knoble", title = "Common Zeros of Two {Bessel} Functions", journal = j-MATH-COMPUT, volume = "32", number = "142", pages = "533--535", month = apr, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra)", corpsource = "Pennsylvania State Univ., University Park, PA, USA", keywords = "Bessel functions; common zeros; poles and zeros; positive zeros; zeros", treatment = "T Theoretical or Mathematical", } @Article{Blair:1978:RCA, author = "J. M. Blair and C. A. Edwards and J. H. Johnson", title = "Rational {Chebyshev} approximations for the {Bickley} functions {$Ki_n(x)$}", journal = j-MATH-COMPUT, volume = "32", number = "143", pages = "876--886", month = jul, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Atomic Energy of Canada Ltd., Chalk River, Ont., Canada", keywords = "approximation; Bessel functions; Bickley functions; Chebyshev approximation; Chebyshev approximations; function; recurrence; relation", treatment = "T Theoretical or Mathematical", } @Article{Chin:1978:DAD, author = "R. C. Y. Chin and G. W. Hedstrom", title = "A dispersion analysis for difference schemes: tables of generalized {Airy} functions", journal = j-MATH-COMPUT, volume = "32", number = "144", pages = "1163--1170", month = oct, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation); C4170 (Differential equations)", corpsource = "Univ. of California, Lawrence Livermore Lab., Livermore, CA, USA", keywords = "artificial viscosity; difference schemes; dispersion analysis; function approximation; functions; generalized Airy; linear hyperbolic equation", treatment = "T Theoretical or Mathematical", } @Article{DiDonato:1978:AR, author = "A. R. DiDonato", title = "An Approximation for $\int^\infty_x e^{-t^2/2} t^p dt, x > 0, p$ Real", journal = j-MATH-COMPUT, volume = "32", number = "141", pages = "271--275", month = jan, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C4160 (Numerical integration and differentiation)", corpsource = "Naval Surface Weapons Center, Dahlgren, VA, USA", keywords = "integral approximation; integration; numerical analysis", treatment = "A Application; N New Development; T Theoretical or Mathematical", } @Article{Dzjadyk:1978:CRP, author = "V. K. Dzjadyk and L. \=I. F{\'\i}lozof", title = "The convergence rate of Pad{\'e} approximants for some elementary functions. ({Russian})", journal = "Mat. Sb. (N.S.)", volume = "107(149)", number = "3", pages = "347--363, 463", year = "1978", ISSN = "0368-8666", MRclass = "41A21 (30E10 41A25)", MRnumber = "81b:41043", MRreviewer = "B. D. Donevski", bibdate = "Sat Jan 11 17:44:01 MST 1997", acknowledgement = ack-nhfb, } @InProceedings{Frankowski:1978:RME, author = "Krzysztof S. Frankowski", title = "A Realistic Model for Error Estimates in the Evaluation of Elementary Functions", crossref = "IEEE:1978:PSC", pages = "70--74", year = "1978", MRclass = "65G05 (65D20)", MRnumber = "80g:65050", bibdate = "Sat Jan 11 17:44:01 MST 1997", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nhfb, } @Article{Gautschi:1978:CMB, author = "Walter Gautschi and Josef Slavik", title = "On the computation of modified {Bessel} function ratios", journal = j-MATH-COMPUT, volume = "32", number = "143", pages = "865--875", month = jul, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", acknowledgement = ack-nhfb, classcodes = "C1120 (Mathematical analysis); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Computer Sci., Purdue Univ., Lafayette, IN, USA", keywords = "Bessel; Bessel functions; continued fraction; fraction; function approximation; functions; Gauss' continued; modified Bessel function ratios; Perron's continued fraction", treatment = "T Theoretical or Mathematical", } @InProceedings{Hull:1978:DFP, author = "T. E. Hull", title = "Desirable Floating-Point Arithmetic and Elementary Functions for Numerical Computation", crossref = "IEEE:1978:PSC", pages = "63--69", year = "1978", bibdate = "Thu Sep 01 12:14:34 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", acknowledgement = ack-nj, } @Article{Pexton:1978:RTT, author = "Robert L. Pexton and Arno D. Steiger", title = "Roots of two transcendental equations as functions of a continuous real parameter", journal = j-MATH-COMPUT, volume = "32", number = "142", pages = "511--518", month = apr, year = "1978", CODEN = "MCMPAF", ISSN = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "JSTOR database", ack