# bibtab

bibtype: article
filename: elefunt.bib
label: Proinov:1988:ISF
author: Petko D. Proinov
title: Integration of smooth functions and $ phi $-discrepancy
journal: j-J-APPROX-THEORY
volume: 52
number: 3
pages: 284--292
month: mar
monthnumber: 3
year: 1988
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
affiliation: Univ. of Plovdiv, Plovdiv, Bulgaria
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Petko D. Proinov
rawtitle: Integration of smooth functions and $ \phi $-discrepancy
entry:
@Article{Proinov:1988:ISF,
  author =       "Petko D. Proinov",
  title =        "Integration of smooth functions and $ \phi
                 $-discrepancy",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "3",
  pages =        "284--292",
  month =        mar,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Plovdiv, Plovdiv, Bulgaria",
  bibno =        "49659",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10111",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "March 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Puoskari:1988:MCB
author: M. Puoskari
title: A method for computing Bessel function integrals
journal: j-J-COMPUT-PHYS
volume: 75
number: 2
pages: 334--344
month: apr
monthnumber: 4
year: 1988
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(88)90116-7
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:40 MST 2012
bibtimestamp: 2012.01.01 15:59:40 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999188901167
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: M. Puoskari
rawtitle: A method for computing {Bessel} function integrals
entry:
@Article{Puoskari:1988:MCB,
  author =       "M. Puoskari",
  title =        "A method for computing {Bessel} function integrals",
  journal =      j-J-COMPUT-PHYS,
  volume =       "75",
  number =       "2",
  pages =        "334--344",
  month =        apr,
  year =         "1988",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(88)90116-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:40 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999188901167",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Richardson:1988:NMT
author: Daniel Richardson
title: Nonstandard models of the theory of elementary functions of a real variable
journal: j-Z-MATH-LOGIK-GRUNDL-MATH
volume: 34
number: 4
pages: 355--372
year: 1988
CODEN: ZMLGAQ
ISBN: 0044-3050 OR 00443050
ISBN13: 0044-3050 OR 00443050
ISSN: 0044-3050 OR 00443050
MRclass: 03B30 (03C62 03H15 26E35)
MRnumber: 90a:03009
MRreviewer: Reuven H. Gurevi{\v{c}}
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
fjournal: Zeitschrift fur mathematische Logik und Grundlagen der Mathematik
acknowledgement: ack-nhfb
rawauthor: Daniel Richardson
rawtitle: Nonstandard models of the theory of elementary functions of a real variable
entry:
@Article{Richardson:1988:NMT,
  author =       "Daniel Richardson",
  title =        "Nonstandard models of the theory of elementary
                 functions of a real variable",
  journal =      j-Z-MATH-LOGIK-GRUNDL-MATH,
  volume =       "34",
  number =       "4",
  pages =        "355--372",
  year =         "1988",
  CODEN =        "ZMLGAQ",
  ISBN =         "0044-3050",
  ISBN-13 =      "0044-3050",
  ISSN =         "0044-3050",
  MRclass =      "03B30 (03C62 03H15 26E35)",
  MRnumber =     "90a:03009",
  MRreviewer =   "Reuven H. Gurevi{\v{c}}",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r mathematische Logik und
                 Grundlagen der Mathematik}",
}


bibtype: article
filename: elefunt.bib
label: Ruscheweyh:1988:EST
author: Stephan Ruscheweyh
title: Extension of Szego's theorem on the sections of univalent functions
journal: j-SIAM-J-MATH-ANA
volume: 19
number: 6
pages: 1442--1449
month: nov
monthnumber: 11
year: 1988
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: Stephan Ruscheweyh
rawtitle: Extension of {Szeg{\H{o}}}'s theorem on the sections of univalent functions
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

entry:
@Article{Ruscheweyh:1988:EST,
  author =       "Stephan Ruscheweyh",
  title =        "Extension of {Szeg{\H{o}}}'s theorem on the sections
                 of univalent functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "19",
  number =       "6",
  pages =        "1442--1449",
  month =        nov,
  year =         "1988",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "58899",
  catcode =      "G.1.2; G.1.9; F.2.2; F.2.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.9 Integral Equations; G.1.9
                 Integro-differential equations; F.2.2 Nonnumerical
                 Algorithms and Problems; F.2.2 Computations on discrete
                 structures; F.2.2 Nonnumerical Algorithms and Problems;
                 F.2.2 Geometrical problems and computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  fjournal =     "SIAM Journal on Mathematical Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1988-13739",
  journal-URL =  "http://epubs.siam.org/sima",
  journalabbrev = "SIAM J. Math. Anal.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}


bibtype: article
filename: elefunt.bib
label: Schappacher:1988:EIG
author: Norbert Schappacher
title: Elliptic integrals and the gamma function
journal: j-LECT-NOTES-MATH
volume: 1301
pages: 117--127
year: 1988
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0082098
ISBN: 3-540-18915-7 (print), 3-540-38842-7 (e-book) OR 3540189157 (print), 3540388427 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
bibdate: Fri May 9 19:07:24 MDT 2014
bibtimestamp: 2014.05.09 19:07:24 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0082098/
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0082094
bookURL: http://www.springerlink.com/content/978-3-540-38842-5
journalURL: http://link.springer.com/bookseries/304
rawauthor: Norbert Schappacher
rawtitle: Elliptic integrals and the gamma function
ISBN13:
978-3-540-18915-2 (print), 978-3-540-38842-5 (e-book) OR 9783540189152 (print), 9783540388425 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lnm1985.bib

entry:
@Article{Schappacher:1988:EIG,
  author =       "Norbert Schappacher",
  title =        "Elliptic integrals and the gamma function",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1301",
  pages =        "117--127",
  year =         "1988",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0082098",
  ISBN =         "3-540-18915-7 (print), 3-540-38842-7 (e-book)",
  ISBN-13 =      "978-3-540-18915-2 (print), 978-3-540-38842-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:07:24 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1985.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0082098/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0082094",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38842-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schwarz:1988:CLI
author: Jerry Schwarz
title: A C++ Library for Infinite Precision Floating Point
crossref: USENIX:1988:UPC
pages: 271--281
year: 1988
bibdate: Tue Dec 12 09:20:21 MST 1995
bibsource: ftp://ftp.uu.net/library/bibliography; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.12 09:20:21 MST
acknowledgement: ack-nhfb
affiliation: AT&T Bell Laboratories, Murray Hill
bookpages: 362
thesaurus: C language; Digital arithmetic; Object-oriented programming; Subroutines
rawauthor: Jerry Schwarz
rawtitle: A {C++} Library for Infinite Precision Floating Point
abstract:
The Real library supports infinite precision floating point computation in C++. Arbitrary precision rational arithmetic and transcendental functions are supported.

keywords:
C++ library; Infinite precision floating point; Rational arithmetic; Real library; Transcendental functions

rawabstract:
The Real library supports infinite precision floating point computation in C++. Arbitrary precision rational arithmetic and transcendental functions are supported.

entry:
@InProceedings{Schwarz:1988:CLI,
  author =       "Jerry Schwarz",
  title =        "A {C++} Library for Infinite Precision Floating
                 Point",
  crossref =     "USENIX:1988:UPC",
  bookpages =    "362",
  pages =        "271--281",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The Real library supports infinite precision floating
                 point computation in C++. Arbitrary precision rational
                 arithmetic and transcendental functions are
                 supported.",
  acknowledgement = ack-nhfb,
  affiliation =  "AT\&T Bell Laboratories, Murray Hill",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  confdate =     "17--21 Oct. 1988",
  conflocation = "Denver, CO, USA",
  keywords =     "C++ library; Infinite precision floating point;
                 Rational arithmetic; Real library; Transcendental
                 functions",
  pubcountry =   "USA",
  thesaurus =    "C language; Digital arithmetic; Object-oriented
                 programming; Subroutines",
}


bibtype: inproceedings
filename: elefunt.bib
label: Sobczyk:1988:SMA
author: Kazimierz Sobczyk
editor: W. Schiehlen and W. Wedig
booktitle: Analysis and estimation of stochastic mechanical systems
title: Stochastic modelling and analysis of fatigue
volume: 303
publisher: pub-SV
address: pub-SV:adr
pages: 269--313
year: 1988
ISBN: 0-387-82058-2 OR 0387820582
ISBN13: 978-0-387-82058-3 OR 9780387820583
LCCN: TA350.3.I5 no.303; TJ173 .A531 1988
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
series: Courses and lectures
acknowledgement: ack-nhfb
bookpages: 350
rawauthor: Kazimierz Sobczyk
rawbooktitle: Analysis and estimation of stochastic mechanical systems
raweditor: W. Schiehlen and W. Wedig
rawtitle: Stochastic modelling and analysis of fatigue
subject:
J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@InProceedings{Sobczyk:1988:SMA,
  author =       "Kazimierz Sobczyk",
  editor =       "W. Schiehlen and W. Wedig",
  booktitle =    "Analysis and estimation of stochastic mechanical
                 systems",
  title =        "Stochastic modelling and analysis of fatigue",
  volume =       "303",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "350",
  pages =        "269--313",
  year =         "1988",
  ISBN =         "0-387-82058-2",
  ISBN-13 =      "978-0-387-82058-3",
  LCCN =         "TA350.3.I5 no.303; TJ173 .A531 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Courses and lectures",
  acknowledgement = ack-nhfb,
  bibno =        "58064",
  catcode =      "J.2; I.6.3; G.1.8; G.3; G.1.2; G.1.9",
  CRclass =      "J.2 Engineering; I.6.3 Applications; G.1.8 Partial
                 Differential Equations; G.1.8 Difference methods; G.3
                 Probabilistic algorithms (including Monte Carlo); G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.9 Integral Equations; G.1.9 Integro-differential
                 equations",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering; Computing Methodologies,
                 SIMULATION AND MODELING, Applications; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Difference methods; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Integral Equations,
                 Integro-differential equations",
  genterm =      "algorithms; theory; design; measurement; reliability",
  guideno =      "1988-17476",
  procdate =     "1987",
  procloc =      "International Centre for Mechanical Sciences in
                 Udine",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
  waffil =       "Univ. of Stuttgart; Univ. of Karlsruhe",
}


bibtype: article
filename: elefunt.bib
label: Stephens:1988:SCR
author: A. J. Stephens and H. C. Williams
title: Some computational results on a problem concerning powerful numbers
journal: j-MATH-COMPUT
volume: 50
number: 182
pages: 619--632
month: apr
monthnumber: 4
year: 1988
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11R11 (11A51 11R27 11Y16 11Y40)
MRnumber: 89d:11091
MRreviewer: H. J. Godwin
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical; X Experimental
rawauthor: A. J. Stephens and H. C. Williams
rawtitle: Some computational results on a problem concerning powerful numbers
keywords:
computational complexity; continued; fractions; free integer; fundamental unit; number theory; positive square-; real quadratic number fields; regulator algorithm Amdahl 5850; step algorithm; time complexity $O(D^1/4+epsilon )$

classcodes:
B0210 (Algebra); B0250 (Combinatorial mathematics); C1110 (Algebra); C1160 (Combinatorial mathematics)

entry:
@Article{Stephens:1988:SCR,
  author =       "A. J. Stephens and H. C. Williams",
  title =        "Some computational results on a problem concerning
                 powerful numbers",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "182",
  pages =        "619--632",
  month =        apr,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11R11 (11A51 11R27 11Y16 11Y40)",
  MRnumber =     "89d:11091",
  MRreviewer =   "H. J. Godwin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0210 (Algebra); B0250 (Combinatorial mathematics);
                 C1110 (Algebra); C1160 (Combinatorial mathematics)",
  corpsource =   "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; continued; fractions; free
                 integer; fundamental unit; number theory; positive
                 square-; real quadratic number fields; regulator
                 algorithm Amdahl 5850; step algorithm; time complexity
                 $O(D^{1/4+\epsilon})$",
  treatment =    "T Theoretical or Mathematical; X Experimental",
}


bibtype: inproceedings
filename: elefunt.bib
label: Stillinger:1988:CPS
author: Frank H. Stillinger
editor: Donald G. Truhlar
booktitle: Mathematical frontiers in computational chemical physics
title: Collective phenomena in statistical mechanics and the geometry of potential energy hypersurfaces
volume: 15
publisher: pub-SV
address: pub-SV:adr
pages: 157--173
year: 1988
ISBN: 0-387-96782-6 OR 0387967826
ISBN13: 978-0-387-96782-0 OR 9780387967820
LCCN: QD455.3.M3 M38 1988
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
series: The IMA volumes in mathematics and its applications
acknowledgement: ack-nhfb
bookpages: xii + 349
rawauthor: Frank H. Stillinger
rawbooktitle: Mathematical frontiers in computational chemical physics
raweditor: Donald G. Truhlar
rawtitle: Collective phenomena in statistical mechanics and the geometry of potential energy hypersurfaces
note:
Proceedings of the Workshop on Atomic and Molecular Structure and Dynamics, held June 15--July 24, 1987, at the Institute for Mathematics and Its Applications, University of Minnesota.

subject:
J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

rawnote:
Proceedings of the Workshop on Atomic and Molecular Structure and Dynamics, held June 15--July 24, 1987, at the Institute for Mathematics and Its Applications, University of Minnesota.

entry:
@InProceedings{Stillinger:1988:CPS,
  author =       "Frank H. Stillinger",
  editor =       "Donald G. Truhlar",
  booktitle =    "Mathematical frontiers in computational chemical
                 physics",
  title =        "Collective phenomena in statistical mechanics and the
                 geometry of potential energy hypersurfaces",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xii + 349",
  pages =        "157--173",
  year =         "1988",
  ISBN =         "0-387-96782-6",
  ISBN-13 =      "978-0-387-96782-0",
  LCCN =         "QD455.3.M3 M38 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the Workshop on Atomic and Molecular
                 Structure and Dynamics, held June 15--July 24, 1987, at
                 the Institute for Mathematics and Its Applications,
                 University of Minnesota.",
  price =        "US\$36.80",
  series =       "The IMA volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  bibno =        "58051",
  catcode =      "J.2; J.2; J.2; F.2.2; G.3; G.1.2",
  CRclass =      "J.2 Physics; J.2 Chemistry; J.2 Engineering; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; G.3 Statistical computing;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Chemistry; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Engineering; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations; Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical computing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "1988-17776",
  procdate =     "1982",
  procloc =      "Univ. of Minnesota, Minneapolis",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING; J. Computer Applications; J.2
                 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of
                 Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
  waffil =       "Univ. of Minnesota, Minneapolis",
}


bibtype: article
filename: elefunt.bib
label: Sun:1988:SAF
author: Xiehua Sun
journal: j-J-APPROX-THEORY
volume: 55
number: 3
pages: 279--288
month: dec
monthnumber: 12
year: 1988
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Xiehua Sun
title:
On the simultaneous approximation of functions and their derivatives by the Szasz--Mirakyan operator

rawtitle:
On the simultaneous approximation of functions and their derivatives by the {Szasz--Mirakyan} operator

entry:
@Article{Sun:1988:SAF,
  author =       "Xiehua Sun",
  title =        "On the simultaneous approximation of functions and
                 their derivatives by the {Szasz--Mirakyan} operator",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "279--288",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56048",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10194",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: techreport
filename: elefunt.bib
label: Tang:1988:PIG
author: Ping Tak Peter Tang
title: Portable Implementation of a Generic Exponential Function
type: Technical report
number: ANL-88-3
institution: inst-ANL
address: inst-ANL:adr
pages: 279--288
year: 1988
bibdate: Fri Dec 28 11:27:51 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.12.28 11:27:51 ???
acknowledgement: ack-nhfb
rawauthor: Ping Tak Peter Tang
rawtitle: Portable Implementation of a Generic Exponential Function
entry:
@TechReport{Tang:1988:PIG,
  author =       "Ping Tak Peter Tang",
  title =        "Portable Implementation of a Generic Exponential
                 Function",
  type =         "Technical report",
  number =       "ANL-88-3",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1988",
  bibdate =      "Fri Dec 28 11:27:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: vanRijckevorsek:1988:CCA
editor: Jan L. A. van Rijckevorsek and Jan de Leeus
title: Component and correspondence analysis: dimension reduction by functional approximation
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiii + 146
year: 1988
ISBN: 0-471-91847-4 OR 0471918474
ISBN13: 978-0-471-91847-9 OR 9780471918479
LCCN: QA278.5 .C6571 1988
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
series: Wiley series in probability and mathematical statistics
acknowledgement: ack-nhfb
raweditor: Jan L. A. van Rijckevorsek and Jan de Leeus
rawtitle: Component and correspondence analysis: dimension reduction by functional approximation
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS

entry:
@Book{vanRijckevorsek:1988:CCA,
  editor =       "Jan L. A. van Rijckevorsek and Jan de Leeus",
  title =        "Component and correspondence analysis: dimension
                 reduction by functional approximation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 146",
  year =         "1988",
  ISBN =         "0-471-91847-4",
  ISBN-13 =      "978-0-471-91847-9",
  LCCN =         "QA278.5 .C6571 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$40",
  series =       "Wiley series in probability and mathematical
                 statistics",
  acknowledgement = ack-nhfb,
  bibno =        "59092",
  catcode =      "G.1.2; G.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.3 Statistical computing",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing",
  genterm =      "theory; algorithms",
  guideno =      "1988-03042",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS",
}


bibtype: book
filename: elefunt.bib
label: Vilenkin:1988:SFT
author: N. Ja. (Naum Jakovlevich) Vilenkin
title: Special functions and the theory of group representations
volume: 22
publisher: pub-AMS
address: pub-AMS:adr
pages: x + 613
year: 1988
ISBN: 0-8218-1572-5 OR 0821815725
ISBN13: 978-0-8218-1572-4 OR 9780821815724
LCCN: QA3 .A5 v.22 1988
bibdate: Sat Oct 30 17:01:56 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:01:56 MDT
note: Reprint of 1968 edition.
series: Translations of mathematical monographs
subject: Representations of groups; Functions, Special
acknowledgement: ack-nhfb
rawauthor: N. Ja. (Naum Jakovlevich) Vilenkin
rawnote: Reprint of 1968 edition.
rawtitle: Special functions and the theory of group representations
entry:
@Book{Vilenkin:1988:SFT,
  author =       "N. Ja. (Naum Jakovlevich) Vilenkin",
  title =        "Special functions and the theory of group
                 representations",
  volume =       "22",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "x + 613",
  year =         "1988",
  ISBN =         "0-8218-1572-5",
  ISBN-13 =      "978-0-8218-1572-4",
  LCCN =         "QA3 .A5 v.22 1988",
  bibdate =      "Sat Oct 30 17:01:56 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Reprint of 1968 edition.",
  series =       "Translations of mathematical monographs",
  acknowledgement = ack-nhfb,
  subject =      "Representations of groups; Functions, Special",
}


bibtype: article
filename: elefunt.bib
label: Wong:1988:AE
author: R. Wong
title: Asymptotic Expansion of $ int ^pi / 2_0 J^2_nu (lambda cos theta ) d theta $
journal: j-MATH-COMPUT
volume: 50
number: 181
pages: 229--234
month: jan
monthnumber: 1
year: 1988
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 41A60 (33A40)
MRnumber: 89g:41022
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: R. Wong
rawtitle: Asymptotic Expansion of $ \int^{\pi / 2}_0 {J}^2_\nu (\lambda \cos \theta) d \theta $
keywords:
asymptotic expansion; Bessel function; Bessel functions; crystallography; diffraction theory; function approximation; integral; integration

classcodes:
A0260 (Numerical approximation and analysis); A0270 (Computational techniques); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)

entry:
@Article{Wong:1988:AE,
  author =       "R. Wong",
  title =        "Asymptotic Expansion of $ \int^{\pi / 2}_0 {J}^2_\nu
                 (\lambda \cos \theta) d \theta $",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "229--234",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A60 (33A40)",
  MRnumber =     "89g:41022",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "A0260 (Numerical approximation and analysis); A0270
                 (Computational techniques); C4130 (Interpolation and
                 function approximation); C4160 (Numerical integration
                 and differentiation)",
  corpsource =   "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansion; Bessel function; Bessel
                 functions; crystallography; diffraction theory;
                 function approximation; integral; integration",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ahmed:1989:EEF
author: H. M. Ahmed
title: Efficient Elementary Function Generation with Multipliers
crossref: Ercegovac:1989:PSC
pages: 52--59
year: 1989
bibdate: Sat Nov 27 14:19:10 MST 2004
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.27 14:19:10 MST
acknowledgement: ack-nhfb
rawauthor: H. M. Ahmed
rawtitle: Efficient Elementary Function Generation with Multipliers
entry:
@InProceedings{Ahmed:1989:EEF,
  author =       "H. M. Ahmed",
  title =        "Efficient Elementary Function Generation with
                 Multipliers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "52--59",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Armbruster:1989:KSD
author: Dieter Armbruster and John Guckenheimer and Philip Holmes
title: Kuramoto--Sivashinsky dynamics on the center-unstable manifold
journal: j-SIAM-J-APPL-MATH
volume: 49
number: 3
pages: 676--691
month: jun
monthnumber: 6
year: 1989
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
affiliation: Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY
journalURL: http://epubs.siam.org/siap
rawauthor: Dieter Armbruster and John Guckenheimer and Philip Holmes
rawtitle: {Kuramoto--Sivashinsky} dynamics on the center-unstable manifold
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Armbruster:1989:KSD,
  author =       "Dieter Armbruster and John Guckenheimer and Philip
                 Holmes",
  title =        "{Kuramoto--Sivashinsky} dynamics on the
                 center-unstable manifold",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "676--691",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY;
                 Cornell Univ., Ithaca, NY",
  bibno =        "64938",
  catcode =      "G.1.7; G.1.7; G.1.0; J.2; G.1.2; G.1.8",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability; G.1.7 Ordinary Differential
                 Equations; G.1.7 Boundary value problems; G.1.0
                 General; G.1.0 Numerical algorithms; J.2 Physics; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.8 Partial Differential Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Physics; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09707",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Avellaneda:1989:OBE
author: Marco Avellaneda and Graeme W. Milton
title: Optimal bounds on the effective bulk modulus of polycrystals
journal: j-SIAM-J-APPL-MATH
volume: 49
number: 3
pages: 824--837
month: jun
monthnumber: 6
year: 1989
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: Marco Avellaneda and Graeme W. Milton
rawtitle: Optimal bounds on the effective bulk modulus of polycrystals
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Avellaneda:1989:OBE,
  author =       "Marco Avellaneda and Graeme W. Milton",
  title =        "Optimal bounds on the effective bulk modulus of
                 polycrystals",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "824--837",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64947",
  catcode =      "G.1.8; J.2; G.1.2; G.1.6",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Difference
                 methods; J.2 Physics; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.6 Optimization;
                 G.1.6 Constrained optimization",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Difference methods; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09716",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Bauer:1989:BKR
author: Friedrich L. Bauer
journal: Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber.
pages: 27--33 (1990)
year: 1989
ISSN: 0340-7586 OR 03407586
MRclass: 11Y60 (65D20) 26A06 11Y60 65D20
MRnumber: 1086008
MRreviewer: F. Beukers
bibdate: Thu Aug 20 18:22:34 2020
bibtimestamp: 2020.08.20 18:22:34 ???
keywords: asymptotic expansion; Euler's constant; series representation
language: German
ZMnumber: 0777.26004
acknowledgement: ack-nhfb
authordates: Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26 March 2015)
rawauthor: Friedrich L. Bauer
title:
Eine Bemerkung zu Koechers Reihen fur die Eulersche Konstante. (German) [A remark on Koecher's series for the Euler's constant]

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

fjournal:
Bayerische Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse. Sitzungsberichte

rawtitle:
{Eine Bemerkung zu Koechers Reihen f{\"u}r die Eulersche Konstante}. ({German}) [{A} remark on {Koecher}'s series for the {Euler}'s constant]

entry:
@Article{Bauer:1989:BKR,
  author =       "Friedrich L. Bauer",
  title =        "{Eine Bemerkung zu Koechers Reihen f{\"u}r die
                 Eulersche Konstante}. ({German}) [{A} remark on
                 {Koecher}'s series for the {Euler}'s constant]",
  journal =      "Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber.",
  pages =        "27--33 (1990)",
  year =         "1989",
  ISSN =         "0340-7586",
  MRclass =      "11Y60 (65D20) 26A06 11Y60 65D20",
  MRnumber =     "1086008",
  MRreviewer =   "F. Beukers",
  bibdate =      "Thu Aug 20 18:22:34 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMID =         "00005959",
  ZMnumber =     "0777.26004",
  acknowledgement = ack-nhfb,
  author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
                 March 2015)",
  fjournal =     "Bayerische Akademie der Wissenschaften.
                 Mathematisch-Naturwissenschaftliche Klasse.
                 Sitzungsberichte",
  keywords =     "asymptotic expansion; Euler's constant; series
                 representation",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Belaga:1989:TMM
author: E. G. Belaga
journal: j-ACTA-INFO
volume: 26
number: 4
pages: 381--407
month: feb
monthnumber: 2
year: 1989
CODEN: AINFA2
ISSN: 0001-5903 (print), 1432-0525 (electronic) OR 00015903 (print), 14320525 (electronic)
ISSNL: 0001-5903 OR 00015903
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Acta Informatica
acknowledgement: ack-nhfb
affiliation: Univ. Louis Pasteur, Strasbourg Cedex, France and Univ. su Pisa, Pisa, Italy
journalURL: http://www.springerlink.com/content/0001-5903
rawauthor: E. G. Belaga
title:
Through the mincing machine with a Boolean layer cake: nonstandard computations over Boolean circuits in the lower-bounds-to-circuit-size complexity proving

subject:
F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

rawtitle:
Through the mincing machine with a {Boolean} layer cake: nonstandard computations over {Boolean} circuits in the lower-bounds-to-circuit-size complexity proving

entry:
@Article{Belaga:1989:TMM,
  author =       "E. G. Belaga",
  title =        "Through the mincing machine with a {Boolean} layer
                 cake: nonstandard computations over {Boolean} circuits
                 in the lower-bounds-to-circuit-size complexity
                 proving",
  journal =      j-ACTA-INFO,
  volume =       "26",
  number =       "4",
  pages =        "381--407",
  month =        feb,
  year =         "1989",
  CODEN =        "AINFA2",
  ISSN =         "0001-5903 (print), 1432-0525 (electronic)",
  ISSN-L =       "0001-5903",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Louis Pasteur, Strasbourg Cedex, France and
                 Univ. su Pisa, Pisa, Italy",
  bibno =        "69310",
  catcode =      "F.4.1; B.6.1; F.1.1; F.1.3; F.2.2; F.1.2; G.1.2;
                 F.2.2",
  CRclass =      "F.4.1 Mathematical Logic; F.4.1 Computational logic;
                 B.6.1 Design Styles; B.6.1 Combinational logic; F.1.1
                 Models of Computation; F.1.1 Unbounded-action devices;
                 F.1.3 Complexity Classes; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Complexity of proof procedures;
                 F.1.2 Modes of Computation; F.1.2 Alternation and
                 nondeterminism; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Computations on discrete
                 structures",
  descriptor =   "Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic, Computational logic;
                 Hardware, LOGIC DESIGN, Design Styles, Combinational
                 logic; Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Unbounded-action
                 devices; Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Complexity Classes; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Complexity of
                 proof procedures; Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Alternation and
                 nondeterminism; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures",
  fjournal =     "Acta Informatica",
  genterm =      "algorithms; theory",
  guideno =      "1989-03239",
  journal-URL =  "http://www.springerlink.com/content/0001-5903",
  journalabbrev = "Acta Inf.",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; F. Theory of Computation; F.1 COMPUTATION BY
                 ABSTRACT DEVICES; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY",
}


bibtype: article
filename: elefunt.bib
label: Birge:1989:SUB
author: John R. Birge and Roger J. Wets
title: Sublinear upper bounds for stochastic programs with recourse
journal: j-MATH-PROG
volume: 43
number: 2
pages: 131--149
month: feb
monthnumber: 2
year: 1989
CODEN: MHPGA4
ISSN: 0025-5610 OR 00255610
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Mathematical Programming
acknowledgement: ack-nhfb
affiliation: Univ. of Michigan, Ann Arbor; Univ. of California, Davis
journalURL: http://link.springer.com/journal/10107
rawauthor: John R. Birge and Roger J. Wets
rawtitle: Sublinear upper bounds for stochastic programs with recourse
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Birge:1989:SUB,
  author =       "John R. Birge and Roger J. Wets",
  title =        "Sublinear upper bounds for stochastic programs with
                 recourse",
  journal =      j-MATH-PROG,
  volume =       "43",
  number =       "2",
  pages =        "131--149",
  month =        feb,
  year =         "1989",
  CODEN =        "MHPGA4",
  ISSN =         "0025-5610",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Michigan, Ann Arbor; Univ. of California,
                 Davis",
  bibno =        "65226",
  catcode =      "G.1.6; G.1.7; G.3; G.1.6; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.7
                 Ordinary Differential Equations; G.1.7 Convergence and
                 stability; G.3 Probabilistic algorithms (including
                 Monte Carlo); G.1.6 Optimization; G.1.6 Gradient
                 methods; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Convergence and stability; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Mathematical Programming",
  genterm =      "algorithms; theory; performance",
  guideno =      "1989-09042",
  journal-URL =  "http://link.springer.com/journal/10107",
  journalabbrev = "Math. Program.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Borwein:1989:MI
author: J. M. Borwein and P. B. Borwein
title: On the Mean Iteration $ (a, b) leftarrow big (frac a + 3b4, frac sqrt ab + b2 big ) $
journal: j-MATH-COMPUT
volume: 53
number: 187
pages: 311--326
month: jul
monthnumber: 7
year: 1989
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2008364
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 30D05 (33A25)
MRnumber: 968148, 90a:30075
MRreviewer: Carl C. Cowen
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1586/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4130 (Interpolation and function approximation)
corpsource: Dept. of Math. Stat. and Comput. Sci., Dalhousie Univ., Halifax, NS, Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. M. Borwein and P. B. Borwein
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database

keywords:
computation; convergence of numerical methods; converging process; iterative methods; iterative process; limit; mean iteration; nontrivial identifications; quadratically; symbolic; uniformizing parameters

rawtitle:
On the Mean Iteration $ (a, b) \leftarrow \big (\frac {a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $

entry:
@Article{Borwein:1989:MI,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Mean Iteration $ (a, b) \leftarrow \big (\frac
                 {a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "311--326",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008364",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "30D05 (33A25)",
  MRnumber =     "968148, 90a:30075",
  MRreviewer =   "Carl C. Cowen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://docserver.carma.newcastle.edu.au/1586/",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math. Stat. and Comput. Sci., Dalhousie
                 Univ., Halifax, NS, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computation; convergence of numerical methods;
                 converging process; iterative methods; iterative
                 process; limit; mean iteration; nontrivial
                 identifications; quadratically; symbolic; uniformizing
                 parameters",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Borwein:1989:RME
author: J. M. Borwein and P. B. Borwein and D. H. Bailey
journal: j-AMER-MATH-MONTHLY
volume: 96
number: 3
pages: 201--219
month: mar
monthnumber: 3
year: 1989
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
affiliation: Dalhousie Univ., Halifax; Dalhousie Univ., Halifax
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: J. M. Borwein and P. B. Borwein and D. H. Bailey
title:
Ramanujan, modular equations, and approximations to $ pi $ or how to compute one billion digits of $ pi $

subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

rawtitle:
{Ramanujan}, modular equations, and approximations to $ \pi $ or how to compute one billion digits of $ \pi $

entry:
@Article{Borwein:1989:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "{Ramanujan}, modular equations, and approximations to
                 $ \pi $ or how to compute one billion digits of $ \pi
                 $",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "96",
  number =       "3",
  pages =        "201--219",
  month =        mar,
  year =         "1989",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Dalhousie Univ., Halifax; Dalhousie Univ., Halifax",
  bibno =        "65243",
  catcode =      "I.1.2; G.1.2; G.1.8; G.1.4; I.1.3; F.2.1; F.2.1",
  CRclass =      "I.1.2 Algorithms; I.1.2 Algebraic algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.8 Partial Differential Equations; G.1.8 Elliptic
                 equations; G.1.4 Quadrature and Numerical
                 Differentiation; G.1.4 Multiple quadrature; I.1.3
                 Languages and Systems; F.2.1 Numerical Algorithms and
                 Problems; F.2.1 Computation of transforms; F.2.1
                 Numerical Algorithms and Problems; F.2.1
                 Number-theoretic computations",
  descriptor =   "Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Elliptic equations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Multiple quadrature; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Languages and
                 Systems; Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computation of transforms; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations",
  fjournal =     "American Mathematical Monthly",
  genterm =      "algorithms; theory",
  guideno =      "1989-03459",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "March 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}


bibtype: article
filename: elefunt.bib
label: Bos:1989:CPR
author: L. Bos
title: A characteristic of points in $ R^2 $ having Lebesgue function of polynomial growth
journal: j-J-APPROX-THEORY
volume: 56
number: 3
pages: 316--329
month: mar
monthnumber: 3
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: L. Bos
rawtitle: A characteristic of points in {$ R^2 $} having {Lebesgue} function of polynomial growth
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Bos:1989:CPR,
  author =       "L. Bos",
  title =        "A characteristic of points in {$ R^2 $} having
                 {Lebesgue} function of polynomial growth",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "316--329",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72254",
  catcode =      "F.2.1; G.1.1; G.1.2; F.2.2; G.1.2; G.1.3",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on matrices; G.1.1 Interpolation; G.1.1
                 Interpolation formulas; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.2 Nonnumerical
                 Algorithms and Problems; F.2.2 Geometrical problems and
                 computations; G.1.2 Approximation; G.1.2 Chebyshev
                 approximation and theory; G.1.3 Numerical Linear
                 Algebra; G.1.3 Sparse and very large systems",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation, Interpolation
                 formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Chebyshev approximation and theory;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Sparse and very large systems",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07812",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: book
filename: elefunt.bib
label: Boyd:1989:CFS
author: John Philip Boyd
title: Chebyshev and Fourier spectral methods
volume: 49
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 798
year: 1989
ISBN: 0-387-51487-2, 3-540-51487-2 OR 0387514872, 3540514872
ISBN13: 978-0-387-51487-1, 978-3-540-51487-9 OR 9780387514871, 9783540514879
LCCN: QA404.5 .B69 1989
bibdate: Sat Feb 17 14:00:30 MST 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.17 14:00:30 MST
series: Lecture notes in engineering
acknowledgement: ack-nhfb
rawauthor: John Philip Boyd
rawtitle: {Chebyshev} and {Fourier} spectral methods
subject:
Chebyshev polynomials; Fourier analysis; Spectral theory (Mathematics); Polynyomes de Tchebychev; Analyse de Fourier; Spectre (Mathyematiques); Chebyshev polynomials; Fourier analysis; Spectral theory (Mathematics)

entry:
@Book{Boyd:1989:CFS,
  author =       "John Philip Boyd",
  title =        "{Chebyshev} and {Fourier} spectral methods",
  volume =       "49",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 798",
  year =         "1989",
  ISBN =         "0-387-51487-2, 3-540-51487-2",
  ISBN-13 =      "978-0-387-51487-1, 978-3-540-51487-9",
  LCCN =         "QA404.5 .B69 1989",
  bibdate =      "Sat Feb 17 14:00:30 MST 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture notes in engineering",
  acknowledgement = ack-nhfb,
  subject =      "Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics); Polyn{\'y}omes de Tchebychev;
                 Analyse de Fourier; Spectre (Math{\'y}ematiques);
                 Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics)",
}


bibtype: article
filename: elefunt.bib
label: Bronstein:1989:AIE
author: Manuel Bronstein
title: An algorithm for the integration of elementary functions
journal: j-LECT-NOTES-COMP-SCI
volume: 378
pages: 491--497
year: 1989
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
MRclass: 65D30
MRnumber: 91a:65050
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
note: EUROCAL '87 (Leipzig, 1987).
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Manuel Bronstein
rawnote: EUROCAL '87 (Leipzig, 1987).
rawtitle: An algorithm for the integration of elementary functions
entry:
@Article{Bronstein:1989:AIE,
  author =       "Manuel Bronstein",
  title =        "An algorithm for the integration of elementary
                 functions",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "378",
  pages =        "491--497",
  year =         "1989",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "65D30",
  MRnumber =     "91a:65050",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "EUROCAL '87 (Leipzig, 1987).",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bronstein:1989:SRE
author: M. Bronstein
title: Simplification of real elementary functions
crossref: ACM:1989:PAI
pages: 207--211
year: 1989
bibdate: Tue Sep 17 06:46:18 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/issac.bib
bibtimestamp: 1996.09.17 06:46:18 MDT
keywords: Computer algebra system; Real elementary functions; Real structure theorem; Scratchpad
acknowledgement: ack-nhfb
affiliation: IBM Res. Div., T. J. Watson Res. Center, Yorktown Heights, NY, USA
thesaurus: Functions; Mathematics computing; Symbol manipulation
rawauthor: M. Bronstein
rawtitle: Simplification of real elementary functions
abstract:
The author describes an algorithm, based on Risch's real structure theorem, that determines explicitly all the algebraic relations among a given set of real elementary functions. He provides examples from its implementation in the Scratchpad computer algebra system that illustrate the advantages over the use of complex logarithms and exponentials.

rawabstract:
The author describes an algorithm, based on Risch's real structure theorem, that determines explicitly all the algebraic relations among a given set of real elementary functions. He provides examples from its implementation in the Scratchpad computer algebra system that illustrate the advantages over the use of complex logarithms and exponentials.

entry:
@InProceedings{Bronstein:1989:SRE,
  author =       "M. Bronstein",
  title =        "Simplification of real elementary functions",
  crossref =     "ACM:1989:PAI",
  pages =        "207--211",
  year =         "1989",
  bibdate =      "Tue Sep 17 06:46:18 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author describes an algorithm, based on Risch's
                 real structure theorem, that determines explicitly all
                 the algebraic relations among a given set of real
                 elementary functions. He provides examples from its
                 implementation in the Scratchpad computer algebra
                 system that illustrate the advantages over the use of
                 complex logarithms and exponentials.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., T. J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Computer algebra system; Real elementary functions;
                 Real structure theorem; Scratchpad",
  thesaurus =    "Functions; Mathematics computing; Symbol
                 manipulation",
}


bibtype: article
filename: elefunt.bib
label: Cao:1989:ABS
author: J.-D. Cao and H. H. Gonska
title: Approximation by Boolean sums of positive linear operators. II. Gopengauz-type estimates
journal: j-J-APPROX-THEORY
volume: 57
number: 1
pages: 77--89
month: apr
monthnumber: 4
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: J.-D. Cao and H. H. Gonska
rawtitle: Approximation by {Boolean} sums of positive linear operators. {II}. {Gopengauz}-type estimates
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS

entry:
@Article{Cao:1989:ABS,
  author =       "J.-D. Cao and H. H. Gonska",
  title =        "Approximation by {Boolean} sums of positive linear
                 operators. {II}. {Gopengauz}-type estimates",
  journal =      j-J-APPROX-THEORY,
  volume =       "57",
  number =       "1",
  pages =        "77--89",
  month =        apr,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72266",
  catcode =      "G.1.2; G.1.2; G.3; G.2.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Nonlinear approximation;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.3 Statistical computing; G.2.1
                 Combinatorics; G.2.1 Generating functions",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-07823",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.2 DISCRETE
                 MATHEMATICS",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1989:TEI
author: B. C. Carlson
title: A Table of Elliptic Integrals: Cubic Cases
journal: j-MATH-COMPUT
volume: 53
number: 187
pages: 327--333
month: jul
monthnumber: 7
year: 1989
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (33A25 65D20)
MRnumber: 89m:65009
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: C4180 (Integral equations); C1120 (Analysis)
corpsource: Dept. of Math., Iowa State Univ., Ames, IA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawtitle: A Table of Elliptic Integrals: Cubic Cases
keywords:
cubic polynomial; elliptic; elliptic integral; first kind; Fortran codes; functions; integral equations; integrals; integration interval; R-; rational integrands; real zeros; second kind; square root; table; third kind

entry:
@Article{Carlson:1989:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals: Cubic Cases",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "327--333",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (33A25 65D20)",
  MRnumber =     "89m:65009",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations); C1120 (Analysis)",
  corpsource =   "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cubic polynomial; elliptic; elliptic integral; first
                 kind; Fortran codes; functions; integral equations;
                 integrals; integration interval; R-; rational
                 integrands; real zeros; second kind; square root;
                 table; third kind",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Chen:1989:EMB
author: X. R. Chen and P. R. Krishnaiah and W. W. Liang
title: Estimation of multivariate binary density using orthogonal functions
journal: j-J-MULTIVAR-ANAL
volume: 31
number: 2
pages: 178--186
month: nov
monthnumber: 11
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
acknowledgement: ack-nhfb
rawauthor: X. R. Chen and P. R. Krishnaiah and W. W. Liang
rawtitle: Estimation of multivariate binary density using orthogonal functions
subject:
D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

affiliation:
Univ. of Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh, Pittsburgh, PA

entry:
@Article{Chen:1989:EMB,
  author =       "X. R. Chen and P. R. Krishnaiah and W. W. Liang",
  title =        "Estimation of multivariate binary density using
                 orthogonal functions",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "178--186",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Pittsburgh, Pittsburgh, PA; Univ. of
                 Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh,
                 Pittsburgh, PA",
  bibno =        "69313",
  catcode =      "D.3.3; G.3; G.1.3; G.1.2",
  CRclass =      "D.3.3 Language Constructs; D.3.3 Procedures,
                 functions, and subroutines; G.3 Statistical computing;
                 G.1.3 Numerical Linear Algebra; G.1.3 Linear systems
                 (direct and iterative methods); G.1.2 Approximation;
                 G.1.2 Elementary function approximation",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Language Constructs,
                 Procedures, functions, and subroutines; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; verification",
  guideno =      "1989-08483",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
                 of Computing; G.3 PROBABILITY AND STATISTICS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Chen:1989:FCR
author: S.-G. Chen and P. Y. Hsieh
title: Fast computation of the $ N $ th root
journal: j-COMPUT-MATH-APPL
volume: 17
number: 10
pages: 1423--1427
year: 1989
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(89)90024-2
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Thu Dec 29 08:01:37 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.29 08:01:37 ???
URL: http://www.sciencedirect.com/science/article/pii/0898122189900242
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S.-G. Chen and P. Y. Hsieh
rawtitle: Fast computation of the $ {N} $ th root
remark:
From the abstract: ``A new class of iterative methods for computing a differentiable function is proposed, which is based on Pade approximation to Taylor's series of the function. It leads to a faster algorithm than Newton's method for $ x^1 / N $ and a different interpretation of Newton's method.''

entry:
@Article{Chen:1989:FCR,
  author =       "S.-G. Chen and P. Y. Hsieh",
  title =        "Fast computation of the $ {N} $ th root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "17",
  number =       "10",
  pages =        "1423--1427",
  month =        "????",
  year =         "1989",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(89)90024-2",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Dec 29 08:01:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122189900242",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``A new class of iterative methods
                 for computing a differentiable function is proposed,
                 which is based on Pad{\'e} approximation to Taylor's
                 series of the function. It leads to a faster algorithm
                 than Newton's method for $ x^{1 / N} $ and a different
                 interpretation of Newton's method.''",
}


bibtype: article
filename: elefunt.bib
label: Chen:1989:FCTa
author: S.-G. Chen and P. Y. Hsieh
title: Fast computation of the $N$-th root
journal: j-COMPUT-MATH-APPL
volume: 17
number: 10
pages: 1423--1427
year: 1989
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(89)90024-2
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 19:01:11 MST 2017
bibtimestamp: 2017.03.01 19:01:11 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122189900242
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nj
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S.-G. Chen and P. Y. Hsieh
rawtitle: Fast computation of the {$N$}-th root
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
From the abstract: ``A new class of iterative methods for computing a differentiable function is proposed, which is based on Pade approximation to Taylor's series of the function. It leads to a faster algorithm than Newton's method for $ x^1 / N $ and a different interpretation of Newton's method.''

entry:
@Article{Chen:1989:FCTa,
  author =       "S.-G. Chen and P. Y. Hsieh",
  title =        "Fast computation of the {$N$}-th root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "17",
  number =       "10",
  pages =        "1423--1427",
  month =        "????",
  year =         "1989",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(89)90024-2",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:01:11 MST 2017",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122189900242",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``A new class of iterative methods
                 for computing a differentiable function is proposed,
                 which is based on Pad{\'e} approximation to Taylor's
                 series of the function. It leads to a faster algorithm
                 than Newton's method for $ x^{1 / N} $ and a different
                 interpretation of Newton's method.''",
}


bibtype: article
filename: elefunt.bib
label: Corliss:1989:IIV
author: George Corliss and Gary Krenz
editor: L. Gatteschi
title: Indefinite Integration with Validation
journal: j-TOMS
volume: 15
number: 4
pages: 375--393
month: dec
monthnumber: 12
year: 1989
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D30 (65-04)
MRnumber: 1 062 497
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: George Corliss and Gary Krenz
raweditor: L. Gatteschi
rawtitle: Indefinite Integration with Validation
URL:
http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/; http://www.acm.org/pubs/toc/Abstracts/toms/76915.html

subject:
bf G.1.4: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory.

entry:
@Article{Corliss:1989:IIV,
  author =       "George Corliss and Gary Krenz",
  editor =       "L. Gatteschi",
  title =        "Indefinite Integration with Validation",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "375--393",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65-04)",
  MRnumber =     "1 062 497",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/76915.html",
  acknowledgement = ack-nhfb,
  bibno =        "393",
  content =      "ALGORITHMS; THEORY",
  CRclass =      "G.1.4 Quadrature and Numerical Differentiation; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.2 Approximation; G.1.2 Chebyshev approximation and
                 theory",
  CRnumber =     "1989-03199",
  descriptor =   "mathematics of computing, numerical analysis,
                 quadrature and numerical differentiation; mathematics
                 of computing, numerical analysis, approximation,
                 elementary function approximation; mathematics of
                 computing, numerical analysis, approximation, Chebyshev
                 approximation and theory",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  fortitle =     "ACM Trans. Math. Softw.",
  guideno =      "4",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 9007-0598",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory.",
  waffil =       "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Critchfield:1989:CEF
author: Charles L. Critchfield
title: Computation of elliptic functions
journal: j-J-MATH-PHYS
volume: 30
number: 2
pages: 295--297
month: feb
monthnumber: 2
year: 1989
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.528444
ISSNL: 0022-2488 OR 00222488
MRclass: 33A25 (65D20)
MRnumber: 89k:33004
MRreviewer: H. Hochstadt
bibdate: Mon Oct 31 11:58:32 MDT 2011
bibtimestamp: 2011.10.31 11:58:32 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v30/i2/p295_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Charles L. Critchfield
rawtitle: Computation of elliptic functions
entry:
@Article{Critchfield:1989:CEF,
  author =       "Charles L. Critchfield",
  title =        "Computation of elliptic functions",
  journal =      j-J-MATH-PHYS,
  volume =       "30",
  number =       "2",
  pages =        "295--297",
  month =        feb,
  year =         "1989",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.528444",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A25 (65D20)",
  MRnumber =     "89k:33004",
  MRreviewer =   "H. Hochstadt",
  bibdate =      "Mon Oct 31 11:58:32 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v30/i2/p295_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "3",
}


bibtype: misc
filename: elefunt.bib
label: Darley:1989:FPI
author: H. M. Darley and others
title: Floating Point / Integer Processor with Divide and Square Root Functions
pages: 295--297
year: 1989
bibdate: Thu Apr 2 08:38:35 1998
bibtimestamp: 1998.04.02 08:38:35 ???
note: U.S. Patent No. 4,878,190.
acknowledgement: ack-sfo
rawauthor: H. M. Darley and others
rawnote: U.S. Patent No. 4,878,190.
rawtitle: Floating Point\slash Integer Processor with Divide and Square Root Functions
entry:
@Misc{Darley:1989:FPI,
  author =       "H. M. Darley and others",
  title =        "Floating Point\slash Integer Processor with Divide and
                 Square Root Functions",
  year =         "1989",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 4,878,190.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dehling:1989:FLI
author: Herold Dehling
journal: j-J-MULTIVAR-ANAL
volume: 28
number: 2
pages: 177--189
month: feb
monthnumber: 2
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
acknowledgement: ack-nhfb
affiliation: Univ. of Gottingen, Gottingen, FRG
rawauthor: Herold Dehling
title:
The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals

subject:
G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

rawtitle:
The functional law of the iterated logarithm for {von Mises} functionals and multiple {Wiener} integrals

entry:
@Article{Dehling:1989:FLI,
  author =       "Herold Dehling",
  title =        "The functional law of the iterated logarithm for {von
                 Mises} functionals and multiple {Wiener} integrals",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "177--189",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of G{\"o}ttingen, G{\"o}ttingen, FRG",
  bibno =        "64336",
  catcode =      "G.3; G.1.9; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.9 Integral Equations;
                 G.1.9 Integro-differential equations; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
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                 NUMERICAL ANALYSIS, Integral Equations,
                 Integro-differential equations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08462",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Demirbas:1989:MSE
author: K. Demirbas
title: Multidimensional state estimation using stacks for dynamic systems with interference
journal: j-AUTOMATICA
volume: 25
number: 4
pages: 617--621
month: jul
monthnumber: 7
year: 1989
CODEN: ATCAA9
ISSN: 0005-1098 (print), 1873-2836 (electronic) OR 00051098 (print), 18732836 (electronic)
ISSNL: 0005-1098 OR 00051098
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Automatica: the journal of IFAC, the International Federation of Automatic Control
acknowledgement: ack-nhfb
rawauthor: K. Demirbas
rawtitle: Multidimensional state estimation using stacks for dynamic systems with interference
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; H. Information Systems; H.1 MODELS AND PRINCIPLES

entry:
@Article{Demirbas:1989:MSE,
  author =       "K. Demirbas",
  title =        "Multidimensional state estimation using stacks for
                 dynamic systems with interference",
  journal =      j-AUTOMATICA,
  volume =       "25",
  number =       "4",
  pages =        "617--621",
  month =        jul,
  year =         "1989",
  CODEN =        "ATCAA9",
  ISSN =         "0005-1098 (print), 1873-2836 (electronic)",
  ISSN-L =       "0005-1098",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72661",
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                 Roots of Nonlinear Equations; H.1.1 Systems and
                 Information Theory; H.1.1 Information theory",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
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                 Mathematics of Computing, NUMERICAL ANALYSIS,
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                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
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  fjournal =     "Automatica: the journal of IFAC, the International
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  genterm =      "algorithms; theory",
  guideno =      "1989-03952",
  jrldate =      "July 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
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}


bibtype: techreport
filename: elefunt.bib
label: Dritz:1989:RPS
author: K. W. Dritz
title: Rationale for the Proposed Standard for a Generic Package of Elementary Functions for Ada
type: Report
number: ANL-89/2 Rev. 1
institution: Argonne National Laboratory, Mathematics and Computer Science Division
address: Argonne, IL, USA
month: oct
monthnumber: 10
year: 1989
bibdate: Thu Sep 01 12:08:24 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 12:08:24 ???
acknowledgement: ack-nj
rawauthor: K. W. Dritz
rawtitle: Rationale for the Proposed Standard for a Generic Package of Elementary Functions for {Ada}
entry:
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  author =       "K. W. Dritz",
  title =        "Rationale for the Proposed Standard for a Generic
                 Package of Elementary Functions for {Ada}",
  type =         "Report",
  number =       "ANL-89/2 Rev. 1",
  institution =  "Argonne National Laboratory, Mathematics and Computer
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  address =      "Argonne, IL, USA",
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  year =         "1989",
  bibdate =      "Thu Sep 01 12:08:24 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
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  acknowledgement = ack-nj,
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bibtype: inproceedings
filename: elefunt.bib
label: Duprat:1989:SRA
author: J. Duprat and Y. Herreros and J.-M. Muller
title: Some results about on-line computation of functions
crossref: Ercegovac:1989:PSC
pages: 112--118
year: 1989
bibdate: Sat Nov 27 14:19:10 MST 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.27 14:19:10 MST
acknowledgement: ack-nhfb
rawauthor: J. Duprat and Y. Herreros and J.-M. Muller
rawtitle: Some results about on-line computation of functions
entry:
@InProceedings{Duprat:1989:SRA,
  author =       "J. Duprat and Y. Herreros and J.-M. Muller",
  title =        "Some results about on-line computation of functions",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "112--118",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dyn:1989:PEB
author: N. Dyn and A. Ron
title: Periodic exponential box splines on a three direction mesh
journal: j-J-APPROX-THEORY
volume: 56
number: 3
pages: 287--296
month: mar
monthnumber: 3
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: N. Dyn and A. Ron
rawtitle: Periodic exponential box splines on a three direction mesh
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3 PROBABILITY AND STATISTICS

entry:
@Article{Dyn:1989:PEB,
  author =       "N. Dyn and A. Ron",
  title =        "Periodic exponential box splines on a three direction
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  volume =       "56",
  number =       "3",
  pages =        "287--296",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
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  acknowledgement = ack-nhfb,
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  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
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  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
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  jrldate =      "Mar. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
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                 G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3
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bibtype: article
filename: elefunt.bib
label: Eberlein:1989:SAC
author: E. Eberlein
title: Strong approximation of continuous time stochastic processes
journal: j-J-MULTIVAR-ANAL
volume: 31
number: 2
pages: 220--235
month: nov
monthnumber: 11
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
acknowledgement: ack-nhfb
affiliation: Univ. Freiburg, Freiburg, W. Germany
rawauthor: E. Eberlein
rawtitle: Strong approximation of continuous time stochastic processes
subject:
D. Software; D.4 OPERATING SYSTEMS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Eberlein:1989:SAC,
  author =       "E. Eberlein",
  title =        "Strong approximation of continuous time stochastic
                 processes",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "220--235",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
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  acknowledgement = ack-nhfb,
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  descriptor =   "Software, OPERATING SYSTEMS, Performance, Stochastic
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  guideno =      "1989-08486",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "D. Software; D.4 OPERATING SYSTEMS; F. Theory of
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bibtype: article
filename: elefunt.bib
label: Egger:1989:PAC
author: A. Egger and R. Huotari
title: The Polya algorithm on convex sets
journal: j-J-APPROX-THEORY
volume: 56
number: 2
pages: 212--216
month: feb
monthnumber: 2
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: A. Egger and R. Huotari
rawtitle: The {Polya} algorithm on convex sets
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
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  author =       "A. Egger and R. Huotari",
  title =        "The {Polya} algorithm on convex sets",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "2",
  pages =        "212--216",
  month =        feb,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
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  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
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bibtype: article
filename: elefunt.bib
label: Ehrenmark:1989:ONF
author: Ulf T. Ehrenmark
journal: j-SIAM-J-APPL-MATH
volume: 49
number: 3
pages: 799--815
month: jun
monthnumber: 6
year: 1989
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: Ulf T. Ehrenmark
title:
Overconvergence of the near-field expansion for linearized waves normally incident on a sloping beach

subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

rawtitle:
Overconvergence of the near-field expansion for linearized waves normally incident on a sloping beach

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  title =        "Overconvergence of the near-field expansion for
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  volume =       "49",
  number =       "3",
  pages =        "799--815",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
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  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
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                 Mathematics of Computing, NUMERICAL ANALYSIS,
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                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
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  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
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bibtype: article
filename: elefunt.bib
label: Einmahl:1989:ERK
author: U. Einmahl
title: Extensions of results of Komlos, Major, and Tusnady to the multivariate case
journal: j-J-MULTIVAR-ANAL
volume: 28
number: 1
pages: 20--68
month: jan
monthnumber: 1
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
acknowledgement: ack-nhfb
affiliation: Univ. zu Koln, West Germany
rawauthor: U. Einmahl
rawtitle: Extensions of results of {Komlos}, {Major}, and {Tusnady} to the multivariate case
subject:
G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

entry:
@Article{Einmahl:1989:ERK,
  author =       "U. Einmahl",
  title =        "Extensions of results of {Komlos}, {Major}, and
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  volume =       "28",
  number =       "1",
  pages =        "20--68",
  month =        jan,
  year =         "1989",
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  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
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  bibno =        "66700",
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  guideno =      "1989-08456",
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  jrldate =      "Jan. 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
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}


bibtype: article
filename: elefunt.bib
label: Epperson:1989:UIM
author: J. F. Epperson
title: On the use of iteration methods for approximating the natural logarithm
journal: j-AMER-MATH-MONTHLY
volume: 96
number: 9
pages: 831--835
month: nov
monthnumber: 11
year: 1989
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 26A06 (26A09)
MRnumber: 91a:26002
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: J. F. Epperson
rawtitle: On the use of iteration methods for approximating the natural logarithm
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K. Computing Milieux; K.3 COMPUTERS AND EDUCATION

entry:
@Article{Epperson:1989:UIM,
  author =       "J. F. Epperson",
  title =        "On the use of iteration methods for approximating the
                 natural logarithm",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "96",
  number =       "9",
  pages =        "831--835",
  month =        nov,
  year =         "1989",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26A06 (26A09)",
  MRnumber =     "91a:26002",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "71703",
  catcode =      "G.1.2; G.1.2; K.3.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation; K.3.2 Computer and
                 Information Science Education",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Computing Milieux, COMPUTERS AND
                 EDUCATION, Computer and Information Science Education",
  fjournal =     "American Mathematical Monthly",
  genterm =      "algorithms; theory",
  guideno =      "1989-03518",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "Nov. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K.
                 Computing Milieux; K.3 COMPUTERS AND EDUCATION",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:1989:FRD
author: M. D. Ercegovac and T. Lang
title: On-the-fly rounding for division and square root
crossref: Ercegovac:1989:PSC
pages: 169--173
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
URL: http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf
keywords: ARITH-9
acknowledgement: ack-nhfb
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: On-the-fly rounding for division and square root
entry:
@InProceedings{Ercegovac:1989:FRD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly rounding for division and square root",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "169--173",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "In division and square root implementation based on
                 digit-recurrence algorithms, the result is obtained in
                 digit-serial form, from most significant digit to least
                 significant. To reduce the complexity of the
                 result-digit selection and to allow the \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:1989:IMC
author: M. D. Ercegovac and T. Lang
booktitle: IEEE International Symposium on Circuits and Systems, 8--11 May 1989
title: Implementation of module combining multiplication, division, and square root
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 150--153
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: M. D. Ercegovac and T. Lang
rawbooktitle: {IEEE} International Symposium on Circuits and Systems, 8--11 May 1989
rawtitle: Implementation of module combining multiplication, division, and square root
entry:
@InProceedings{Ercegovac:1989:IMC,
  author =       "M. D. Ercegovac and T. Lang",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 8--11 May 1989",
  title =        "Implementation of module combining multiplication,
                 division, and square root",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "150--153",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The implementation of a module that performs radix-$2$
                 multiplication, division, and square root is presented.
                 The module is compact because most of the components
                 are shared by all three operations, the complexity
                 being similar to that of a radix-$2$ \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:1989:RSR
author: Milos D. Ercegovac and Tomas Lang
title: Radix-4 square root without initial PLA
crossref: Ercegovac:1989:PSC
pages: 162--168
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
URL: http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf
keywords: ARITH-9
acknowledgement: ack-nhfb
rawauthor: Milo{\v{s}} D. Ercegovac and Tomas Lang
rawtitle: Radix-4 square root without initial {PLA}
entry:
@InProceedings{Ercegovac:1989:RSR,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "Radix-4 square root without initial {PLA}",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "162--168",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "A systematic derivation of a radix-$4$ square root
                 algorithm using redundance in the partial residuals and
                 the result is presented. Unlike other similar schemes,
                 the algorithm does not use a table-lookup or
                 programmable logic array (PLA) for the \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Fandrianto:1989:AHS
author: Jan Fandrianto
title: Algorithms for high-speed shared radix 8 division and radix 8 square root
crossref: Ercegovac:1989:PSC
pages: 68--75
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
URL: http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf
keywords: ARITH-9
acknowledgement: ack-sfo
rawauthor: Jan Fandrianto
rawtitle: Algorithms for high-speed shared radix 8 division and radix 8 square root
entry:
@InProceedings{Fandrianto:1989:AHS,
  author =       "Jan Fandrianto",
  title =        "Algorithms for high-speed shared radix 8 division and
                 radix 8 square root",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "68--75",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "An algorithm for performing radix-$8$ division and
                 square root in a shared hardware is described. To
                 achieve short iteration cycle time, it utilizes an
                 optimized `next quotient/root prediction PLA' generally
                 used in a radix-$4$ SRT division with minimal
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Ge:1989:OCL
author: Renpu Ge
title: Optimal choice of linear interval extension
journal: j-APPL-MATH-COMP
volume: 30
number: 2
pages: 165--189
month: mar
monthnumber: 3
year: 1989
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Renpu Ge
rawtitle: Optimal choice of linear interval extension
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS

entry:
@Article{Ge:1989:OCL,
  author =       "Renpu Ge",
  title =        "Optimal choice of linear interval extension",
  journal =      j-APPL-MATH-COMP,
  volume =       "30",
  number =       "2",
  pages =        "165--189",
  month =        mar,
  year =         "1989",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64710",
  catcode =      "G.1.6; G.1.2; G.1.2; G.2.1; F.2.2; G.1.2; G.1.1;
                 G.1.0",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Linear approximation; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.1 Combinatorics; G.2.1 Combinatorial algorithms;
                 F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Computations on discrete structures; G.1.2
                 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.1 Interpolation; G.1.1 Difference
                 formulas; G.1.0 General; G.1.0 Numerical algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Linear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Combinatorial algorithms;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Computations on discrete structures;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Minimax approximation and algorithms;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Difference formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms",
  fjournal =     "Applied Mathematics and Computation",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-03670",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  journalabbrev = "Appl. Math. Comput.",
  jrldate =      "March 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS",
}


bibtype: article
filename: elefunt.bib
label: Gersch:1989:SPT
author: W. Gersch and G. Kitagawa
title: Smoothness priors transfer function estimation
journal: j-AUTOMATICA
volume: 25
number: 4
pages: 603--608
month: jul
monthnumber: 7
year: 1989
CODEN: ATCAA9
ISSN: 0005-1098 (print), 1873-2836 (electronic) OR 00051098 (print), 18732836 (electronic)
ISSNL: 0005-1098 OR 00051098
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Automatica: the journal of IFAC, the International Federation of Automatic Control
acknowledgement: ack-nhfb
rawauthor: W. Gersch and G. Kitagawa
rawtitle: Smoothness priors transfer function estimation
entry:
@Article{Gersch:1989:SPT,
  author =       "W. Gersch and G. Kitagawa",
  title =        "Smoothness priors transfer function estimation",
  journal =      j-AUTOMATICA,
  volume =       "25",
  number =       "4",
  pages =        "603--608",
  month =        jul,
  year =         "1989",
  CODEN =        "ATCAA9",
  ISSN =         "0005-1098 (print), 1873-2836 (electronic)",
  ISSN-L =       "0005-1098",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72658",
  catcode =      "G.1.1; G.1.2; G.1.6",
  CRclass =      "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.6 Optimization; G.1.6 Gradient methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Smoothing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Gradient methods",
  fjournal =     "Automatica: the journal of IFAC, the International
                 Federation of Automatic Control",
  genterm =      "algorithms; theory",
  guideno =      "1989-03949",
  jrldate =      "July 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: incollection
filename: elefunt.bib
label: Glover:1989:THN
author: Keith Glover
editor: Jan C. Willems
booktitle: From data to model
title: A tutorial on Hankel-norm approximation
publisher: pub-SV
address: pub-SV:adr
pages: 26--48
year: 1989
ISBN: 0-387-51571-2 OR 0387515712
ISBN13: 978-0-387-51571-7 OR 9780387515717
LCCN: QA279 .F76 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
bookpages: 246
rawauthor: Keith Glover
rawbooktitle: From data to model
raweditor: Jan C. Willems
rawtitle: A tutorial on {Hankel}-norm approximation
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

entry:
@InCollection{Glover:1989:THN,
  author =       "Keith Glover",
  editor =       "Jan C. Willems",
  booktitle =    "From data to model",
  title =        "A tutorial on {Hankel}-norm approximation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "246",
  pages =        "26--48",
  year =         "1989",
  ISBN =         "0-387-51571-2",
  ISBN-13 =      "978-0-387-51571-7",
  LCCN =         "QA279 .F76 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "70545",
  catcode =      "G.1.2; F.2.1; F.2.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; F.2.1 Numerical Algorithms and Problems;
                 F.2.1 Computations on matrices; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms",
  genterm =      "algorithms; theory",
  guideno =      "1989-01692",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
  waffil =       "Univ. of Groningen, Groningen, The Netherlands",
}


bibtype: inproceedings
filename: elefunt.bib
label: Glynn:1989:OSS
author: P. W. Glynn
editor: Edward A. MacNair and Kenneth J. Musselman and Philip Heidelberger
title: Optimization of stochastic systems via simulation
publisher: pub-ACM
address: pub-ACM:adr
pages: 90--105
year: 1989
ISBN: 0-911801-58-8 OR 0911801588
ISBN13: 978-0-911801-58-3 OR 9780911801583
LCCN: QA76.9.C65 W56 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
note: IEEE order no. 89CH2778-9.
URL: http://ieeexplore.ieee.org/servlet/opac?punumber=5823
acknowledgement: ack-nhfb
bookpages: xx + 1139
rawauthor: P. W. Glynn
raweditor: Edward A. MacNair and Kenneth J. Musselman and Philip Heidelberger
rawnote: IEEE order no. 89CH2778-9.
rawtitle: Optimization of stochastic systems via simulation
booktitle:
1989 Winter Simulation Conference proceedings: December 4--6, 1989, the Capital Hilton Hotel, Washington, DC

subject:
I. Computing Methodologies; I.6 SIMULATION AND MODELING; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

rawbooktitle:
1989 Winter Simulation Conference proceedings: December 4--6, 1989, the Capital Hilton Hotel, Washington, {DC}

entry:
@InProceedings{Glynn:1989:OSS,
  author =       "P. W. Glynn",
  editor =       "Edward A. MacNair and Kenneth J. Musselman and Philip
                 Heidelberger",
  booktitle =    "1989 Winter Simulation Conference proceedings:
                 December 4--6, 1989, the Capital Hilton Hotel,
                 Washington, {DC}",
  title =        "Optimization of stochastic systems via simulation",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "xx + 1139",
  pages =        "90--105",
  year =         "1989",
  ISBN =         "0-911801-58-8",
  ISBN-13 =      "978-0-911801-58-3",
  LCCN =         "QA76.9.C65 W56 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE order no. 89CH2778-9.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
  acknowledgement = ack-nhfb,
  bibno =        "76750",
  catcode =      "I.6.3; G.1.6; G.3; G.1.2",
  CRclass =      "I.6.3 Applications; G.1.6 Optimization; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Applications; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization; Mathematics of Computing,
                 PROBABILITY AND STATISTICS; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; design; performance",
  guideno =      "1989-12012",
  procdate =     "December 4-6, 1989",
  procloc =      "Washington, D. C.",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
                 AND STATISTICS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Gomes:1989:GGL
author: M. I. Gomes
title: Generalized Gumbel and likelihood ratio test statistics in the multivariate GEV model
journal: j-COMPUT-STAT-DATA-ANAL
volume: 7
number: 3
pages: 259--267
month: feb
monthnumber: 2
year: 1989
CODEN: CSDADW
ISSN: 0167-9473 (print), 1872-7352 (electronic) OR 01679473 (print), 18727352 (electronic)
ISSNL: 0167-9473 OR 01679473
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Computational Statistics & Data Analysis
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01679473
rawauthor: M. I. Gomes
rawtitle: Generalized {Gumbel} and likelihood ratio test statistics in the multivariate {GEV} model
subject:
G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.5 PATTERN RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Gomes:1989:GGL,
  author =       "M. I. Gomes",
  title =        "Generalized {Gumbel} and likelihood ratio test
                 statistics in the multivariate {GEV} model",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "7",
  number =       "3",
  pages =        "259--267",
  month =        feb,
  year =         "1989",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "70043",
  catcode =      "G.3; G.1.7; I.5.1; G.1.6; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.7 Ordinary Differential
                 Equations; G.1.7 Convergence and stability; I.5.1
                 Models; I.5.1 Statistical; G.1.6 Optimization; G.1.6
                 Nonlinear programming; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Convergence and stability; Computing Methodologies,
                 PATTERN RECOGNITION, Models, Statistical; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Optimization,
                 Nonlinear programming; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Computational Statistics \& Data Analysis",
  genterm =      "algorithms; measurement; reliability; theory",
  guideno =      "1989-04403",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
  journalabbrev = "Comput. Stat. Data Anal.",
  jrldate =      "Feb. 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gonzaga:1989:ASL
author: Clovis C. Gonzaga
title: An algorithm for solving linear programming programs in $ O(n^3 L) $ operations
crossref: Megiddo:1989:PMP
pages: 1--28
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
rawauthor: Cl{\'o}vis C. Gonzaga
rawtitle: An algorithm for solving linear programming programs in {$ O(n^3 L) $} operations
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

entry:
@InProceedings{Gonzaga:1989:ASL,
  author =       "Cl{\'o}vis C. Gonzaga",
  title =        "An algorithm for solving linear programming programs
                 in {$ O(n^3 L) $} operations",
  crossref =     "Megiddo:1989:PMP",
  pages =        "1--28",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74172",
  catcode =      "G.1.6; G.1.2; F.2.1; I.1.2; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on matrices; I.1.2 Algorithms; I.1.2
                 Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis
                 of algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms; Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12474",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}


bibtype: techreport
filename: elefunt.bib
label: Gragg:1989:FSE
author: W. Gragg and B. Neta
title: Fortran Subroutines for the Evaluation of the Confluent Hypergeometric Functions
number: NPS-MA-89-014
institution: inst-MATH-NPS
address: inst-MATH-NPS:adr
pages: 1--28
year: 1989
bibdate: Fri Nov 11 14:50:24 MST 1994
bibtimestamp: 1994.11.11 14:50:24 MST
note: Software available URL http://math.nps.navy.mil
rawauthor: W. Gragg and B. Neta
rawnote: Software available URL http://math.nps.navy.mil
rawtitle: {Fortran} Subroutines for the Evaluation of the Confluent Hypergeometric Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/n/neta-beny.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Gragg:1989:FSE,
  author =       "W. Gragg and B. Neta",
  title =        "{Fortran} Subroutines for the Evaluation of the
                 Confluent Hypergeometric Functions",
  number =       "NPS-MA-89-014",
  institution =  inst-MATH-NPS,
  address =      inst-MATH-NPS:adr,
  year =         "1989",
  bibdate =      "Fri Nov 11 14:50:24 MST 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/n/neta-beny.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Software available URL http://math.nps.navy.mil",
}


bibtype: article
filename: elefunt.bib
label: Guo:1989:RCS
author: S.-S. Guo and M. K. Khan
title: On the rate of convergence of some operators on functions of bounded variation
journal: j-J-APPROX-THEORY
volume: 58
number: 1
pages: 90--101
month: jul
monthnumber: 7
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: S.-S. Guo and M. K. Khan
rawtitle: On the rate of convergence of some operators on functions of bounded variation
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Guo:1989:RCS,
  author =       "S.-S. Guo and M. K. Khan",
  title =        "On the rate of convergence of some operators on
                 functions of bounded variation",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "1",
  pages =        "90--101",
  month =        jul,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "69424",
  catcode =      "F.2.1; G.1.2",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on polynomials; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07854",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "July 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Hornik:1989:MFN
author: K. Hornik and M. Stinchcombe and H. White
title: Multilayer feedforward networks are universal approximators
journal: j-NEURAL-NETWORKS
volume: 2
number: 5
pages: 359--366
year: 1989
CODEN: NNETEB
ISSN: 0893-6080 (print), 1879-2782 (electronic) OR 08936080 (print), 18792782 (electronic)
ISSNL: 0893-6080 OR 08936080
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Neural Networks
acknowledgement: ack-nhfb
rawauthor: K. Hornik and M. Stinchcombe and H. White
rawtitle: Multilayer feedforward networks are universal approximators
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE

affiliation:
Technisce Univ. Wien, Vienna, Austria; Univ. of California, San Diego; Univ. of California, San Diego

entry:
@Article{Hornik:1989:MFN,
  author =       "K. Hornik and M. Stinchcombe and H. White",
  title =        "Multilayer feedforward networks are universal
                 approximators",
  journal =      j-NEURAL-NETWORKS,
  volume =       "2",
  number =       "5",
  pages =        "359--366",
  year =         "1989",
  CODEN =        "NNETEB",
  ISSN =         "0893-6080 (print), 1879-2782 (electronic)",
  ISSN-L =       "0893-6080",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Technisce Univ. Wien, Vienna, Austria; Univ. of
                 California, San Diego; Univ. of California, San Diego",
  bibno =        "70408",
  catcode =      "F.2.1; G.1.2; F.1.1; I.2.4",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; G.1.2
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                 F.1.1 Models of Computation; F.1.1 Unbounded-action
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                 Methods",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
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                 Mathematics of Computing, NUMERICAL ANALYSIS,
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                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Models of Computation, Unbounded-action devices;
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Knowledge Representation Formalisms and Methods",
  fjournal =     "Neural Networks",
  genterm =      "design; performance",
  guideno =      "1989-09273",
  journalabbrev = "Neural Networks",
  jrldate =      "1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1
                 COMPUTATION BY ABSTRACT DEVICES; I. Computing
                 Methodologies; I.2 ARTIFICIAL INTELLIGENCE",
}


bibtype: article
filename: elefunt.bib
label: Jamieson:1989:RCI
author: M. J. Jamieson
title: Rapidly converging iterative formulae for finding square roots and their computational efficiencies
journal: j-COMP-J
volume: 32
number: 1
pages: 93--94
month: feb
monthnumber: 2
year: 1989
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/32.1.93
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
MRclass: 65H05
MRnumber: 89k:65063
bibdate: Tue Mar 25 13:51:56 MST 1997
bibtimestamp: 1997.03.25 13:51:56 MST
note: This work generalizes the Pythagorean sums in cite Dubrulle:1983:CNM,Moler:1983:RSR.
fjournal: The Computer Journal
acknowledgement: ack-nhfb
affiliation: Dept. of Comput. Sci., Glasgow Univ., UK
affiliationaddress: Glasgow, Scotl
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
corpsource: Dept. of Comput. Sci., Glasgow Univ., UK
journalURL: http://comjnl.oxfordjournals.org/
thesaurus: Convergence of numerical methods; Function approximation; Iterative methods
treatment: P Practical
rawauthor: M. J. Jamieson
rawnote: This work generalizes the Pythagorean sums in \cite{Dubrulle:1983:CNM,Moler:1983:RSR}.
bibsource:
Compendex database; http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif

abstract:
A derivation is given of rapidly converging iterative formulae for finding square roots which include, as special cases, some recently published examples. Their computational efficiencies are investigated for sequential and parallel implementation. It is concluded that the most efficient method is equivalent to sequential application of the Newton Raphson formula; a simple modification is suggested which brings the advantage of root bracketing at little extra computational cost.

keywords:
computational; Computational efficiencies; Computational Efficiency; Computer Metatheory; Convergence; convergence of numerical methods; Converging iterative formulae; converging iterative formulae; efficiencies; formula; function approximation; Iterative Methods; iterative methods; Newton Raphson; Newton Raphson formula, Mathematical Techniques; Parallel implementation; parallel implementation; Square Roots; Square roots; square roots

rawabstract:
A derivation is given of rapidly converging iterative formulae for finding square roots which include, as special cases, some recently published examples. Their computational efficiencies are investigated for sequential and parallel implementation. It is concluded that the most efficient method is equivalent to sequential application of the Newton Raphson formula; a simple modification is suggested which brings the advantage of root bracketing at little extra computational cost.

entry:
@Article{Jamieson:1989:RCI,
  author =       "M. J. Jamieson",
  title =        "Rapidly converging iterative formulae for finding
                 square roots and their computational efficiencies",
  journal =      j-COMP-J,
  volume =       "32",
  number =       "1",
  pages =        "93--94",
  month =        feb,
  year =         "1989",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/32.1.93",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
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  MRclass =      "65H05",
  MRnumber =     "89k:65063",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "This work generalizes the Pythagorean sums in
                 \cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
  abstract =     "A derivation is given of rapidly converging iterative
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                 special cases, some recently published examples. Their
                 computational efficiencies are investigated for
                 sequential and parallel implementation. It is concluded
                 that the most efficient method is equivalent to
                 sequential application of the Newton Raphson formula; a
                 simple modification is suggested which brings the
                 advantage of root bracketing at little extra
                 computational cost.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Glasgow Univ., UK",
  affiliationaddress = "Glasgow, Scotl",
  classcodes =   "B0290F (Interpolation and function approximation);
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  classification = "723; 921; B0290F (Interpolation and function
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  corpsource =   "Dept. of Comput. Sci., Glasgow Univ., UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "computational; Computational efficiencies;
                 Computational Efficiency; Computer Metatheory;
                 Convergence; convergence of numerical methods;
                 Converging iterative formulae; converging iterative
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                 Newton Raphson; Newton Raphson formula, Mathematical
                 Techniques; Parallel implementation; parallel
                 implementation; Square Roots; Square roots; square
                 roots",
  thesaurus =    "Convergence of numerical methods; Function
                 approximation; Iterative methods",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Jeffries:1989:GFA
author: John S. Jeffries and Donald R. Smith
title: A Green function approach for a singularly perturbed vector boundary-value problem
journal: j-ADV-APPL-MATH
volume: 10
number: 1
pages: 1--50
month: mar
monthnumber: 3
year: 1989
ISSN: 0196-8858 (print), 1090-2074 (electronic) OR 01968858 (print), 10902074 (electronic)
ISSNL: 0196-8858 OR 01968858
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Advances in Applied Mathematics
acknowledgement: ack-nhfb
affiliation: Univ. of California at San Diego, La Jolla; Univ. of California at San Diego, La Jolla
journalURL: http://www.sciencedirect.com/science/journal/01968858
rawauthor: John S. Jeffries and Donald R. Smith
rawtitle: A {Green} function approach for a singularly perturbed vector boundary-value problem
subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Jeffries:1989:GFA,
  author =       "John S. Jeffries and Donald R. Smith",
  title =        "A {Green} function approach for a singularly perturbed
                 vector boundary-value problem",
  journal =      j-ADV-APPL-MATH,
  volume =       "10",
  number =       "1",
  pages =        "1--50",
  month =        mar,
  year =         "1989",
  CODEN =        "????",
  ISSN =         "0196-8858 (print), 1090-2074 (electronic)",
  ISSN-L =       "0196-8858",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California at San Diego, La Jolla; Univ. of
                 California at San Diego, La Jolla",
  bibno =        "64833",
  catcode =      "G.1.7; G.1.7; F.2.1; G.1.2; G.1.3; G.1.2; G.1.3",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7 Boundary
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                 G.1.7 Convergence and stability; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; G.1.3 Numerical Linear Algebra; G.1.3
                 Eigenvalues; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; G.1.3 Numerical Linear Algebra;
                 G.1.3 Linear systems (direct and iterative methods)",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computation of transforms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Nonlinear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
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                 methods)",
  fjournal =     "Advances in Applied Mathematics",
  genterm =      "algorithms; theory",
  guideno =      "1989-03271",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01968858",
  journalabbrev = "Adv. Appl. Math.",
  jrldate =      "March 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Johnson:1989:IMA
author: K. R. Johnson
title: An Iterative Method for Approximating Square Roots
journal: j-MATH-MAG
volume: 62
number: 4
pages: 253--259
month: oct
monthnumber: 10
year: 1989
CODEN: MAMGA8
ISSN: 0025-570X OR 0025570X
bibdate: Thu Sep 1 10:15:42 1994
bibtimestamp: 1994.09.01 10:15:42 ???
fjournal: Mathematics Magazine
acknowledgement: ack-nj
journalURL: http://www.maa.org/pubs/mathmag.html
rawauthor: K. R. Johnson
rawtitle: An Iterative Method for Approximating Square Roots
entry:
@Article{Johnson:1989:IMA,
  author =       "K. R. Johnson",
  title =        "An Iterative Method for Approximating Square Roots",
  journal =      j-MATH-MAG,
  volume =       "62",
  number =       "4",
  pages =        "253--259",
  month =        oct,
  year =         "1989",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  acknowledgement = ack-nj,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}


bibtype: article
filename: elefunt.bib
label: Kaishev:1989:SSC
author: A. I. Kaishev
journal: Voprosy Kibernet. (Moscow)
volume: 149
pages: 14--18
year: 1989
ISBN: 0134-6388 OR 01346388
ISBN13: 0134-6388 OR 01346388
MRclass: 65G10
MRnumber: 91i:65090
MRreviewer: I. N. Molchanov
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: A. I. Kaishev
title:
A sharpened scheme for constructing an a posteriori interval extension of an elementary function. (Russian)

rawtitle:
A sharpened scheme for constructing an a posteriori interval extension of an elementary function. ({Russian})

entry:
@Article{Kaishev:1989:SSC,
  author =       "A. I. Kaishev",
  title =        "A sharpened scheme for constructing an a posteriori
                 interval extension of an elementary function.
                 ({Russian})",
  journal =      "Voprosy Kibernet. (Moscow)",
  volume =       "149",
  pages =        "14--18",
  year =         "1989",
  ISBN =         "0134-6388",
  ISBN-13 =      "0134-6388",
  MRclass =      "65G10",
  MRnumber =     "91i:65090",
  MRreviewer =   "I. N. Molchanov",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kak:1989:BAS
author: S. C. Kak and A. O. Barbir
booktitle: Proceedings of the Twenty-First Southeastern Symposium on System Theory, 26--28 March 1989
title: The Brahmagupta algorithm for square rooting
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 456--459
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: S. C. Kak and A. O. Barbir
rawbooktitle: Proceedings of the Twenty-First Southeastern Symposium on System Theory, 26--28 March 1989
rawtitle: The {Brahmagupta} algorithm for square rooting
entry:
@InProceedings{Kak:1989:BAS,
  author =       "S. C. Kak and A. O. Barbir",
  booktitle =    "Proceedings of the Twenty-First Southeastern Symposium
                 on System Theory, 26--28 March 1989",
  title =        "The {Brahmagupta} algorithm for square rooting",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "456--459",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root evaluation is introduced.
                 Novel features of the algorithm include suitability for
                 parallel processing and multi-initial guesses of the
                 root. An extension of the algorithm to the nth rooting
                 is provided. A VLSI \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Kogan:1989:GBF
author: B. J. Kogan
title: General background of functional memory algorithms
journal: j-TRANS-SOC-COMP-SIM
volume: 5
number: 4
pages: 285--317
month: oct
monthnumber: 10
year: 1989
CODEN: TSCSEV
ISSN: 0740-6797 OR 07406797
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Transactions of the Society for Computer Simulation
acknowledgement: ack-nhfb
affiliation: Univ. of California, Los Angeles
rawauthor: B. J. Kogan
rawtitle: General background of functional memory algorithms
subject:
C. Computer Systems Organization; C.3 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING AND INFORMATION THEORY

entry:
@Article{Kogan:1989:GBF,
  author =       "B. J. Kogan",
  title =        "General background of functional memory algorithms",
  journal =      j-TRANS-SOC-COMP-SIM,
  volume =       "5",
  number =       "4",
  pages =        "285--317",
  month =        oct,
  year =         "1989",
  CODEN =        "TSCSEV",
  ISSN =         "0740-6797",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California, Los Angeles",
  bibno =        "69149",
  catcode =      "C.3; G.1.2; G.1.2; E.4",
  CRclass =      "C.3 Signal processing systems; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; G.1.2
                 Approximation; G.1.2 Linear approximation; E.4 Data
                 compaction and compression",
  descriptor =   "Computer Systems Organization, SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS, Signal processing systems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Data, CODING AND
                 INFORMATION THEORY, Data compaction and compression",
  fjournal =     "Transactions of the Society for Computer Simulation",
  genterm =      "algorithms; design",
  guideno =      "1989-10680",
  journalabbrev = "Trans. Soc. Comput. Simul.",
  jrldate =      "Oct. 1989",
  subject =      "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
                 AND APPLICATION-BASED SYSTEMS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING
                 AND INFORMATION THEORY",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kojima:1989:PDI
author: M. Kojima and S. Mizuno and A. Yoshise
title: A primal-dual interior point algorithm for linear programming
crossref: Megiddo:1989:PMP
pages: 29--47
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
bookpages: x + 158
rawauthor: M. Kojima and S. Mizuno and A. Yoshise
rawtitle: A primal-dual interior point algorithm for linear programming
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

entry:
@InProceedings{Kojima:1989:PDI,
  author =       "M. Kojima and S. Mizuno and A. Yoshise",
  title =        "A primal-dual interior point algorithm for linear
                 programming",
  crossref =     "Megiddo:1989:PMP",
  bookpages =    "x + 158",
  pages =        "29--47",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74173",
  catcode =      "G.1.6; F.2.1; G.1.2; F.2.2; F.2.1; I.1.2; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; F.2.1
                 Numerical Algorithms and Problems; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; F.2.1 Numerical Algorithms
                 and Problems; F.2.1 Computations on matrices; I.1.2
                 Algorithms; I.1.2 Algebraic algorithms; I.1.2
                 Algorithms; I.1.2 Analysis of algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations; Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms; Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12475",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}


bibtype: article
filename: elefunt.bib
label: Kraaikamp:1989:SEP
author: Cor Kraaikamp
title: Statistic and ergodic properties of Minkowski's diagonal continued fraction
journal: j-THEOR-COMP-SCI
volume: 65
number: 2
pages: 197--212
day: 28
month: jun
monthnumber: 6
year: 1989
CODEN: TCSCDI
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Theoretical Computer Science
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
affiliation: Amsterdam Univ., Amsterdam, The Netherlands and Univ. de Provence, Marseille, France
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Cor Kraaikamp
rawtitle: Statistic and ergodic properties of {Minkowski}'s diagonal continued fraction
entry:
@Article{Kraaikamp:1989:SEP,
  author =       "Cor Kraaikamp",
  title =        "Statistic and ergodic properties of {Minkowski}'s
                 diagonal continued fraction",
  journal =      j-THEOR-COMP-SCI,
  volume =       "65",
  number =       "2",
  pages =        "197--212",
  day =          "28",
  month =        jun,
  year =         "1989",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Amsterdam Univ., Amsterdam, The Netherlands and Univ.
                 de Provence, Marseille, France",
  bibno =        "70095",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Theoretical Computer Science",
  genterm =      "algorithms; theory",
  guideno =      "1989-10594",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  journalabbrev = "Theor. Comput. Sci.",
  jrldate =      "28 June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Kreider:1989:WSA
author: K. L. Kreider
title: A wave splitting approach to time dependent inverse scattering for the stratified cylinder
journal: j-SIAM-J-APPL-MATH
volume: 49
number: 3
pages: 932--943
month: jun
monthnumber: 6
year: 1989
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: K. L. Kreider
rawtitle: A wave splitting approach to time dependent inverse scattering for the stratified cylinder
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

entry:
@Article{Kreider:1989:WSA,
  author =       "K. L. Kreider",
  title =        "A wave splitting approach to time dependent inverse
                 scattering for the stratified cylinder",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "932--943",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64953",
  catcode =      "G.1.7; G.1.2; J.2; J.2; F.2.2; G.1.3; I.1.1",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7 Initial
                 value problems; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; J.2 Physics; J.2 Electronics;
                 F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Geometrical problems and computations; G.1.3 Numerical
                 Linear Algebra; G.1.3 Linear systems (direct and
                 iterative methods); I.1.1 Expressions and Their
                 Representation; I.1.1 Simplification of expressions",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Initial value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Electronics; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods);
                 Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation; measurement",
  guideno =      "1989-09722",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I.
                 Computing Methodologies; I.1 ALGEBRAIC MANIPULATION",
}


bibtype: article
filename: elefunt.bib
label: Lin:1989:ANT
author: Jinn Tyan Lin
title: Approximating the normal tail probability and its inverse for use on a pocket calculator
journal: j-APPL-STAT
volume: 38
number: 1
pages: 69--70
year: 1989
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
MRclass: 62E15
MRnumber: 983 303
bibdate: Sat Apr 21 10:25:25 MDT 2001
bibtimestamp: 2001.04.21 10:25:25 MDT
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: Jinn Tyan Lin
rawtitle: Approximating the normal tail probability and its inverse for use on a pocket calculator
bibsource:
https://www.math.utah.edu/pub/tex/bib/as1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

entry:
@Article{Lin:1989:ANT,
  author =       "Jinn Tyan Lin",
  title =        "Approximating the normal tail probability and its
                 inverse for use on a pocket calculator",
  journal =      j-APPL-STAT,
  volume =       "38",
  number =       "1",
  pages =        "69--70",
  year =         "1989",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  MRclass =      "62E15",
  MRnumber =     "983 303",
  bibdate =      "Sat Apr 21 10:25:25 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: phdthesis
filename: elefunt.bib
label: Littlestone:1989:MBL
author: N. Littlestone
title: Mistake bounds and logarithmic linear-threshold learning algorithms
type: Ph.D Thesis
school: University of California at Santa Cruz
address: Santa Cruz, CA, USA
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
rawauthor: N. Littlestone
rawtitle: Mistake bounds and logarithmic linear-threshold learning algorithms
subject:
I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@PhdThesis{Littlestone:1989:MBL,
  author =       "N. Littlestone",
  title =        "Mistake bounds and logarithmic linear-threshold
                 learning algorithms",
  type =         "{Ph.D} Thesis",
  school =       "University of California at Santa Cruz",
  address =      "Santa Cruz, CA, USA",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "76493",
  catcode =      "I.2.6; J.4; H.1.2; G.1.2",
  CRclass =      "I.2.6 Learning; J.4 Psychology; H.1.2 User/Machine
                 Systems; H.1.2 Human information processing; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Learning; Computer Applications, SOCIAL AND BEHAVIORAL
                 SCIENCES, Psychology; Information Systems, MODELS AND
                 PRINCIPLES, User/Machine Systems, Human information
                 processing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; human factors; performance",
  guideno =      "1989-12934",
  source =       "UMI Order No: GAX89-26506",
  subject =      "I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND
                 BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS
                 AND PRINCIPLES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Lo:1989:RBP
author: Shaw-Hwa Lo and Jane-Ling Wang
title: Representations for the bivariate product limit estimators and the bootstrap versions
journal: j-J-MULTIVAR-ANAL
volume: 28
number: 2
pages: 211--226
month: feb
monthnumber: 2
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.3 PROBABILITY AND STATISTICS
acknowledgement: ack-nhfb
affiliation: Univ. of California, Davis; Univ. of California, Davis
rawauthor: Shaw-Hwa Lo and Jane-Ling Wang
rawtitle: Representations for the bivariate product limit estimators and the bootstrap versions
entry:
@Article{Lo:1989:RBP,
  author =       "Shaw-Hwa Lo and Jane-Ling Wang",
  title =        "Representations for the bivariate product limit
                 estimators and the bootstrap versions",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "211--226",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California, Davis; Univ. of California,
                 Davis",
  bibno =        "64339",
  catcode =      "G.3; G.1.2; G.1.4; G.1.7",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.4 Quadrature and
                 Numerical Differentiation; G.1.4 Gaussian quadrature;
                 G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Gaussian quadrature; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Convergence and stability",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08465",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.3 PROBABILITY AND STATISTICS",
}


bibtype: article
filename: elefunt.bib
label: Lorentz:1989:NA
author: G. G. Lorentz
title: Notes on approximation
journal: j-J-APPROX-THEORY
volume: 56
number: 3
pages: 360--365
month: mar
monthnumber: 3
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: G. G. Lorentz
rawtitle: Notes on approximation
entry:
@Article{Lorentz:1989:NA,
  author =       "G. G. Lorentz",
  title =        "Notes on approximation",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "360--365",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72258",
  catcode =      "G.1.1; G.1.2; G.1.1",
  CRclass =      "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.1 Interpolation; G.1.1 Spline and piecewise
                 polynomial interpolation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Smoothing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07816",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: incollection
filename: elefunt.bib
label: Lovelace:1989:SAE
author: Augusta Ada Lovelace
title: Sketch of the Analytical Engine (1843)
crossref: Campbell-Kelly:1989:WCB-3
pages: 89--170
year: 1989
bibdate: Tue Jan 22 17:54:41 2013
bibtimestamp: 2013.01.22 17:54:41 ???
keywords: Bernoulli numbers
acknowledgement: ack-nhfb
rawauthor: Augusta Ada Lovelace
rawtitle: Sketch of the {Analytical Engine} (1843)
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Lovelace:1989:SAE,
  author =       "Augusta Ada Lovelace",
  title =        "Sketch of the {Analytical Engine} (1843)",
  crossref =     "Campbell-Kelly:1989:WCB-3",
  pages =        "89--170",
  year =         "1989",
  bibdate =      "Tue Jan 22 17:54:41 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bernoulli numbers",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lu:1989:VMI
author: P. Y. Lu and K. Dawallu
title: A VLSI Module for IEEE Floating-Point Multiplication / Division / Square Root
crossref: IEEE:1989:PII
pages: 366--368
year: 1989
bibdate: Wed Nov 06 12:08:38 2002
bibtimestamp: 2002.11.06 12:08:38 ???
acknowledgement: ack-nhfb
affiliation: LSI Logic Corp., Menlo Park, CA, USA
bookpages: xvii + 587
rawauthor: P. Y. Lu and K. Dawallu
rawtitle: A {VLSI} Module for {IEEE} Floating-Point Multiplication\slash Division\slash Square Root
abstract:
The major objective of this VLSI module design is to determine how to modify a fast floating-point multiplier so that it can perform division and square root in accordance with IEEE standards. This has been achieved by applying the Newton-Ralphson iteration only on the mantissa and adjusting the iterated result by a rounding algorithm. Using 1.0- mu m CMOS standard cell technology, the total area of this module is approximately 7.0 mm*6.5 mm, which is just 25% larger than the floating-point multiplier. The module can compute multiplication, division, and square root in 3, 31, and 43 cycles, respectively. The cycle time, under nominal conditions, is expected to be 20 ns. (2 Refs.)

keywords:
1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell technology; Cycle time; Fast floating-point multiplier; Floating point division; Floating point square root; IEEE standards; Iterated result; Mantissa; Multiplier modification; Newton-Ralphson iteration; Rounding algorithm; VLSI module design

thesaurus:
Cellular arrays; CMOS integrated circuits; Digital arithmetic; Dividing circuits; Iterative methods; Modules; Multiplying circuits; VLSI

rawabstract:
The major objective of this VLSI module design is to determine how to modify a fast floating-point multiplier so that it can perform division and square root in accordance with IEEE standards. This has been achieved by applying the Newton-Ralphson iteration only on the mantissa and adjusting the iterated result by a rounding algorithm. Using 1.0- mu m CMOS standard cell technology, the total area of this module is approximately 7.0 mm*6.5 mm, which is just 25\% larger than the floating-point multiplier. The module can compute multiplication, division, and square root in 3, 31, and 43 cycles, respectively. The cycle time, under nominal conditions, is expected to be 20 ns. (2 Refs.)

entry:
@InProceedings{Lu:1989:VMI,
  author =       "P. Y. Lu and K. Dawallu",
  title =        "A {VLSI} Module for {IEEE} Floating-Point
                 Multiplication\slash Division\slash Square Root",
  crossref =     "IEEE:1989:PII",
  bookpages =    "xvii + 587",
  pages =        "366--368",
  year =         "1989",
  bibdate =      "Wed Nov 06 12:08:38 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The major objective of this VLSI module design is to
                 determine how to modify a fast floating-point
                 multiplier so that it can perform division and square
                 root in accordance with IEEE standards. This has been
                 achieved by applying the Newton-Ralphson iteration only
                 on the mantissa and adjusting the iterated result by a
                 rounding algorithm. Using 1.0- mu m CMOS standard cell
                 technology, the total area of this module is
                 approximately 7.0 mm*6.5 mm, which is just 25\% larger
                 than the floating-point multiplier. The module can
                 compute multiplication, division, and square root in 3,
                 31, and 43 cycles, respectively. The cycle time, under
                 nominal conditions, is expected to be 20 ns. (2
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "LSI Logic Corp., Menlo Park, CA, USA",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5230 (Digital arithmetic methods)",
  keywords =     "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
                 technology; Cycle time; Fast floating-point multiplier;
                 Floating point division; Floating point square root;
                 IEEE standards; Iterated result; Mantissa; Multiplier
                 modification; Newton-Ralphson iteration; Rounding
                 algorithm; VLSI module design",
  numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
                 7.0E-03 m",
  thesaurus =    "Cellular arrays; CMOS integrated circuits; Digital
                 arithmetic; Dividing circuits; Iterative methods;
                 Modules; Multiplying circuits; VLSI",
}


bibtype: article
filename: elefunt.bib
label: Macleod:1989:SAA
author: Allan J. Macleod
journal: j-APPL-STAT
volume: 38
number: 2
pages: 397--402
month: jun
monthnumber: 6
year: 1989
CODEN: APSTAG
ISSN: 0035-9254 (print), 1467-9876 (electronic) OR 00359254 (print), 14679876 (electronic)
ISSNL: 0035-9254 OR 00359254
bibdate: Sat Apr 21 10:25:27 MDT 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 2001.04.21 10:25:27 MDT
URL: http://lib.stat.cmu.edu/apstat/245
fjournal: Applied Statistics
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues
rawauthor: Allan J. Macleod
title:
Statistical Algorithms: Algorithm AS 245: a Robust and Reliable Algorithm for the Logarithm of the Gamma Function

rawtitle:
Statistical Algorithms: {Algorithm AS 245}: a Robust and Reliable Algorithm for the Logarithm of the Gamma Function

entry:
@Article{Macleod:1989:SAA,
  author =       "Allan J. Macleod",
  title =        "Statistical Algorithms: {Algorithm AS 245}: a Robust
                 and Reliable Algorithm for the Logarithm of the Gamma
                 Function",
  journal =      j-APPL-STAT,
  volume =       "38",
  number =       "2",
  pages =        "397--402",
  month =        jun,
  year =         "1989",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:25:27 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://lib.stat.cmu.edu/apstat/245",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}


bibtype: inproceedings
filename: elefunt.bib
label: Mansour:1989:CAS
author: Y. Mansour and B. Schieber and P. Tiwari
booktitle: 30th Annual Symposium on Foundations of Computer Science, 1989
title: The complexity of approximating the square root
crossref: IEEE:1989:ASF
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 325--330
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: Y. Mansour and B. Schieber and P. Tiwari
rawbooktitle: 30th Annual Symposium on Foundations of Computer Science, 1989
rawtitle: The complexity of approximating the square root
entry:
@InProceedings{Mansour:1989:CAS,
  author =       "Y. Mansour and B. Schieber and P. Tiwari",
  booktitle =    "30th Annual Symposium on Foundations of Computer
                 Science, 1989",
  title =        "The complexity of approximating the square root",
  crossref =     "IEEE:1989:ASF",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "325--330",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors prove upper and lower bounds for
                 approximately computing the square root using a given
                 set of operations. The bounds are extended to hold for
                 approximating the kth root, for any fixed k. Several
                 tools from approximation \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Martin:1989:TPQ
author: Pablo Martin and Antonio Luis Guerrero
title: Two-point quasi-fractional approximations to the Bessel function $ J_nu (x) $ of fractional order
journal: j-J-COMPUT-PHYS
volume: 85
number: 2
pages: 487--492
month: dec
monthnumber: 12
year: 1989
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(89)90161-7
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:48 MST 2012
bibtimestamp: 2012.01.01 15:59:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999189901617
fjournal: Journal of Computational Physics
remark: This work produces only 3D approximations.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Pablo Martin and Antonio Luis Guerrero
rawtitle:
Two-point quasi-fractional approximations to the {Bessel} function {$ J_\nu (x) $} of fractional order

entry:
@Article{Martin:1989:TPQ,
  author =       "Pablo Martin and Antonio Luis Guerrero",
  title =        "Two-point quasi-fractional approximations to the
                 {Bessel} function {$ J_\nu (x) $} of fractional order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "85",
  number =       "2",
  pages =        "487--492",
  month =        dec,
  year =         "1989",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(89)90161-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:48 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999189901617",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "This work produces only 3D approximations.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Megiddo:1989:POS
author: N. Megiddo
title: Pathways to the optimal set in linear programming
crossref: Megiddo:1989:PMP
pages: 131--158
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
rawauthor: N. Megiddo
rawtitle: Pathways to the optimal set in linear programming
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE

entry:
@InProceedings{Megiddo:1989:POS,
  author =       "N. Megiddo",
  title =        "Pathways to the optimal set in linear programming",
  crossref =     "Megiddo:1989:PMP",
  pages =        "131--158",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74179",
  catcode =      "G.1.6; G.1.2; G.2.2; G.1.2; G.1.5; F.2.1; I.1.2; G.4;
                 G.4",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.2 Graph Theory; G.2.2 Path and circuit problems;
                 G.1.2 Approximation; G.1.2 Spline and piecewise
                 polynomial approximation; G.1.5 Roots of Nonlinear
                 Equations; G.1.5 Iterative methods; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations on
                 matrices; I.1.2 Algorithms; I.1.2 Analysis of
                 algorithms; G.4 Algorithm analysis; G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, DISCRETE MATHEMATICS, Graph Theory, Path and
                 circuit problems; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Spline and piecewise
                 polynomial approximation; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Iterative methods; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
                 Analysis of algorithms; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Efficiency",
  genterm =      "algorithms; performance; theory",
  guideno =      "1989-12481",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
                 G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing;
                 G.4 MATHEMATICAL SOFTWARE",
}


bibtype: phdthesis
filename: elefunt.bib
label: Miler:1989:EEM
author: T. H. Miler
title: Error evaluation of microcomputer intrinsic functions
type: Ph.D Thesis
school: University of Idaho
address: Moscow, ID
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
rawauthor: T. H. Miler
rawtitle: Error evaluation of microcomputer intrinsic functions
subject:
G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING

entry:
@PhdThesis{Miler:1989:EEM,
  author =       "T. H. Miler",
  title =        "Error evaluation of microcomputer intrinsic
                 functions",
  type =         "{Ph.D} Thesis",
  school =       "University of Idaho",
  address =      "Moscow, ID",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "76168",
  catcode =      "G.4; G.1.2; J.2",
  CRclass =      "G.4 Reliability and robustness; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; J.2
                 Mathematics and statistics",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Computer Applications, PHYSICAL SCIENCES
                 AND ENGINEERING, Mathematics and statistics",
  genterm =      "algorithms; reliability",
  guideno =      "1989-12941",
  source =       "UMI order no: GAX89-22813",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING",
}


bibtype: inproceedings
filename: elefunt.bib
label: Montuschi:1989:EIH
author: Paolo Montuschi and Luigi Cinimera
title: On the efficient implementation of higher radix square root algorithms
crossref: Ercegovac:1989:PSC
pages: 154--161
year: 1989
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
URL: http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf
keywords: ARITH-9
acknowledgement: ack-nhfb
rawauthor: Paolo Montuschi and Luigi Cinimera
rawtitle: On the efficient implementation of higher radix square root algorithms
entry:
@InProceedings{Montuschi:1989:EIH,
  author =       "Paolo Montuschi and Luigi Cinimera",
  title =        "On the efficient implementation of higher radix square
                 root algorithms",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "154--161",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "Square root nonrestoring algorithms operating with a
                 radix higher than two (but power of 2) are discussed.
                 Formulas are derived delimiting the feasibility space
                 of the class of algorithms considered as a function of
                 the different parameters. This \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Moshier:1989:MPM
author: Stephen L. B. Moshier
title: Methods and Programs for Mathematical Functions
publisher: pub-ELLIS-HORWOOD
address: pub-ELLIS-HORWOOD:adr
pages: vii + 415
year: 1989
ISBN: 0-7458-0289-3 OR 0745802893
ISBN13: 978-0-7458-0289-3 OR 9780745802893
LCCN: QA331 .M84 1989
MRclass: *65D20, 26-04, 33-04, 65-02, 65C99
bibdate: Thu Sep 01 10:33:40 1994
bibtimestamp: 1994.09.01 10:33:40 ???
URL: http://www.moshier.net/; http://www.netlib.org/cephes
ZMnumber: 0701.65011
acknowledgement: ack-nj
rawauthor: Stephen L. B. Moshier
rawtitle: Methods and Programs for Mathematical Functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

TOC:
Preface / vii 1: Floating Point Arithmetic / 1 1.1 Numeric Data Structures / 1 1.2 Rounding / 5 1.3 Addition and Subtraction / 6 1.4 Multiplication / 7 1.4.1 Long Multiplication in Binary Radix / 8 1.4.2 Multiplication in Word Integer Radix / 8 1.4.3 Fast Multiplication / 9 1.5 Division / 10 1.5.1 Long Division / 10 1.5.2 Division by Taylor Series / 11 1.5.3 Newton--Raphson Division / 11 1.6 C Language / 12 1.7 An Extended Double Arithmetic: ieee.c / 13 1.8 Binary - Decimal Conversion / 46 1.8.1 etoasc.c / 47 1.8.2 asctoe.c / 54 1.9 Analysis of Error / 58 1.9.1 Roundoff and Cancellation / 58 1.9.2 Error Propagation / 60 1.9.3 Error as a Random Variable / 61 1.9.4 Order of Summation / 62 1.10 Complex Arithmetic / 62 1.10.1 cmplx.c / 64 1.10.2 Absolute Value: cabs.c / 67 1.11 Rational Arithmetic / 69 1.11.1 euclid.c / 70 2: Approximation Methods / 75 2.1 Power Series / 75 2.2 Chebyshev Expansions / 76 2.2.1 chbevl.c / 79 2.3 Pade Approximations / 80 2.4 Least Maximum Approximations / 82 2.4.1 Best Polynomial Approximations / 82 2.4.2 Best Rational Approximations / 85 2.4.3 Special Rational Forms / 87 2.5 A Program to Find Best Approximations: remes.c / 88 2.6 Forms of Approximation / 111 2.7 Asymptotic Expansions / 113 2.8 Continued Fractions / 114 2.8.1 Continued Fractions from Recurrences / 115 2.8.2 Recurrences from Differential Equations / 116 2.8.3 Computing Continued Fractions / 117 2.9 Polynomials / 117 2.9.1 polevl.c / 118 2.10 Newton--Raphson Iterations / 119 2.10.1 Division / 120 2.10.2 Exponent Separation / 121 2.10.3 Square Root / 122 2.10.4 sqrt.c / 123 2.10.5 Longhand Square Root / 124 2.10.6 esqrt.c / 124 2.10.7 Cube Root / 126 2.10.8 cbrt.c / 127 3: Software Notes / 129 3.1 Design Strategy / 129 3.2 Testing / 131 3.3 System Utilities / 132 3.3.1 mconf.h / 132 3.3.2 mtherr.c / 134 3.3.3 const.c / 136 3.4 Arithmetic Utilities / 137 3.4.1 efloor.c / 138 3.4.2 efrexp.c / 140 3.4.3 eldexp.c / 140 4: Elementary Functions / 143 4.1 $e^x$ / 143 4.1.1 exp.c / 145 4.2 $ln x$ / 147 4.2.1 log.c / 149 4.3 Argument Transformation for Circular Functions / 152 4.4 Sine and cosine / 153 4.4.1 sin.c / 154 4.4.2 cos.c / 156 4.5 Tangent and Cotangent / 157 4.5.1 tan.c / 158 4.6 Complex Circular Functions / 161 4.7 $sin ^-1 x $ / 162 4.7.1 asin.c / 163 4.8 $cos ^-1 x $ / 165 4.8.1 acos.c / 165 4.9 $tan ^-1 x$ / 166 4.9.1 atan.c / 168 4.9.2 atan2.c / 169 4.10 Complex Inverse Circular Functions / 170 4.11 $sinh x$ / 170 4.11.1 sinh.c / 171 4.12 $cosh x$ / 172 4.12.1 cosh.c / 173 4.13 $tanh x$ / 173 4.13.1 tanh.c / 174 4.14 $sinh ^-1 x $ / 175 4.14.1 asinh.c / 176 4.15 $cosh ^-1 x $ / 177 4.15.1 acosh.c / 178 4.16 $tanh ^-1 x$ / 179 4.16.1 atanh.c / 180 4.17 Power Function / 181 4.17.1 Real Exponent / 182 4.17.2 pow.c / 182 4.17.3 Integer Exponent / 189 4.17.4 powi.c / 190 4.18 Testing / 192 4.19 Single Precision Polynomial Approximations / 193 4.19.1 $cos x$ / 193 4.19.2 $cosh ^-1 x $ / 193 4.19.3 $exp x$ / 196 4.19.4 $ln x$ / 196 4.19.5 $sin x$ / 197 4.19.6 $sin ^-1 x $ / 197 4.19.7 Square Root / 197 4.19.8 $tan x$ / 198 4.19.9 $tan ^-1 x$ / 198 4.19.10 $tanh x$ / 199 4.19.11 $tanh^-1 x$ / 199 5: Probability Distributions and Related Functions / 201 5.1 $n!$ / 202 5.1.1 fac.c / 204 5.2 $Gamma (x)$ / 206 5.2.1 gamma.c / 210 5.2.2 lgam.c / 214 5.3 Incomplete Gamma Integral / 217 5.3.1 igamc.c / 218 5.3.2 igam.c / 220 5.3.3 Functional Inverse of Incomplete Gamma Integral / 221 5.3.4 igami.c / 221 5.4 Gamma Distribution / 222 5.4.1 gdtr c / 222 5.4.2 gdtrc.c / 223 5.5 $chi ^2$ Distribution / 223 5.5.1 chdtrc.c / 224 5.5.2 chdtr.c / 224 5.5.3 chdtrl.c / 224 5.6 Poisson Distribution / 225 5.6.1 pdtrc.c / 225 5.6.2 pdtr.c / 226 5.6.3 pdtri.c / 226 5.7 Beta Function / 227 5.7.1 beta.c / 227 5.8 Incomplete Beta Integral / 229 5.8.1 ibet.c / 231 5.8.2 Functional Inverse of Incomplete Beta Integral / 238 5.9 Beta Distribution / 241 5.9.1 btdtr.c / 241 5.10 Binomial Distribution / 241 5.10.1 bdtrc.c / 242 5.10.2 bdtr.c / 243 5.10.3 bdtri.c / 244 5.11 Negative Binomial Distribution / 244 5.11.1 nbdtr.c / 245 5.11.2 nbdtrc.c / 245 5.12 F Distribution / 246 5.12.1 fdtrc.c / 247 5.12.2 fdtr.c / 247 5.12.3 fdtrci.c / 248 5.13 Student's $t$ distribution / 249 5.13.1 stdtr.c / 250 5.14 Gaussian Distribution / 252 5.14.1 ndtr.c / 254 5.14.2 erfc.c / 256 5.14.3 erf.c / 257 5.14.4 Functional Inverse of Gaussian Distribution / 258 5.14.5 ndtri.c / 259 6: Bessel Functions / 263 6.1 $J_0(x)$ / 263 6.1.1 jO.c / 265 6.2 $Y_0(x)$ / 268 6.2.1 yO.c / 269 6.3 Modulus and Phase / 270 6.4 $J_1(x)$ / 271 6.4.1 jl.c / 272 6.5 $Y_1(x)$ / 275 6.5.1 yl.c / 275 6.6 $J_n(x)$ / 276 6.1 $I_0(x)$ / 277 6.7.1 i0.c / 278 6.8 $I_1(x)$ / 281 6.8.1 i1.c / 283 6.9 $I_nu (x)$ / 285 6.9.1 iv.c / 286 6.10 $K_0(x)$ / 287 6.10.1 kO.c / 287 6.11 $K_1(x)$ / 291 6.11.1 kl.c / 291 6.12 $K_n(x)$ / 294 6.12.1 kn.c / 295 6.13 $J_nu (x)$ / 299 6.13.1 jv.c / 301 6.14 Airy Functions / 315 6.14.1 airy.c / 322 6.15 $Y_n(x)$ / 328 6.15.1 yn.c / 329 6.16 Testing / 330 7: Other Special Functions / 333 7.1 Hypergeometric Functions / 333 7.1.1 $_2F_1$ / 334 7.1.2 hyp2fi.c / 335 7.1.3 $_1F_1$ / 341 7.1.4 hyplfi.c / 342 7.1.5 $_2F_0$ / 346 7.1.6 hyp2ffi.c / 346 7.2 Struve Functions / 348 7.2.1 hypl1f2.c / 348 7.2.2 hyp3f0.c / 349 7.2.3 yv.c / 351 7.2.4 struve.c / 351 7.3 $psi (x)$ / 352 7.3.1 psi.c / 354 7.4 Exponential Integral / 355 7.4.1 en.c / 356 7.5 Sine and Cosine Integrals / 360 7.5.1 sici.c / 362 7.5.2 Hyperbolic Sine and Cosine Integrals / 367 7.5.3 shichi.c / 370 7.6 Dilogarithm / 374 7.6.1 spence.c / 375 7.7 Dawson's Integral / 377 7.7.1 dawsn.c / 378 7.8 Fresnel Integrals / 381 7.8.1 fresnl.c / 383 7.9 Elliptic Functions / 387 7.9.1 $K(m)$ / 387 7.9.2 ellpk.c / 388 7.9.3 $F(phi |m)$ / 389 7.9.4 ellik.c / 390 7.9.5 $E(m)$ / 392 7.9.6 ellpe.c / 392 7.9.7 $E(phi |m)$ / 393 7.9.8 ellie.c / 394 7.9.9 Jacobian Elliptic Functions / 396 7.9.10 ellpj.c / 398 7.10 Zeta Functions / 400 7.10.1 hurwiz.c / 400 7.10.2 Riemann Zeta Function / 402 7.10.3 zetac.c / 405 Bibliography / 411 Index / 413

shortTOC:
Preface / vii 1: Floating Point Arithmetic / 1 2: Approximation Methods / 75 3: Software Notes / 129 4: Elementary Functions / 143 5: Probability Distributions and Related Functions / 201 6: Bessel Functions / 263 7: Other Special Functions / 333 Bibliography / 411 Index / 413

rawshortTOC:
Preface / vii \\ 1: Floating Point Arithmetic / 1 \\ 2: Approximation Methods / 75 \\ 3: Software Notes / 129 \\ 4: Elementary Functions / 143 \\ 5: Probability Distributions and Related Functions / 201 \\ 6: Bessel Functions / 263 \\ 7: Other Special Functions / 333 \\ Bibliography / 411 \\ Index / 413

rawTOC:
Preface / vii \\ 1: Floating Point Arithmetic / 1 \\ 1.1 Numeric Data Structures / 1 \\ 1.2 Rounding / 5 \\ 1.3 Addition and Subtraction / 6 \\ 1.4 Multiplication / 7 \\ 1.4.1 Long Multiplication in Binary Radix / 8 \\ 1.4.2 Multiplication in Word Integer Radix / 8 \\ 1.4.3 Fast Multiplication / 9 \\ 1.5 Division / 10 \\ 1.5.1 Long Division / 10 \\ 1.5.2 Division by Taylor Series / 11 \\ 1.5.3 Newton--Raphson Division / 11 \\ 1.6 C Language / 12 \\ 1.7 An Extended Double Arithmetic: ieee.c / 13 \\ 1.8 Binary - Decimal Conversion / 46 \\ 1.8.1 etoasc.c / 47 \\ 1.8.2 asctoe.c / 54 \\ 1.9 Analysis of Error / 58 \\ 1.9.1 Roundoff and Cancellation / 58 \\ 1.9.2 Error Propagation / 60 \\ 1.9.3 Error as a Random Variable / 61 \\ 1.9.4 Order of Summation / 62 \\ 1.10 Complex Arithmetic / 62 \\ 1.10.1 cmplx.c / 64 \\ 1.10.2 Absolute Value: cabs.c / 67 \\ 1.11 Rational Arithmetic / 69 \\ 1.11.1 euclid.c / 70 \\ 2: Approximation Methods / 75 \\ 2.1 Power Series / 75 \\ 2.2 Chebyshev Expansions / 76 \\ 2.2.1 chbevl.c / 79 \\ 2.3 Pad{\'e} Approximations / 80 \\ 2.4 Least Maximum Approximations / 82 \\ 2.4.1 Best Polynomial Approximations / 82 \\ 2.4.2 Best Rational Approximations / 85 \\ 2.4.3 Special Rational Forms / 87 \\ 2.5 A Program to Find Best Approximations: remes.c / 88 \\ 2.6 Forms of Approximation / 111 \\ 2.7 Asymptotic Expansions / 113 \\ 2.8 Continued Fractions / 114 \\ 2.8.1 Continued Fractions from Recurrences / 115 \\ 2.8.2 Recurrences from Differential Equations / 116 \\ 2.8.3 Computing Continued Fractions / 117 \\ 2.9 Polynomials / 117 \\ 2.9.1 polevl.c / 118 \\ 2.10 Newton--Raphson Iterations / 119 \\ 2.10.1 Division / 120 \\ 2.10.2 Exponent Separation / 121 \\ 2.10.3 Square Root / 122 \\ 2.10.4 sqrt.c / 123 \\ 2.10.5 Longhand Square Root / 124 \\ 2.10.6 esqrt.c / 124 \\ 2.10.7 Cube Root / 126 \\ 2.10.8 cbrt.c / 127 \\ 3: Software Notes / 129 \\ 3.1 Design Strategy / 129 \\ 3.2 Testing / 131 \\ 3.3 System Utilities / 132 \\ 3.3.1 mconf.h / 132 \\ 3.3.2 mtherr.c / 134 \\ 3.3.3 const.c / 136 \\ 3.4 Arithmetic Utilities / 137 \\ 3.4.1 efloor.c / 138 \\ 3.4.2 efrexp.c / 140 \\ 3.4.3 eldexp.c / 140 \\ 4: Elementary Functions / 143 \\ 4.1 $e^x$ / 143 \\ 4.1.1 exp.c / 145 \\ 4.2 $\ln x$ / 147 \\ 4.2.1 log.c / 149 \\ 4.3 Argument Transformation for Circular Functions / 152 \\ 4.4 Sine and cosine / 153 \\ 4.4.1 sin.c / 154 \\ 4.4.2 cos.c / 156 \\ 4.5 Tangent and Cotangent / 157 \\ 4.5.1 tan.c / 158 \\ 4.6 Complex Circular Functions / 161 \\ 4.7 $\sin^{-1} x $ / 162 \\ 4.7.1 asin.c / 163 \\ 4.8 $\cos^{-1} x $ / 165 \\ 4.8.1 acos.c / 165 \\ 4.9 $\tan^{-1} x$ / 166 \\ 4.9.1 atan.c / 168 \\ 4.9.2 atan2.c / 169 \\ 4.10 Complex Inverse Circular Functions / 170 \\ 4.11 $\sinh x$ / 170 \\ 4.11.1 sinh.c / 171 \\ 4.12 $\cosh x$ / 172 \\ 4.12.1 cosh.c / 173 \\ 4.13 $\tanh x$ / 173 \\ 4.13.1 tanh.c / 174 \\ 4.14 $\sinh^{-1} x $ / 175 \\ 4.14.1 asinh.c / 176 \\ 4.15 $\cosh^{-1} x $ / 177 \\ 4.15.1 acosh.c / 178 \\ 4.16 $\tanh^{-1} x$ / 179 \\ 4.16.1 atanh.c / 180 \\ 4.17 Power Function / 181 \\ 4.17.1 Real Exponent / 182 \\ 4.17.2 pow.c / 182 \\ 4.17.3 Integer Exponent / 189 \\ 4.17.4 powi.c / 190 \\ 4.18 Testing / 192 \\ 4.19 Single Precision Polynomial Approximations / 193 \\ 4.19.1 $\cos x$ / 193 \\ 4.19.2 $\cosh^{-1} x $ / 193 \\ 4.19.3 $\exp x$ / 196 \\ 4.19.4 $\ln x$ / 196 \\ 4.19.5 $\sin x$ / 197 \\ 4.19.6 $\sin^{-1} x $ / 197 \\ 4.19.7 Square Root / 197 \\ 4.19.8 $\tan x$ / 198 \\ 4.19.9 $\tan^{-1} x$ / 198 \\ 4.19.10 $\tanh x$ / 199 \\ 4.19.11 $tanh^{-1} x$ / 199 \\ 5: Probability Distributions and Related Functions / 201 \\ 5.1 $n!$ / 202 \\ 5.1.1 fac.c / 204 \\ 5.2 $\Gamma(x)$ / 206 \\ 5.2.1 gamma.c / 210 \\ 5.2.2 lgam.c / 214 \\ 5.3 Incomplete Gamma Integral / 217 \\ 5.3.1 igamc.c / 218 \\ 5.3.2 igam.c / 220 \\ 5.3.3 Functional Inverse of Incomplete Gamma Integral / 221 \\ 5.3.4 igami.c / 221 \\ 5.4 Gamma Distribution / 222 \\ 5.4.1 gdtr c / 222 \\ 5.4.2 gdtrc.c / 223 \\ 5.5 $\chi^2$ Distribution / 223 \\ 5.5.1 chdtrc.c / 224 \\ 5.5.2 chdtr.c / 224 \\ 5.5.3 chdtrl.c / 224 \\ 5.6 Poisson Distribution / 225 \\ 5.6.1 pdtrc.c / 225 \\ 5.6.2 pdtr.c / 226 \\ 5.6.3 pdtri.c / 226 \\ 5.7 Beta Function / 227 \\ 5.7.1 beta.c / 227 \\ 5.8 Incomplete Beta Integral / 229 \\ 5.8.1 ibet.c / 231 \\ 5.8.2 Functional Inverse of Incomplete Beta Integral / 238 \\ 5.9 Beta Distribution / 241 \\ 5.9.1 btdtr.c / 241 \\ 5.10 Binomial Distribution / 241 \\ 5.10.1 bdtrc.c / 242 \\ 5.10.2 bdtr.c / 243 \\ 5.10.3 bdtri.c / 244 \\ 5.11 Negative Binomial Distribution / 244 \\ 5.11.1 nbdtr.c / 245 \\ 5.11.2 nbdtrc.c / 245 \\ 5.12 F Distribution / 246 \\ 5.12.1 fdtrc.c / 247 \\ 5.12.2 fdtr.c / 247 \\ 5.12.3 fdtrci.c / 248 \\ 5.13 Student's $t$ distribution / 249 \\ 5.13.1 stdtr.c / 250 \\ 5.14 Gaussian Distribution / 252 \\ 5.14.1 ndtr.c / 254 \\ 5.14.2 erfc.c / 256 \\ 5.14.3 erf.c / 257 \\ 5.14.4 Functional Inverse of Gaussian Distribution / 258 \\ 5.14.5 ndtri.c / 259 \\ 6: Bessel Functions / 263 \\ 6.1 $J_0(x)$ / 263 \\ 6.1.1 jO.c / 265 \\ 6.2 $Y_0(x)$ / 268 \\ 6.2.1 yO.c / 269 \\ 6.3 Modulus and Phase / 270 \\ 6.4 $J_1(x)$ / 271 \\ 6.4.1 jl.c / 272 \\ 6.5 $Y_1(x)$ / 275 \\ 6.5.1 yl.c / 275 \\ 6.6 $J_n(x)$ / 276 \\ 6.1 $I_0(x)$ / 277 \\ 6.7.1 i0.c / 278 \\ 6.8 $I_1(x)$ / 281 \\ 6.8.1 i1.c / 283 \\ 6.9 $I_\nu(x)$ / 285 \\ 6.9.1 iv.c / 286 \\ 6.10 $K_0(x)$ / 287 \\ 6.10.1 kO.c / 287 \\ 6.11 $K_1(x)$ / 291 \\ 6.11.1 kl.c / 291 \\ 6.12 $K_n(x)$ / 294 \\ 6.12.1 kn.c / 295 \\ 6.13 $J_\nu(x)$ / 299 \\ 6.13.1 jv.c / 301 \\ 6.14 Airy Functions / 315 \\ 6.14.1 airy.c / 322 \\ 6.15 $Y_n(x)$ / 328 \\ 6.15.1 yn.c / 329 \\ 6.16 Testing / 330 \\ 7: Other Special Functions / 333 \\ 7.1 Hypergeometric Functions / 333 \\ 7.1.1 $_2F_1$ / 334 \\ 7.1.2 hyp2fi.c / 335 \\ 7.1.3 $_1F_1$ / 341 \\ 7.1.4 hyplfi.c / 342 \\ 7.1.5 $_2F_0$ / 346 \\ 7.1.6 hyp2ffi.c / 346 \\ 7.2 Struve Functions / 348 \\ 7.2.1 hypl1f2.c / 348 \\ 7.2.2 hyp3f0.c / 349 \\ 7.2.3 yv.c / 351 \\ 7.2.4 struve.c / 351 \\ 7.3 $\psi(x)$ / 352 \\ 7.3.1 psi.c / 354 \\ 7.4 Exponential Integral / 355 \\ 7.4.1 en.c / 356 \\ 7.5 Sine and Cosine Integrals / 360 \\ 7.5.1 sici.c / 362 \\ 7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\ 7.5.3 shichi.c / 370 \\ 7.6 Dilogarithm / 374 \\ 7.6.1 spence.c / 375 \\ 7.7 Dawson's Integral / 377 \\ 7.7.1 dawsn.c / 378 \\ 7.8 Fresnel Integrals / 381 \\ 7.8.1 fresnl.c / 383 \\ 7.9 Elliptic Functions / 387 \\ 7.9.1 $K(m)$ / 387 \\ 7.9.2 ellpk.c / 388 \\ 7.9.3 $F(\phi|m)$ / 389 \\ 7.9.4 ellik.c / 390 \\ 7.9.5 $E(m)$ / 392 \\ 7.9.6 ellpe.c / 392 \\ 7.9.7 $E(\phi|m)$ / 393 \\ 7.9.8 ellie.c / 394 \\ 7.9.9 Jacobian Elliptic Functions / 396 \\ 7.9.10 ellpj.c / 398 \\ 7.10 Zeta Functions / 400 \\ 7.10.1 hurwiz.c / 400 \\ 7.10.2 Riemann Zeta Function / 402 \\ 7.10.3 zetac.c / 405 \\ Bibliography / 411 \\ Index / 413

entry:
@Book{Moshier:1989:MPM,
  author =       "Stephen L. B. Moshier",
  title =        "Methods and Programs for Mathematical Functions",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "vii + 415",
  year =         "1989",
  ISBN =         "0-7458-0289-3",
  ISBN-13 =      "978-0-7458-0289-3",
  LCCN =         "QA331 .M84 1989",
  MRclass =      "*65D20, 26-04, 33-04, 65-02, 65C99",
  bibdate =      "Thu Sep 01 10:33:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\pounds 48.00",
  URL =          "http://www.moshier.net/;
                 http://www.netlib.org/cephes",
  ZMnumber =     "0701.65011",
  acknowledgement = ack-nj,
  shorttableofcontents = "Preface / vii \\
                 1: Floating Point Arithmetic / 1 \\
                 2: Approximation Methods / 75 \\
                 3: Software Notes / 129 \\
                 4: Elementary Functions / 143 \\
                 5: Probability Distributions and Related Functions /
                 201 \\
                 6: Bessel Functions / 263 \\
                 7: Other Special Functions / 333 \\
                 Bibliography / 411 \\
                 Index / 413",
  tableofcontents = "Preface / vii \\
                 1: Floating Point Arithmetic / 1 \\
                 1.1 Numeric Data Structures / 1 \\
                 1.2 Rounding / 5 \\
                 1.3 Addition and Subtraction / 6 \\
                 1.4 Multiplication / 7 \\
                 1.4.1 Long Multiplication in Binary Radix / 8 \\
                 1.4.2 Multiplication in Word Integer Radix / 8 \\
                 1.4.3 Fast Multiplication / 9 \\
                 1.5 Division / 10 \\
                 1.5.1 Long Division / 10 \\
                 1.5.2 Division by Taylor Series / 11 \\
                 1.5.3 Newton--Raphson Division / 11 \\
                 1.6 C Language / 12 \\
                 1.7 An Extended Double Arithmetic: ieee.c / 13 \\
                 1.8 Binary - Decimal Conversion / 46 \\
                 1.8.1 etoasc.c / 47 \\
                 1.8.2 asctoe.c / 54 \\
                 1.9 Analysis of Error / 58 \\
                 1.9.1 Roundoff and Cancellation / 58 \\
                 1.9.2 Error Propagation / 60 \\
                 1.9.3 Error as a Random Variable / 61 \\
                 1.9.4 Order of Summation / 62 \\
                 1.10 Complex Arithmetic / 62 \\
                 1.10.1 cmplx.c / 64 \\
                 1.10.2 Absolute Value: cabs.c / 67 \\
                 1.11 Rational Arithmetic / 69 \\
                 1.11.1 euclid.c / 70 \\
                 2: Approximation Methods / 75 \\
                 2.1 Power Series / 75 \\
                 2.2 Chebyshev Expansions / 76 \\
                 2.2.1 chbevl.c / 79 \\
                 2.3 Pad{\'e} Approximations / 80 \\
                 2.4 Least Maximum Approximations / 82 \\
                 2.4.1 Best Polynomial Approximations / 82 \\
                 2.4.2 Best Rational Approximations / 85 \\
                 2.4.3 Special Rational Forms / 87 \\
                 2.5 A Program to Find Best Approximations: remes.c / 88
                 \\
                 2.6 Forms of Approximation / 111 \\
                 2.7 Asymptotic Expansions / 113 \\
                 2.8 Continued Fractions / 114 \\
                 2.8.1 Continued Fractions from Recurrences / 115 \\
                 2.8.2 Recurrences from Differential Equations / 116 \\
                 2.8.3 Computing Continued Fractions / 117 \\
                 2.9 Polynomials / 117 \\
                 2.9.1 polevl.c / 118 \\
                 2.10 Newton--Raphson Iterations / 119 \\
                 2.10.1 Division / 120 \\
                 2.10.2 Exponent Separation / 121 \\
                 2.10.3 Square Root / 122 \\
                 2.10.4 sqrt.c / 123 \\
                 2.10.5 Longhand Square Root / 124 \\
                 2.10.6 esqrt.c / 124 \\
                 2.10.7 Cube Root / 126 \\
                 2.10.8 cbrt.c / 127 \\
                 3: Software Notes / 129 \\
                 3.1 Design Strategy / 129 \\
                 3.2 Testing / 131 \\
                 3.3 System Utilities / 132 \\
                 3.3.1 mconf.h / 132 \\
                 3.3.2 mtherr.c / 134 \\
                 3.3.3 const.c / 136 \\
                 3.4 Arithmetic Utilities / 137 \\
                 3.4.1 efloor.c / 138 \\
                 3.4.2 efrexp.c / 140 \\
                 3.4.3 eldexp.c / 140 \\
                 4: Elementary Functions / 143 \\
                 4.1 $e^x$ / 143 \\
                 4.1.1 exp.c / 145 \\
                 4.2 $\ln x$ / 147 \\
                 4.2.1 log.c / 149 \\
                 4.3 Argument Transformation for Circular Functions /
                 152 \\
                 4.4 Sine and cosine / 153 \\
                 4.4.1 sin.c / 154 \\
                 4.4.2 cos.c / 156 \\
                 4.5 Tangent and Cotangent / 157 \\
                 4.5.1 tan.c / 158 \\
                 4.6 Complex Circular Functions / 161 \\
                 4.7 $\sin^{-1} x $ / 162 \\
                 4.7.1 asin.c / 163 \\
                 4.8 $\cos^{-1} x $ / 165 \\
                 4.8.1 acos.c / 165 \\
                 4.9 $\tan^{-1} x$ / 166 \\
                 4.9.1 atan.c / 168 \\
                 4.9.2 atan2.c / 169 \\
                 4.10 Complex Inverse Circular Functions / 170 \\
                 4.11 $\sinh x$ / 170 \\
                 4.11.1 sinh.c / 171 \\
                 4.12 $\cosh x$ / 172 \\
                 4.12.1 cosh.c / 173 \\
                 4.13 $\tanh x$ / 173 \\
                 4.13.1 tanh.c / 174 \\
                 4.14 $\sinh^{-1} x $ / 175 \\
                 4.14.1 asinh.c / 176 \\
                 4.15 $\cosh^{-1} x $ / 177 \\
                 4.15.1 acosh.c / 178 \\
                 4.16 $\tanh^{-1} x$ / 179 \\
                 4.16.1 atanh.c / 180 \\
                 4.17 Power Function / 181 \\
                 4.17.1 Real Exponent / 182 \\
                 4.17.2 pow.c / 182 \\
                 4.17.3 Integer Exponent / 189 \\
                 4.17.4 powi.c / 190 \\
                 4.18 Testing / 192 \\
                 4.19 Single Precision Polynomial Approximations / 193
                 \\
                 4.19.1 $\cos x$ / 193 \\
                 4.19.2 $\cosh^{-1} x $ / 193 \\
                 4.19.3 $\exp x$ / 196 \\
                 4.19.4 $\ln x$ / 196 \\
                 4.19.5 $\sin x$ / 197 \\
                 4.19.6 $\sin^{-1} x $ / 197 \\
                 4.19.7 Square Root / 197 \\
                 4.19.8 $\tan x$ / 198 \\
                 4.19.9 $\tan^{-1} x$ / 198 \\
                 4.19.10 $\tanh x$ / 199 \\
                 4.19.11 $tanh^{-1} x$ / 199 \\
                 5: Probability Distributions and Related Functions /
                 201 \\
                 5.1 $n!$ / 202 \\
                 5.1.1 fac.c / 204 \\
                 5.2 $\Gamma(x)$ / 206 \\
                 5.2.1 gamma.c / 210 \\
                 5.2.2 lgam.c / 214 \\
                 5.3 Incomplete Gamma Integral / 217 \\
                 5.3.1 igamc.c / 218 \\
                 5.3.2 igam.c / 220 \\
                 5.3.3 Functional Inverse of Incomplete Gamma Integral /
                 221 \\
                 5.3.4 igami.c / 221 \\
                 5.4 Gamma Distribution / 222 \\
                 5.4.1 gdtr c / 222 \\
                 5.4.2 gdtrc.c / 223 \\
                 5.5 $\chi^2$ Distribution / 223 \\
                 5.5.1 chdtrc.c / 224 \\
                 5.5.2 chdtr.c / 224 \\
                 5.5.3 chdtrl.c / 224 \\
                 5.6 Poisson Distribution / 225 \\
                 5.6.1 pdtrc.c / 225 \\
                 5.6.2 pdtr.c / 226 \\
                 5.6.3 pdtri.c / 226 \\
                 5.7 Beta Function / 227 \\
                 5.7.1 beta.c / 227 \\
                 5.8 Incomplete Beta Integral / 229 \\
                 5.8.1 ibet.c / 231 \\
                 5.8.2 Functional Inverse of Incomplete Beta Integral /
                 238 \\
                 5.9 Beta Distribution / 241 \\
                 5.9.1 btdtr.c / 241 \\
                 5.10 Binomial Distribution / 241 \\
                 5.10.1 bdtrc.c / 242 \\
                 5.10.2 bdtr.c / 243 \\
                 5.10.3 bdtri.c / 244 \\
                 5.11 Negative Binomial Distribution / 244 \\
                 5.11.1 nbdtr.c / 245 \\
                 5.11.2 nbdtrc.c / 245 \\
                 5.12 F Distribution / 246 \\
                 5.12.1 fdtrc.c / 247 \\
                 5.12.2 fdtr.c / 247 \\
                 5.12.3 fdtrci.c / 248 \\
                 5.13 Student's $t$ distribution / 249 \\
                 5.13.1 stdtr.c / 250 \\
                 5.14 Gaussian Distribution / 252 \\
                 5.14.1 ndtr.c / 254 \\
                 5.14.2 erfc.c / 256 \\
                 5.14.3 erf.c / 257 \\
                 5.14.4 Functional Inverse of Gaussian Distribution /
                 258 \\
                 5.14.5 ndtri.c / 259 \\
                 6: Bessel Functions / 263 \\
                 6.1 $J_0(x)$ / 263 \\
                 6.1.1 jO.c / 265 \\
                 6.2 $Y_0(x)$ / 268 \\
                 6.2.1 yO.c / 269 \\
                 6.3 Modulus and Phase / 270 \\
                 6.4 $J_1(x)$ / 271 \\
                 6.4.1 jl.c / 272 \\
                 6.5 $Y_1(x)$ / 275 \\
                 6.5.1 yl.c / 275 \\
                 6.6 $J_n(x)$ / 276 \\
                 6.1 $I_0(x)$ / 277 \\
                 6.7.1 i0.c / 278 \\
                 6.8 $I_1(x)$ / 281 \\
                 6.8.1 i1.c / 283 \\
                 6.9 $I_\nu(x)$ / 285 \\
                 6.9.1 iv.c / 286 \\
                 6.10 $K_0(x)$ / 287 \\
                 6.10.1 kO.c / 287 \\
                 6.11 $K_1(x)$ / 291 \\
                 6.11.1 kl.c / 291 \\
                 6.12 $K_n(x)$ / 294 \\
                 6.12.1 kn.c / 295 \\
                 6.13 $J_\nu(x)$ / 299 \\
                 6.13.1 jv.c / 301 \\
                 6.14 Airy Functions / 315 \\
                 6.14.1 airy.c / 322 \\
                 6.15 $Y_n(x)$ / 328 \\
                 6.15.1 yn.c / 329 \\
                 6.16 Testing / 330 \\
                 7: Other Special Functions / 333 \\
                 7.1 Hypergeometric Functions / 333 \\
                 7.1.1 $_2F_1$ / 334 \\
                 7.1.2 hyp2fi.c / 335 \\
                 7.1.3 $_1F_1$ / 341 \\
                 7.1.4 hyplfi.c / 342 \\
                 7.1.5 $_2F_0$ / 346 \\
                 7.1.6 hyp2ffi.c / 346 \\
                 7.2 Struve Functions / 348 \\
                 7.2.1 hypl1f2.c / 348 \\
                 7.2.2 hyp3f0.c / 349 \\
                 7.2.3 yv.c / 351 \\
                 7.2.4 struve.c / 351 \\
                 7.3 $\psi(x)$ / 352 \\
                 7.3.1 psi.c / 354 \\
                 7.4 Exponential Integral / 355 \\
                 7.4.1 en.c / 356 \\
                 7.5 Sine and Cosine Integrals / 360 \\
                 7.5.1 sici.c / 362 \\
                 7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\
                 7.5.3 shichi.c / 370 \\
                 7.6 Dilogarithm / 374 \\
                 7.6.1 spence.c / 375 \\
                 7.7 Dawson's Integral / 377 \\
                 7.7.1 dawsn.c / 378 \\
                 7.8 Fresnel Integrals / 381 \\
                 7.8.1 fresnl.c / 383 \\
                 7.9 Elliptic Functions / 387 \\
                 7.9.1 $K(m)$ / 387 \\
                 7.9.2 ellpk.c / 388 \\
                 7.9.3 $F(\phi|m)$ / 389 \\
                 7.9.4 ellik.c / 390 \\
                 7.9.5 $E(m)$ / 392 \\
                 7.9.6 ellpe.c / 392 \\
                 7.9.7 $E(\phi|m)$ / 393 \\
                 7.9.8 ellie.c / 394 \\
                 7.9.9 Jacobian Elliptic Functions / 396 \\
                 7.9.10 ellpj.c / 398 \\
                 7.10 Zeta Functions / 400 \\
                 7.10.1 hurwiz.c / 400 \\
                 7.10.2 Riemann Zeta Function / 402 \\
                 7.10.3 zetac.c / 405 \\
                 Bibliography / 411 \\
                 Index / 413",
}


bibtype: article
filename: elefunt.bib
label: Norton:1989:PCA
author: Robert M. Norton
title: Pocket-Calculator Approximation for Areas under the Standard Normal Curve
journal: j-AMER-STAT
volume: 43
number: 1
pages: 24--26
month: feb
monthnumber: 2
year: 1989
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Jan 27 12:40:30 MST 2012
bibtimestamp: 2012.01.27 12:40:30 MST
URL: http://www.jstor.org/stable/2685163
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Robert M. Norton
rawtitle: Pocket-Calculator Approximation for Areas under the Standard Normal Curve
bibsource:
http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326443; https://www.math.utah.edu/pub/tex/bib/amstat1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Norton:1989:PCA,
  author =       "Robert M. Norton",
  title =        "Pocket-Calculator Approximation for Areas under the
                 Standard Normal Curve",
  journal =      j-AMER-STAT,
  volume =       "43",
  number =       "1",
  pages =        "24--26",
  month =        feb,
  year =         "1989",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 12:40:30 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326443;
                 https://www.math.utah.edu/pub/tex/bib/amstat1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2685163",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: elefunt.bib
label: Rhee:1989:MII
author: W. T. Rhee and M. Talagrand
title: Martingale inequalities, interpolation and NP-complete problems
journal: j-MATH-OP-RES
volume: 14
number: 1
pages: 91--96
month: feb
monthnumber: 2
year: 1989
CODEN: MOREDQ
ISSN: 0364-765x (print), 1526-5471 (electronic) OR 0364765x (print), 15265471 (electronic)
ISSNL: 0364-765X OR 0364765X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Mathematics of Operations Research
acknowledgement: ack-nhfb
affiliation: Univ., Paris, Paris, France; Ohio State Univ., Columbus
journalURL: http://pubsonline.informs.org/loi/moor
rawauthor: W. T. Rhee and M. Talagrand
rawtitle: Martingale inequalities, interpolation and {NP}-complete problems
subject:
F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3 PROBABILITY AND STATISTICS; H. Information Systems; H.1 MODELS AND PRINCIPLES; I. Computing Methodologies; I.6 SIMULATION AND MODELING

entry:
@Article{Rhee:1989:MII,
  author =       "W. T. Rhee and M. Talagrand",
  title =        "Martingale inequalities, interpolation and
                 {NP}-complete problems",
  journal =      j-MATH-OP-RES,
  volume =       "14",
  number =       "1",
  pages =        "91--96",
  month =        feb,
  year =         "1989",
  CODEN =        "MOREDQ",
  ISSN =         "0364-765x (print), 1526-5471 (electronic)",
  ISSN-L =       "0364-765X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ., Paris, Paris, France; Ohio State Univ.,
                 Columbus",
  bibno =        "67063",
  catcode =      "G.2.2; H.1.1; G.1.1; G.1.2; G.3; I.6.4; F.1.3",
  CRclass =      "G.2.2 Graph Theory; G.2.2 Path and circuit problems;
                 H.1.1 Systems and Information Theory; H.1.1 General
                 systems theory; G.1.1 Interpolation; G.1.1
                 Interpolation formulas; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.3 Probabilistic
                 algorithms (including Monte Carlo); I.6.4 Model
                 Validation and Analysis; F.1.3 Complexity Classes;
                 F.1.3 Reducibility and completeness",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Path and circuit problems; Information Systems,
                 MODELS AND PRINCIPLES, Systems and Information Theory,
                 General systems theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation, Interpolation
                 formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Probabilistic algorithms (including Monte Carlo);
                 Computing Methodologies, SIMULATION AND MODELING, Model
                 Validation and Analysis; Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Classes,
                 Reducibility and completeness",
  fjournal =     "Mathematics of Operations Research",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-09079",
  journal-URL =  "http://pubsonline.informs.org/loi/moor",
  journalabbrev = "Math. Oper. Res.",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3 PROBABILITY AND
                 STATISTICS; H. Information Systems; H.1 MODELS AND
                 PRINCIPLES; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING",
}


bibtype: article
filename: elefunt.bib
label: Ruymgaart:1989:SPB
author: F. H. Ruymgaart
title: Some properties of bivariate empirical hazard processes under random censoring
journal: j-J-MULTIVAR-ANAL
volume: 28
number: 2
pages: 271--281
month: feb
monthnumber: 2
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
acknowledgement: ack-nhfb
rawauthor: F. H. Ruymgaart
rawtitle: Some properties of bivariate empirical hazard processes under random censoring
subject:
G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Ruymgaart:1989:SPB,
  author =       "F. H. Ruymgaart",
  title =        "Some properties of bivariate empirical hazard
                 processes under random censoring",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "271--281",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64343",
  catcode =      "G.3; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08469",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Rybicki:1989:DIS
author: George B. Rybicki
title: Dawson's Integral and the Sampling Theorem
journal: j-COMPUT-PHYS
volume: 3
number: 2
pages: 85--87
month: mar
monthnumber: 3
year: 1989
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.4822832
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:17 MDT 2019
bibtimestamp: 2019.04.10 08:45:17 MDT
URL: https://aip.scitation.org/doi/10.1063/1.4822832
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: George B. Rybicki
rawtitle: {Dawson}'s Integral and the Sampling Theorem
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Rybicki:1989:DIS,
  author =       "George B. Rybicki",
  title =        "{Dawson}'s Integral and the Sampling Theorem",
  journal =      j-COMPUT-PHYS,
  volume =       "3",
  number =       "2",
  pages =        "85--87",
  month =        mar,
  year =         "1989",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822832",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:17 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822832",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: incollection
filename: elefunt.bib
label: Saigo:1989:FID
author: Megumi Saigo
title: Fractional integrals and derivatives associated with elementary functions and Bessel functions
crossref: Srivastava:1989:UFF
pages: 283--306
year: 1989
MRclass: 26A33 (33C10)
MRnumber: 93h:26011
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
series: Ellis Horwood Ser. Math. Appl.
acknowledgement: ack-nhfb
rawauthor: Megumi Saigo
rawtitle: Fractional integrals and derivatives associated with elementary functions and {Bessel} functions
entry:
@InCollection{Saigo:1989:FID,
  author =       "Megumi Saigo",
  title =        "Fractional integrals and derivatives associated with
                 elementary functions and {Bessel} functions",
  crossref =     "Srivastava:1989:UFF",
  pages =        "283--306",
  year =         "1989",
  MRclass =      "26A33 (33C10)",
  MRnumber =     "93h:26011",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Ellis Horwood Ser. Math. Appl.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Sala:1989:TJA
author: Kenneth L. Sala
journal: j-SIAM-J-MATH-ANA
volume: 20
number: 6
pages: 1514--1528
month: nov
monthnumber: 11
year: 1989
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33A25 (42A16 70D99)
MRnumber: 90j:33003
MRreviewer: J. M. H. Peters
bibdate: Sun Nov 28 19:24:55 MST 2010
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.11.28 19:24:55 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: Kenneth L. Sala
title:
Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean

rawtitle:
Transformations of the {Jacobian} amplitude function and its calculation via the arithmetic-geometric mean

entry:
@Article{Sala:1989:TJA,
  author =       "Kenneth L. Sala",
  title =        "Transformations of the {Jacobian} amplitude function
                 and its calculation via the arithmetic-geometric mean",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "20",
  number =       "6",
  pages =        "1514--1528",
  month =        nov,
  year =         "1989",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A25 (42A16 70D99)",
  MRnumber =     "90j:33003",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Sun Nov 28 19:24:55 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Smith:1989:EMP
author: David M. Smith
title: Efficient multiple-precision evaluation of elementary functions
journal: j-MATH-COMPUT
volume: 52
number: 185
pages: 131--134
month: jan
monthnumber: 1
year: 1989
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D15 (26-04)
MRnumber: 90c:65034
MRreviewer: Menachem Dishon
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: arithmetic; base b; elementary functions; function evaluation; multiple-precision evaluation
acknowledgement: ack-nhfb
classcodes: C4120 (Functional analysis)
corpsource: Dept. of Math., Loyola Univ., Los Angeles, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: David M. Smith
rawtitle: Efficient multiple-precision evaluation of elementary functions
entry:
@Article{Smith:1989:EMP,
  author =       "David M. Smith",
  title =        "Efficient multiple-precision evaluation of elementary
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "52",
  number =       "185",
  pages =        "131--134",
  month =        jan,
  year =         "1989",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D15 (26-04)",
  MRnumber =     "90c:65034",
  MRreviewer =   "Menachem Dishon",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Dept. of Math., Loyola Univ., Los Angeles, CA, USA",
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  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic; base b; elementary functions; function
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  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Stearns:1989:SFD
author: C. C. Stearns
title: Subtractive floating-point division and square root for VLSI DSP
crossref: IEE:1989:EEC
pages: 405--409
year: 1989
bibdate: Tue Dec 12 09:17:24 MST 1995
bibtimestamp: 1995.12.12 09:17:24 MST
acknowledgement: ack-nhfb
rawauthor: C. C. Stearns
rawtitle: Subtractive floating-point division and square root for {VLSI DSP}
abstract:
This paper describes recent architectural developments in VLSI design for real-time digital signal processing. In particular, floating point division and floating point square root architectures applicable to both adaptive filtering, standard deviation computations, and general purpose processing are discussed. Emphasis here is on the internal architectures of the arithmetic units not on their applications. The research presented in this paper has been proven feasible and reliable from extensive gate-level simulation and fabrication in silicon.

keywords:
Adaptive filtering; Arithmetic units; CMOS technology; Floating point division; Floating point square root architectures; Gate-level simulation; General purpose processing; Real-time digital signal processing; Semiconductor; Standard deviation computations; VLSI DSP

thesaurus:
Adaptive filters; CMOS integrated circuits; Digital arithmetic; Digital signal processing chips; VLSI

rawabstract:
This paper describes recent architectural developments in VLSI design for real-time digital signal processing. In particular, floating point division and floating point square root architectures applicable to both adaptive filtering, standard deviation computations, and general purpose processing are discussed. Emphasis here is on the internal architectures of the arithmetic units not on their applications. The research presented in this paper has been proven feasible and reliable from extensive gate-level simulation and fabrication in silicon.

entry:
@InProceedings{Stearns:1989:SFD,
  author =       "C. C. Stearns",
  title =        "Subtractive floating-point division and square root
                 for {VLSI DSP}",
  crossref =     "IEE:1989:EEC",
  pages =        "405--409",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes recent architectural developments
                 in VLSI design for real-time digital signal processing.
                 In particular, floating point division and floating
                 point square root architectures applicable to both
                 adaptive filtering, standard deviation computations,
                 and general purpose processing are discussed. Emphasis
                 here is on the internal architectures of the arithmetic
                 units not on their applications. The research presented
                 in this paper has been proven feasible and reliable
                 from extensive gate-level simulation and fabrication in
                 silicon.",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B1270F
                 (Digital filters); B2570D (CMOS integrated circuits);
                 C5230 (Digital arithmetic methods); C5240 (Digital
                 filters); C5260 (Digital signal processing)",
  keywords =     "Adaptive filtering; Arithmetic units; CMOS technology;
                 Floating point division; Floating point square root
                 architectures; Gate-level simulation; General purpose
                 processing; Real-time digital signal processing;
                 Semiconductor; Standard deviation computations; VLSI
                 DSP",
  thesaurus =    "Adaptive filters; CMOS integrated circuits; Digital
                 arithmetic; Digital signal processing chips; VLSI",
}


bibtype: techreport
filename: elefunt.bib
label: Tang:1989:TCA
author: Ping Tak Peter Tang
title: Testing Computer Arithmetic by Elementary Number Theory
institution: Mathematics and Computer Science Division, Argonne National Laboratory
address: Argonne, IL, USA
month: aug
monthnumber: 8
year: 1989
bibdate: Fri Jun 11 12:38:06 1999
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.06.11 12:38:06 ???
acknowledgement: ack-nj
rawauthor: Ping Tak Peter Tang
rawtitle: Testing Computer Arithmetic by Elementary Number Theory
entry:
@TechReport{Tang:1989:TCA,
  author =       "Ping Tak Peter Tang",
  title =        "Testing Computer Arithmetic by Elementary Number
                 Theory",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "????",
  month =        aug,
  year =         "1989",
  bibdate =      "Fri Jun 11 12:38:06 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Tang:1989:TDI
author: Ping Tak Peter Tang
title: Table-Driven Implementation of the Exponential Function in IEEE Floating-Point Arithmetic
journal: j-TOMS
volume: 15
number: 2
pages: 144--157
month: jun
monthnumber: 6
year: 1989
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 22:47:40 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.04 22:47:40 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Ping Tak Peter Tang
rawtitle: Table-Driven Implementation of the Exponential Function in {IEEE} Floating-Point Arithmetic
URL:
http://doi.acm.org/10.1145/63522.214389; http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/

abstract:
Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.

entry:
@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:47:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/63522.214389;
                 http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
  abstract =     "Algorithms and implementation details for the
                 exponential function in both single- and
                 double-precision of IEEE 754 arithmetic are presented
                 here. With a table of moderate size, the
                 implementations need only working-precision arithmetic
                 and are provably accurate to within 0.54 ulp as long as
                 the final result does not underflow. When the final
                 result suffers gradual underflow, the error is still no
                 worse than 0.77 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}


bibtype: techreport
filename: elefunt.bib
label: Thomas:1989:SNL
author: Marlin A. Thomas and Gary W. Gemmill and John R. Crigler
title: STATLIB: NSWC Library of Statistical Programs and Subroutines
type: Technical Report
number: NSWC TR 89-97
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA and Silver Spring, MD 20903-5000, USA
pages: viii + 280
month: aug
monthnumber: 8
year: 1989
bibdate: Sat Nov 15 10:39:12 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib
bibtimestamp: 2014.11.15 10:39:12 ???
URL: http://www.dtic.mil/dtic/tr/fulltext/u2/a221538.pdf
acknowledgement: ack-nhfb
onlinedate: 255
rawauthor: Marlin A. Thomas and Gary W. Gemmill and John R. Crigler
rawtitle: {STATLIB}: {NSWC} Library of Statistical Programs and Subroutines
abstract:
This document provides a description of each program and subroutine in STATLIB, THE Naval Surface Warfare Center library of statistical programs and subroutines for its general purpose computers. The Library contains thirty-four programs and twenty-four subroutines for statistical analysis, probability evaluation, and random number generation. It was written to enable Center Scientists and Engineers to efficiently perform a wide variety of analyses and to generate pseudo random numbers from many different probability distributions.

TOC:
Introduction / 1 Overview of STATLIB / 1 Origin of STATLIB / 1 Establishment of STATLIB / 1 Commercial Statistical Packages at NSWC / 2 Using STATLIB / 5 Library Organization / 5 How to Call It / 5 Information Needed to Run It / 5 Examples / 9 Program / 9 Subroutine / 10 Descriptions and Input Guides / 21 Programs / 23 Regression Analysis / 25 GEMREG General Multiple Regression / 29 DAMRCA Dahlgren Multiple Regression Comprehensive Analysis / 35 WEPORU Uncorrelated Weighted Polynomial Regression / 41 WEPORC Correlated Weighted Polynomial Regression / 45 MROP Multiple Regression Using Orthogonal Polynomials / 49 CANON Canonical Analysis of Second Order Response Functions / 57 DURBWAT Durbin--Watson Test for Independence of Residuals / 61 NEARNEB Near Neighbor Estimation of Experimental Error / 63 Goodness of Fit Analysis / 67 UNORGOF Univariate Normal Goodness of Fit / 69 BNORGOF Bivariate Normal Goodness of Fit / 75 EXPGOF Exponential Goodness of Fit / 81 WBLGOF Weibull Goodness ot / 83 PERGOF Pearson System Goodness of Fit / 87 UNKSGOF Univariate Normal Kolmogorov--Smirnov Test of Fit / 93 RANDOM Test of Fit for Uniform Random Number Generators / 99 Power Evaluation / 103 DISCRETE POWER EVALUATION / 107 BINIPOW Power of the Test on a Binomial Proportion / 109 BIN2POW Power of the Test on the Difference of Two Binomial Proportions / 113 POIIPOW Power of the Test on the Poisson Parameter / 121 Continuous Power Evaluation / 125 NORIPOW Power of the One-Sample Normal Test on the Mean / 127 NOR2PWE Power of the Two-Simple Normal Test on Means with ample Sizes / 131 NOR2PWU Power of the Two-Sample Normal Test on Means with Unequal Sample Sizes / 135 T1POW Power of the One-Sample $t$ Test on the Mean / 141 T2POW Power of the Two-Sample (Pooled) $t$ Test on Means / 147 CHIVPOW Power of the Chi-square Test on the Variance / 153 FVARPOW Power of the $F$ Test for the Equality of Variances / 157 FEMPOW Power of the Test for One-Way Fixed Effects Analysis of Variance / 163 REMPOW Power of the Test for One-Way Random Effects Analysis of Variance / 167 Probability Evaluation / 171 BINVARP Binomial Probability Distribution with Unequal Single Trial Probabilities / 173 NEGBIN Negative Binomial Probability Distribution / 177 Confidence Limit Evaluation / 179 BINCL Confidence Limits for the Binomial Parameter p / 181 CEPCL Confidence Limits for the CEP (Circular Probable Error) / 185 SEPCL Confidence Limits for the SEP (Spherical Probable Error) / 191 Miscellaneous Statistical Analysis / 197 LD50EST Estimation of LD50 (Lethal Dose 50th Percentile) / 199 FFAC2K Analysis of the 2**k Fractional Factorial Experiment / 203 Subroutines / 211 Random Number Generation / 213 Discrete Random Number Generators, / 217 RANARB Arbitrary (User Specified) Discrete Distribution / 219 RANBER Bernoulli Distribution / 221 RANBIN Binomial Distribution / 223 RANGEO Geometric Distribution / 225 RANHYP Hypergeometric Distribution / 227 RANNBI Negative Binomial Distribution / 229 RANPOI Poisson Distribution / 231 RANUWO Discrete Uniform Distribution (Without Replacement) / 233 RANUWR Discrete Uniform Distribution (With Replacement) / 235 Continuous Random Number Generators / 237 RANBET Beta Distribution / 239 RANCSQ Chi-square Distribution / 241 RANEXP Exponential Distribution / 243 RANFDI $F$ Distribution / 245 RANGAM Gamma Distribution / 247 RANLGS Logistic Distribution / 249 RANLOG Lognormal Distribution / 251 RANNOR Normal Distribution / 255 RANNVE Multivariate Normal Distribution / 257 RANPDI Pearson Distributions / 261 RANTDI Student's $t$ Distribution / 265 RANUNI Continuous Uniform Distribution (On a Line) / 267 RANCIR Continuous Uniform Distribution (Within a Circle) / 269 RANWEI Three-parameter Weibull Distribution / 271 RANMK1 1st Order Markov Process / 273 Glossary / 275 Distribution / 277

rawabstract:
This document provides a description of each program and subroutine in STATLIB, THE Naval Surface Warfare Center library of statistical programs and subroutines for its general purpose computers. The Library contains thirty-four programs and twenty-four subroutines for statistical analysis, probability evaluation, and random number generation. It was written to enable Center Scientists and Engineers to efficiently perform a wide variety of analyses and to generate pseudo random numbers from many different probability distributions.

rawTOC:
Introduction / 1 \\ Overview of STATLIB / 1 \\ Origin of STATLIB / 1 \\ Establishment of STATLIB / 1 \\ Commercial Statistical Packages at NSWC / 2 \\ Using STATLIB / 5 \\ Library Organization / 5 \\ How to Call It / 5 \\ Information Needed to Run It / 5 \\ Examples / 9 \\ Program / 9 \\ Subroutine / 10 \\ Descriptions and Input Guides / 21 \\ Programs / 23 \\ Regression Analysis / 25 \\ GEMREG General Multiple Regression / 29 \\ DAMRCA Dahlgren Multiple Regression Comprehensive Analysis / 35 \\ WEPORU Uncorrelated Weighted Polynomial Regression / 41 \\ WEPORC Correlated Weighted Polynomial Regression / 45 \\ MROP Multiple Regression Using Orthogonal Polynomials / 49 \\ CANON Canonical Analysis of Second Order Response Functions / 57 \\ DURBWAT Durbin--Watson Test for Independence of Residuals / 61 \\ NEARNEB Near Neighbor Estimation of Experimental Error / 63 \\ Goodness of Fit Analysis / 67 \\ UNORGOF Univariate Normal Goodness of Fit / 69 \\ BNORGOF Bivariate Normal Goodness of Fit / 75 \\ EXPGOF Exponential Goodness of Fit / 81 \\ WBLGOF Weibull Goodness ot / 83 \\ PERGOF Pearson System Goodness of Fit / 87 \\ UNKSGOF Univariate Normal Kolmogorov--Smirnov Test of Fit / 93 \\ RANDOM Test of Fit for Uniform Random Number Generators / 99 \\ Power Evaluation / 103 \\ DISCRETE POWER EVALUATION / 107 \\ BINIPOW Power of the Test on a Binomial Proportion / 109 \\ BIN2POW Power of the Test on the Difference of Two Binomial Proportions / 113 \\ POIIPOW Power of the Test on the Poisson Parameter / 121 \\ Continuous Power Evaluation / 125 \\ NORIPOW Power of the One-Sample Normal Test on the Mean / 127 \\ NOR2PWE Power of the Two-Simple Normal Test on Means with ample Sizes / 131 \\ NOR2PWU Power of the Two-Sample Normal Test on Means with Unequal Sample Sizes / 135 \\ T1POW Power of the One-Sample $t$ Test on the Mean / 141 \\ T2POW Power of the Two-Sample (Pooled) $t$ Test on Means / 147 \\ CHIVPOW Power of the Chi-square Test on the Variance / 153 \\ FVARPOW Power of the $F$ Test for the Equality of Variances / 157 \\ FEMPOW Power of the Test for One-Way Fixed Effects Analysis of Variance / 163 \\ REMPOW Power of the Test for One-Way Random Effects Analysis of Variance / 167 \\ Probability Evaluation / 171 \\ BINVARP Binomial Probability Distribution with Unequal Single Trial Probabilities / 173 \\ NEGBIN Negative Binomial Probability Distribution / 177 \\ Confidence Limit Evaluation / 179 \\ BINCL Confidence Limits for the Binomial Parameter p / 181 \\ CEPCL Confidence Limits for the CEP (Circular Probable Error) / 185 \\ SEPCL Confidence Limits for the SEP (Spherical Probable Error) / 191 \\ Miscellaneous Statistical Analysis / 197 \\ LD50EST Estimation of LD50 (Lethal Dose 50th Percentile) / 199 \\ FFAC2K Analysis of the 2**k Fractional Factorial Experiment / 203 \\ Subroutines / 211 \\ Random Number Generation / 213 \\ Discrete Random Number Generators, / 217 \\ RANARB Arbitrary (User Specified) Discrete Distribution / 219 \\ RANBER Bernoulli Distribution / 221 \\ RANBIN Binomial Distribution / 223 \\ RANGEO Geometric Distribution / 225 \\ RANHYP Hypergeometric Distribution / 227 \\ RANNBI Negative Binomial Distribution / 229 \\ RANPOI Poisson Distribution / 231 \\ RANUWO Discrete Uniform Distribution (Without Replacement) / 233 \\ RANUWR Discrete Uniform Distribution (With Replacement) / 235 \\ Continuous Random Number Generators / 237 \\ RANBET Beta Distribution / 239 \\ RANCSQ Chi-square Distribution / 241 \\ RANEXP Exponential Distribution / 243 \\ RANFDI $F$ Distribution / 245 \\ RANGAM Gamma Distribution / 247 \\ RANLGS Logistic Distribution / 249 \\ RANLOG Lognormal Distribution / 251 \\ RANNOR Normal Distribution / 255 \\ RANNVE Multivariate Normal Distribution / 257 \\ RANPDI Pearson Distributions / 261 \\ RANTDI Student's $t$ Distribution / 265 \\ RANUNI Continuous Uniform Distribution (On a Line) / 267 \\ RANCIR Continuous Uniform Distribution (Within a Circle) / 269 \\ RANWEI Three-parameter Weibull Distribution / 271 \\ RANMK1 1st Order Markov Process / 273 \\ Glossary / 275 \\ Distribution / 277

entry:
@TechReport{Thomas:1989:SNL,
  author =       "Marlin A. Thomas and Gary W. Gemmill and John R.
                 Crigler",
  title =        "{STATLIB}: {NSWC} Library of Statistical Programs and
                 Subroutines",
  type =         "Technical Report",
  number =       "NSWC TR 89-97",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
                 20903-5000, USA",
  pages =        "viii + 280",
  month =        aug,
  year =         "1989",
  bibdate =      "Sat Nov 15 10:39:12 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a221538.pdf",
  abstract =     "This document provides a description of each program
                 and subroutine in STATLIB, THE Naval Surface Warfare
                 Center library of statistical programs and subroutines
                 for its general purpose computers. The Library contains
                 thirty-four programs and twenty-four subroutines for
                 statistical analysis, probability evaluation, and
                 random number generation. It was written to enable
                 Center Scientists and Engineers to efficiently perform
                 a wide variety of analyses and to generate pseudo
                 random numbers from many different probability
                 distributions.",
  acknowledgement = ack-nhfb,
  onlinedate =   "255",
  tableofcontents = "Introduction / 1 \\
                 Overview of STATLIB / 1 \\
                 Origin of STATLIB / 1 \\
                 Establishment of STATLIB / 1 \\
                 Commercial Statistical Packages at NSWC / 2 \\
                 Using STATLIB / 5 \\
                 Library Organization / 5 \\
                 How to Call It / 5 \\
                 Information Needed to Run It / 5 \\
                 Examples / 9 \\
                 Program / 9 \\
                 Subroutine / 10 \\
                 Descriptions and Input Guides / 21 \\
                 Programs / 23 \\
                 Regression Analysis / 25 \\
                 GEMREG General Multiple Regression / 29 \\
                 DAMRCA Dahlgren Multiple Regression Comprehensive
                 Analysis / 35 \\
                 WEPORU Uncorrelated Weighted Polynomial Regression / 41
                 \\
                 WEPORC Correlated Weighted Polynomial Regression / 45
                 \\
                 MROP Multiple Regression Using Orthogonal Polynomials /
                 49 \\
                 CANON Canonical Analysis of Second Order Response
                 Functions / 57 \\
                 DURBWAT Durbin--Watson Test for Independence of
                 Residuals / 61 \\
                 NEARNEB Near Neighbor Estimation of Experimental Error
                 / 63 \\
                 Goodness of Fit Analysis / 67 \\
                 UNORGOF Univariate Normal Goodness of Fit / 69 \\
                 BNORGOF Bivariate Normal Goodness of Fit / 75 \\
                 EXPGOF Exponential Goodness of Fit / 81 \\
                 WBLGOF Weibull Goodness ot / 83 \\
                 PERGOF Pearson System Goodness of Fit / 87 \\
                 UNKSGOF Univariate Normal Kolmogorov--Smirnov Test of
                 Fit / 93 \\
                 RANDOM Test of Fit for Uniform Random Number Generators
                 / 99 \\
                 Power Evaluation / 103 \\
                 DISCRETE POWER EVALUATION / 107 \\
                 BINIPOW Power of the Test on a Binomial Proportion /
                 109 \\
                 BIN2POW Power of the Test on the Difference of Two
                 Binomial Proportions / 113 \\
                 POIIPOW Power of the Test on the Poisson Parameter /
                 121 \\
                 Continuous Power Evaluation / 125 \\
                 NORIPOW Power of the One-Sample Normal Test on the Mean
                 / 127 \\
                 NOR2PWE Power of the Two-Simple Normal Test on Means
                 with ample Sizes / 131 \\
                 NOR2PWU Power of the Two-Sample Normal Test on Means
                 with Unequal Sample Sizes / 135 \\
                 T1POW Power of the One-Sample $t$ Test on the Mean /
                 141 \\
                 T2POW Power of the Two-Sample (Pooled) $t$ Test on
                 Means / 147 \\
                 CHIVPOW Power of the Chi-square Test on the Variance /
                 153 \\
                 FVARPOW Power of the $F$ Test for the Equality of
                 Variances / 157 \\
                 FEMPOW Power of the Test for One-Way Fixed Effects
                 Analysis of Variance / 163 \\
                 REMPOW Power of the Test for One-Way Random Effects
                 Analysis of Variance / 167 \\
                 Probability Evaluation / 171 \\
                 BINVARP Binomial Probability Distribution with Unequal
                 Single Trial Probabilities / 173 \\
                 NEGBIN Negative Binomial Probability Distribution / 177
                 \\
                 Confidence Limit Evaluation / 179 \\
                 BINCL Confidence Limits for the Binomial Parameter p /
                 181 \\
                 CEPCL Confidence Limits for the CEP (Circular Probable
                 Error) / 185 \\
                 SEPCL Confidence Limits for the SEP (Spherical Probable
                 Error) / 191 \\
                 Miscellaneous Statistical Analysis / 197 \\
                 LD50EST Estimation of LD50 (Lethal Dose 50th
                 Percentile) / 199 \\
                 FFAC2K Analysis of the 2**k Fractional Factorial
                 Experiment / 203 \\
                 Subroutines / 211 \\
                 Random Number Generation / 213 \\
                 Discrete Random Number Generators, / 217 \\
                 RANARB Arbitrary (User Specified) Discrete Distribution
                 / 219 \\
                 RANBER Bernoulli Distribution / 221 \\
                 RANBIN Binomial Distribution / 223 \\
                 RANGEO Geometric Distribution / 225 \\
                 RANHYP Hypergeometric Distribution / 227 \\
                 RANNBI Negative Binomial Distribution / 229 \\
                 RANPOI Poisson Distribution / 231 \\
                 RANUWO Discrete Uniform Distribution (Without
                 Replacement) / 233 \\
                 RANUWR Discrete Uniform Distribution (With Replacement)
                 / 235 \\
                 Continuous Random Number Generators / 237 \\
                 RANBET Beta Distribution / 239 \\
                 RANCSQ Chi-square Distribution / 241 \\
                 RANEXP Exponential Distribution / 243 \\
                 RANFDI $F$ Distribution / 245 \\
                 RANGAM Gamma Distribution / 247 \\
                 RANLGS Logistic Distribution / 249 \\
                 RANLOG Lognormal Distribution / 251 \\
                 RANNOR Normal Distribution / 255 \\
                 RANNVE Multivariate Normal Distribution / 257 \\
                 RANPDI Pearson Distributions / 261 \\
                 RANTDI Student's $t$ Distribution / 265 \\
                 RANUNI Continuous Uniform Distribution (On a Line) /
                 267 \\
                 RANCIR Continuous Uniform Distribution (Within a
                 Circle) / 269 \\
                 RANWEI Three-parameter Weibull Distribution / 271 \\
                 RANMK1 1st Order Markov Process / 273 \\
                 Glossary / 275 \\
                 Distribution / 277",
}


bibtype: article
filename: elefunt.bib
label: Ubhaya:1989:LAN
author: V. A. Ubhaya
title: $ L_p $ approximation from nonconvex subsets of special classes of functions
journal: j-J-APPROX-THEORY
volume: 57
number: 2
pages: 223--238
month: may
monthnumber: 5
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: V. A. Ubhaya
rawtitle: {$ L_p $} approximation from nonconvex subsets of special classes of functions
entry:
@Article{Ubhaya:1989:LAN,
  author =       "V. A. Ubhaya",
  title =        "{$ L_p $} approximation from nonconvex subsets of
                 special classes of functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "57",
  number =       "2",
  pages =        "223--238",
  month =        may,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72277",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1989-07833",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "May 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: inproceedings
filename: elefunt.bib
label: Vaidya:1989:LWB
author: P. M. Vaidya
crossref: Megiddo:1989:PMP
pages: 79--90
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
rawauthor: P. M. Vaidya
title:
A locally well-behaved potential function and a simple Newton-type method for finding the center of a polytype

subject:
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION

rawtitle:
A locally well-behaved potential function and a simple {Newton}-type method for finding the center of a polytype

entry:
@InProceedings{Vaidya:1989:LWB,
  author =       "P. M. Vaidya",
  title =        "A locally well-behaved potential function and a simple
                 {Newton}-type method for finding the center of a
                 polytype",
  crossref =     "Megiddo:1989:PMP",
  pages =        "79--90",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74176",
  catcode =      "G.1.6; G.1.6; F.2.2; G.1.2; G.1.5; G.1.5; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.6
                 Optimization; G.1.6 Gradient methods; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.5 Roots of
                 Nonlinear Equations; G.1.5 Convergence; G.1.5 Roots of
                 Nonlinear Equations; G.1.5 Iterative methods; I.1.2
                 Algorithms; I.1.2 Nonalgebraic algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods; Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Convergence; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Iterative methods; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12478",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
  xxpages =      "131--158",
}


bibtype: article
filename: elefunt.bib
label: VanHalen:1989:AAA
author: P. Van Halen
title: Accurate analytical approximations for error function and its integral
journal: j-ELECT-LETTERS
volume: 25
number: 9
pages: 561--563
day: 27
month: apr
monthnumber: 4
year: 1989
CODEN: ELLEAK
DOI: https://doi.org/10.1049/el:19890383
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Dec 16 18:15:17 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 18:15:17 ???
URL: http://ieeexplore.ieee.org/document/19780/
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: P. {Van Halen}
rawtitle: Accurate analytical approximations for error function and its integral
entry:
@Article{VanHalen:1989:AAA,
  author =       "P. {Van Halen}",
  title =        "Accurate analytical approximations for error function
                 and its integral",
  journal =      j-ELECT-LETTERS,
  volume =       "25",
  number =       "9",
  pages =        "561--563",
  day =          "27",
  month =        apr,
  year =         "1989",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19890383",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Dec 16 18:15:17 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/19780/",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}


bibtype: phdthesis
filename: elefunt.bib
label: Vavasis:1989:CFP
author: S. A. Vavasis
title: Complexity of fixed point computations
type: Ph.D Thesis
school: Stanford University
address: Stanford, CA, USA
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
rawauthor: S. A. Vavasis
rawtitle: Complexity of fixed point computations
subject:
J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL SCIENCES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS

entry:
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  author =       "S. A. Vavasis",
  title =        "Complexity of fixed point computations",
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bibtype: inproceedings
filename: elefunt.bib
label: Vial:1989:APP
author: J.-P. Vial
title: Approximate projections in a projective method for the linear feasibility problem
crossref: Megiddo:1989:PMP
pages: 65--78
year: 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
acknowledgement: ack-nhfb
bookpages: x + 158
rawauthor: J.-P. Vial
rawtitle: Approximate projections in a projective method for the linear feasibility problem
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1 ALGEBRAIC MANIPULATION; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@InProceedings{Vial:1989:APP,
  author =       "J.-P. Vial",
  title =        "Approximate projections in a projective method for the
                 linear feasibility problem",
  crossref =     "Megiddo:1989:PMP",
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  pages =        "65--78",
  year =         "1989",
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  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
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  catcode =      "G.1.6; F.2.2; I.1.2; G.1.6; G.1.2; F.2.1; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; F.2.2
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                 Nonalgebraic algorithms; G.1.6 Optimization; G.1.6
                 Constrained optimization; G.1.2 Approximation; G.1.2
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bibtype: article
filename: elefunt.bib
label: vonRosen:1989:MLE
author: D. von Rosen
title: Maximum likelihood estimators in multivariate linear normal models
journal: j-J-MULTIVAR-ANAL
volume: 31
number: 2
pages: 187--200
month: nov
monthnumber: 11
year: 1989
CODEN: JMVAAI
ISSN: 0047-259x (print), 1095-7243 (electronic) OR 0047259x (print), 10957243 (electronic)
ISSNL: 0047-259X OR 0047259X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Multivariate Analysis
acknowledgement: ack-nhfb
affiliation: Univ. of Stockholm, Stockholm, Sweden
rawauthor: D. von Rosen
rawtitle: Maximum likelihood estimators in multivariate linear normal models
entry:
@Article{vonRosen:1989:MLE,
  author =       "D. von Rosen",
  title =        "Maximum likelihood estimators in multivariate linear
                 normal models",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "187--200",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Stockholm, Stockholm, Sweden",
  bibno =        "69314",
  catcode =      "G.1.6; G.1.2; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
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                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
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                 approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1989-08484",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
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bibtype: book
filename: elefunt.bib
label: Wang:1989:SF
author: Z. X. Wang and D. R. Guo
title: Special Functions
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: xvi + 695
year: 1989
LCCN: QA331 .W296 1989
bibdate: Mon Sep 3 16:10:24 MDT 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.09.03 16:10:24 MDT
note: Translation to English by D.R. Guo and X. J. Xia.
subject: Functions
acknowledgement: ack-nhfb
rawauthor: Z. X. Wang and D. R. Guo
rawnote: Translation to English by D.R. Guo and X. J. Xia.
rawtitle: Special Functions
ISBN:
1-283-63565-8, 661394811X, 981-277-936-1 (e-book), 9971-5-0659-9 (hardcover), 9971-5-0667-X (paperback) OR 1283635658, 661394811X, 9812779361 (ebook), 9971506599 (hardcover), 997150667X (paperback)

ISBN13:
978-1-283-63565-3, 661394811X, 978-981-277-936-6 (e-book), 978-9971-5-0659-9 (hardcover), 978-9971-5-0667-4 (paperback) OR 9781283635653, 661394811X, 9789812779366 (ebook), 9789971506599 (hardcover), 9789971506674 (paperback)

remark:
Reprinted in 2010. Library catalogs record two rather different pages values. The one chosen here matches the tableofcontents value.

TOC:
1: THE EXPANSION OF FUNCTIONS IN INFINITE SERIES AND INFINITE PRODUCTS 1.1. Bernoulli Polynomials and Bernoulli Numbers / 1 1.2. Euler Polynomials and Euler Numbers / 5 1.3. Euler--Maclaurin Formula / 8 1.4. Lagrange's Expansion Formula / 14 1.5. Expansion of Meromorphic Functions in Rational Fractions / 17 1.6. Infinite Product / 21 1.7. The Expansion of a Function in Infinite Product Weierstrass Theorem / 25 1.8. Asymptotic Expansion / 29 1.9. The Asymptotic Expansion of the Laplace Integral, Watson's Lemma / 34 1.10. Expansion in Terms of Functions of an Orthonormal Set / 36 Exercise 1 / 41 2: LINEAR ORDINARY DIFFERENTIAL EQUATIONS OF THE SECOND ORDER 2.1. Singular Points of Linear Ordinary Differential Equations of the Second Order / 47 2.2. Solution of the Equation in the Vicinity of an Ordinary Point / 48 2.3. Solutions of the Equation in the Vicinity of a Singular Point / 51 2.4. Regular Solution. Regular Singularities / 55 2.5. Frobenius Method / 61 2.6. Point at Infinity / 63 2.7. Equations of Fuchsian Type / 64 2.8. Equations of Fuchsian Type Having Five Regular Singular Points / 66 2.9. Equations of Fuchsian Type Having Three Regular Singularities / 68 2.10. Irregular Singularities. Formal Regular Solution / 71 2.11. Irregular Singularities. Normal Solutions and Subnormal Solutions / 73 2.12. Method of Solution by Integrals. Basic Principle / 78 2.13. Equations of Laplacian Type and Laplace Transform / 81 2.14. Euler Transform / 85 Exercise 2 / 88 3: THE GAMMA FUNCTION 3.1. Definition of the Gamma Function / 93 3.2. Recurrence Relation / 94 3.3. The Infinite-Product Expression of Euler / 95 3.4. Weierstrass' Infinite Product / 97 3.5. Relation between the $Gamma $-Function and the Trigonometric Function / 98 3.6. Multiplication Formula / 99 3.7. Contour Integral / 101 3.8. Euler Integral of the First Kind. $B$-Function / 103 3.9. Double-Contour Integral / 105 3.10. Dirichlet Integral / 106 3.11. Logarithmic Derivative of the $Gamma $-Function / 107 3.12. Asymptotic Expansions / 111 3.13. Another Derivation of the Asymptotic Expansion / 112 3.14. Riemann $zeta $ Function / 114 3.15. The Functional Equation of the $zeta $-Function / 115 3.16. The Value of $zeta (s,a)$ when $s$ is an Integer / 117 3.17. Hermite Formula / 118 3.18. Relation to the $Gamma $-Function / 120 3.19. Euler Product of the $zeta $-Function / 123 3.20. Riemann Integral of the $zeta $-Function / 124 3.21. Another Derivation of the Asymptotic Expansion of the $Gamma $-Function / 125 3.22. Evaluation of the $zeta $-Function / 128 Exercise 3 / 128 4: HYPERGEOMETRIC FUNCTION 4.1. Hypergeometric Series and Hypergeometric Function / 135 4.2. Recurrence Relations / 137 4.3. Other Solutions of the Hypergeometric Equation Expressed in Terms of Hypergeometric Functions / 139 4.4. The Second Solution of the Hypergeometric Equation when the Difference of the Exponents is an Integer / 144 4.5. Integral Representation of the Hypergeometric Function / 150 4.6. Barnes' Integral Representation of the Hypergeometric Function / 153 4.7. The Value of $F(alpha , beta , gamma , 1)$ / 156 4.8. Connections between the Fundamental Solutions at the Singular Points $0, 1, infty $. Analytic Continuation / 159 4.9. When $gamma - alpha - beta $, $alpha - beta $ are Integers / 162 4.10. Jacobi Polynomials / 169 4.11. Chebyshev Polynomials / 173 4.12. Quadratic Transformations / 177 4.13. Kummer's Formula and Summation Formula Derived from It / 184 4.14. Asymptotic Expansions for Large Parameters / 186 4.15. Generalized Hypergeometric Series / 189 4.16. Hypergeometric Series with Two Variables / 191 4.17. The Transformation Formulae of $F_1$ and $F_2$ / 195 4.18. Reducible Cases / 197 Exercise 4 / 202 5: LEGENDRE FUNCTIONS 5.1. Legendre Equation / 210 5.2. Legendre Polynomials / 212 5.3. The Generating Function of $P_n(i)$. Rodrigues Formula / 215 5.4. Integral Representations of $P_n(x)$ / 216 5.5. Recurrence Relations of $P_n(x)$ / 218 5.6. Legendre Polynomials as a Complete Set of Orthonormal Functions / 219 5.7. Zeros of $P_n(x)$ / 223 5.8. Legendre Functions of the Second Kind, $Q_n(x)$ / 224 5.9. Recurrence Relations of $Q_n(x)$ / 230 5.10. Expansion of the Function $(x - t)^-1$ in Terms of Legendre Functions. Neumann Expansion / 231 5.11. Associate Legendre Functions $P_l^m(x)$ / 233 5.12. Orthogonality Relations of $P_l^m(x)$ / 235 5.13. Recurrence Relations for $P_l^m(x)$ and $Q_l^m(x)$ / 239 5.14. Addition Formula / 241 5.15. Spherical Surface Harmonics $Y_lm(theta , phi )$ / 244 5.16. The General Associate Legendre Functions $P_nu ^mu (z)$ / 247 5.17. $Q_nu ^mu (z)$ / 251 5.18. Definition of $P_nu ^mu (x)$ on the Cut: $-infty < x < 1$ / 255 5.19. Definition of $Q_nu ^mu (x)$ on the Cut: $-infty < x < 1$ / 258 5.20. Other Integral Expressions for $P_nu (z)$ and $P_nu ^m(z)$ / 262 5.21. Addition Formulae / 267 5.22. Asymptotic Expansions of $P_nu ^mu (cos theta )$ and $Q_nu ^mu (cos theta )$ when $nu to infty $ / 270 5.23. Ultra-Spherical Polynomials $C_n^lambda (x)$ / 274 Exercise 5 / 277 6: CONFLUENT HYPERGEOMETRIC FUNCTIONS 6.1. Confluent Hypergeometric Functions / 296 6.2. Relations among the Consecutive Functions / 299 6.3. Whittaker Equation and Whittaker Functions $M_k,m(z)$ / 300 6.4. Integral Representations / 302 6.5. Whittaker Functions $W_k,m(z)$ / 305 6.6. Asymptotic Expansion of $W_k,m(z)$ when $z to infty $ / 307 6.7. Barnes' Integral Representation of $W_k,m(z)$ / 310 6.8. Relations between $W_pm k,m(pm z)$ and $M_pm k,m(pm z)$. Asymptotic Expansion of $F(alpha , gamma , z)$. Stokes Phenomenon / 313 6.9. The Case when $gamma $ (or $2m$) is an Integer / 316 6.10. The Asymptotic Expansions of $F(alpha , gamma , z)$ for Large $|alpha |$, $|gamma |$ / 318 6.11. Differential Equations Reducible to the Confluent Hypergeometric Equation / 318 6.12. Weber Equation. Parabolic Cylinder Functions $D_n(z)$ / 320 6.13. Hermite Functions and Hermite Polynomials / 325 6.14. Laguerre Polynomials / 327 6.15. Other Special Functions Expressible by Whittaker Functions / 332 Exercise 6 / 335 7: BESSEL FUNCTIONS 7.1. Bessel Equation. Its Relation to the Confluent Hypergeometric Equation / 345 7.2. Bessel Functions of the First Kind: $J_pm nu (z)$, $2nu neq $ integer / 347 7.3. Bessel Functions of Order Half an Odd Integer: $J_n + 1/2(z)$ $(n = 0, pm 1, pm 2, ldots )$ / 350 7.4. Integral Representations of $J_nu (z)$ / 351 7.5. Bessel Functions of Integral Order $J_n(z)$ $(n = 0, 1, 2, ldots )$ / 359 7.6. Bessel Functions of the Second Kind $Y_nu (z)$ / 365 7.7. Bessel Functions of the Third Kind (Hankel Functions) $H_nu ^(1)(z)$, $H_nu ^(2)(z)$ / 368 7.8. Modified (or Imaginary Argument) Bessel Functions $I_nu (z)$ and $K_nu (z)$. Thomson Functions $ber _nu (z)$ and $bei _nu (z)$; etc. / 374 7.9. Spherical Bessel Functions $j_l(z)$, $n_l(z)$, $h_l^(1)(z), $h_l^(2)(z) / 376 7.10. Asymptotic Expansions for the Case $|z| to infty $ / 378 7.11. The Method of Steepest Descent / 381 7.12. Asymptotic Expansions of Bessel Functions of Order $nu $ for Large $|nu |$ and $|z|$ / 384 7.13. Addition Formulae / 395 7.14. Integrals Containing Bessel Functions. (1) Finite Integrals / 399 7.15. Integrals Containing Bessel Functions. (2) Infinite Integrals / 401 7.16. Neumann Expansion / 412 7.17. Kapteyn Expansion / 415 7.18. The Zeros of Bessel Functions / 420 7.19. Fourier--Bessel Expansion / 424 Exercise 7 / 425 8: WEIERSTRASS ELLIPTIC FUNCTIONS 8.1. Elliptic Integrals and Elliptic Functions / 456 8.2. The Periods of Elliptic Integrals / 460 8.3. The General Properties of Doubly-Periodic Functions and Elliptic Functions / 462 8.4. The Function $wp (z)$ / 466 8.5. Algebraic Relation between $wp (z)$ and $wp '(z)$ / 468 8.6. The Function $zeta (z)$ / 471 8.7. The Function $sigma (z)$ / 473 8.8. Homogeneity of the Weierstrass Elliptic Function / 476 8.9. Representations of a General Elliptic Function / 476 8.10. Addition Formulae / 481 8.11. Expressing the Coordinates of a Cubic Curve by Elliptic Functions / 485 8.12. The Problem of a Quartic Polynomial / 486 8.13. Curves of Genus (Deficiency) 1 / 489 Exercise 8 / 493 9: THETA FUNCTIONS 9.1. The Theta Function $theta (nu )$ / 498 9.2. The Functions $vartheta _k(nu )$ / 500 9.3. Elliptic Functions Represented by Theta Functions / 502 9.4. Relations among the Squares of $vartheta _k(nu )$ / 503 9.5. Addition Formulae / 504 9.6. Differential Equations Satisfied by Theta Functions / 506 9.7. The Values of Some Constants / 508 9.8. Legendre's Elliptic Integral of the First Kind / 510 9.9. Jacobi's Imaginary Transformation / 514 9.10. Transformation of Landen-Type / 516 9.11. Representation of Theta Functions by Infinite Product / 517 9.12. Fourier Expansion of the Logarithmic Derivatives of Theta Functions / 521 9.13. The Functions $Theta (u)$ and $H(u)$ / 522 Exercise 9 / 523 10: JACOBIAN ELLIPTIC FUNCTIONS 10.1. Jacobian Elliptic Functions $sn u$, $cn u$, $dn u$ / 530 10.2. Geometric Representations of Jacobian Elliptic Functions / 532 10.3. Complete Elliptic Integrals / 535 10.4. Addition Formulae / 537 10.5. The Periodicity of Jacobian Elliptic Functions / 539 10.6. The Zeros and Poles of Jacobian Elliptic Functions / 540 10.7. Transformations of Elliptic Functions / 542 10.8. Reductions of Elliptic Integrals / 545 10.9. Elliptic Integral of the Second Kind / 552 10.10. Elliptic Integral of the Third Kind / 553 10.11. Properties of the Function $E(u)$ / 555 10.12. Differential Equations Satisfied by $K$ and $E$ with Respect to $k$ and Expansions of $K$ and $E$ with Respect to $k$ / 558 10.13. Relations between Jacobian Elliptic Functions and Theta Functions / 561 10.14. Expressing Jacobian Elliptic Functions in Infinite Products and Fourier Series / 566 Exercise 10 / 569 11: LAME FUNCTIONS 11.1. Ellipsoidal Coordinates / 575 11.2. Representing the Coordinates with Elliptic Functions / 578 11.3. Lame Equation / 580 11.4. Four Types of Lame Functions / 583 11.5. Ellipsoidal Harmonics / 589 11.6. Niven's Representation / 591 11.7. On the Zeros of Lame Polynomials / 595 11.8. Lame Functions of the Second Kind / 597 11.9. Generalized Lame Functions / 599 11.10. Integral Equations of Lame Functions / 602 11.11. The Integral Representation of Ellipsoidal Harmonics / 604 Exercise 11 / 607 12: MATHIEU FUNCTIONS 12.1. Mathieu Equation / 610 12.2. General Properties of the Solution. Fundamental Solutions / 612 12.3. Floquet Solution / 614 12.4. Periodic Solutions of Mathieu Equation / 615 12.5. Fourier Expansion of the Floquet Solution / 617 12.6. Formulae for Computing Eigenvalues $lambda (q)$ / 620 12.7. Mathieu Functions $ce _m(z)$, $m = 0, 1, 2, ldots $ and $se _m(z)$, $m = 1, 2 ldots $ / 624 12.8. Expansion of $lambda _nu (q)$ in Powers of $q$ / 627 12.9. Fourier Expansions of $ce _m(z)$ and $se _m(z)$ for Small $q$ / 630 12.10. Infinite Determinant / 632 12.11. Hill Equation / 633 12.12. Stable and Unstable Solutions of Mathieu Equation. Stable Region and Unstable Region / 637 12.13. Approximate Solutions of Mathieu Equation for $lambda gg q > 0$ / 640 12.14. Integral Equations for Mathieu Functions / 643 Exercise 12 / 645 Appendices Appendix I. Roots of a Cubic Equation / 654 Appendix II. Roots of the Quartic Equation / 656 Appendix III. Orthogonal Curvilinear Coordinate Systems / 658 Bibliography / 677 Glossary / 679 Index / 683

shortTOC:
1: The expansion of functions in infinite series and infinite products 2: Linear ordinary differential equations of the second order 3: The gamma function 4: Hypergeometric function 5: Legendre functions 6: Confluent hypergeometric functions 7: Bessel functions 8: Weierstrass elliptic functions 9: Theta functions 10: Jacobian elliptic functions 11: Lame functions 12: Mathieu functions

rawshortTOC:
1: The expansion of functions in infinite series and infinite products \\ 2: Linear ordinary differential equations of the second order \\ 3: The gamma function \\ 4: Hypergeometric function \\ 5: Legendre functions \\ 6: Confluent hypergeometric functions \\ 7: Bessel functions \\ 8: Weierstrass elliptic functions \\ 9: Theta functions \\ 10: Jacobian elliptic functions \\ 11: Lame functions \\ 12: Mathieu functions

rawTOC:
1: THE EXPANSION OF FUNCTIONS IN INFINITE SERIES AND INFINITE PRODUCTS \\ 1.1. Bernoulli Polynomials and Bernoulli Numbers / 1 \\ 1.2. Euler Polynomials and Euler Numbers / 5 \\ 1.3. Euler--Maclaurin Formula / 8 \\ 1.4. Lagrange's Expansion Formula / 14 \\ 1.5. Expansion of Meromorphic Functions in Rational Fractions / 17 \\ 1.6. Infinite Product / 21 \\ 1.7. The Expansion of a Function in Infinite Product Weierstrass Theorem / 25 \\ 1.8. Asymptotic Expansion / 29 \\ 1.9. The Asymptotic Expansion of the Laplace Integral, Watson's Lemma / 34 \\ 1.10. Expansion in Terms of Functions of an Orthonormal Set / 36 \\ Exercise 1 / 41 \\ 2: LINEAR ORDINARY DIFFERENTIAL EQUATIONS OF THE SECOND ORDER \\ 2.1. Singular Points of Linear Ordinary Differential Equations of the Second Order / 47 \\ 2.2. Solution of the Equation in the Vicinity of an Ordinary Point / 48 \\ 2.3. Solutions of the Equation in the Vicinity of a Singular Point / 51 \\ 2.4. Regular Solution. Regular Singularities / 55 \\ 2.5. Frobenius Method / 61 \\ 2.6. Point at Infinity / 63 \\ 2.7. Equations of Fuchsian Type / 64 \\ 2.8. Equations of Fuchsian Type Having Five Regular Singular Points / 66 \\ 2.9. Equations of Fuchsian Type Having Three Regular Singularities / 68 \\ 2.10. Irregular Singularities. Formal Regular Solution / 71 \\ 2.11. Irregular Singularities. Normal Solutions and Subnormal Solutions / 73 \\ 2.12. Method of Solution by Integrals. Basic Principle / 78 \\ 2.13. Equations of Laplacian Type and Laplace Transform / 81 \\ 2.14. Euler Transform / 85 \\ Exercise 2 / 88 \\ 3: THE GAMMA FUNCTION \\ 3.1. Definition of the Gamma Function / 93 \\ 3.2. Recurrence Relation / 94 \\ 3.3. The Infinite-Product Expression of Euler / 95 \\ 3.4. Weierstrass' Infinite Product / 97 \\ 3.5. Relation between the $\Gamma$-Function and the Trigonometric Function / 98 \\ 3.6. Multiplication Formula / 99 \\ 3.7. Contour Integral / 101 \\ 3.8. Euler Integral of the First Kind. $B$-Function / 103 \\ 3.9. Double-Contour Integral / 105 \\ 3.10. Dirichlet Integral / 106 \\ 3.11. Logarithmic Derivative of the $\Gamma$-Function / 107 \\ 3.12. Asymptotic Expansions / 111 \\ 3.13. Another Derivation of the Asymptotic Expansion / 112 \\ 3.14. Riemann $\zeta$ Function / 114 \\ 3.15. The Functional Equation of the $\zeta$-Function / 115 \\ 3.16. The Value of $\zeta(s,a)$ when $s$ is an Integer / 117 \\ 3.17. Hermite Formula / 118 \\ 3.18. Relation to the $\Gamma$-Function / 120 \\ 3.19. Euler Product of the $\zeta$-Function / 123 \\ 3.20. Riemann Integral of the $\zeta$-Function / 124 \\ 3.21. Another Derivation of the Asymptotic Expansion of the $\Gamma$-Function / 125 \\ 3.22. Evaluation of the $\zeta$-Function / 128 \\ Exercise 3 / 128 \\ 4: HYPERGEOMETRIC FUNCTION \\ 4.1. Hypergeometric Series and Hypergeometric Function / 135 \\ 4.2. Recurrence Relations / 137 \\ 4.3. Other Solutions of the Hypergeometric Equation Expressed in Terms of Hypergeometric Functions / 139 \\ 4.4. The Second Solution of the Hypergeometric Equation when the Difference of the Exponents is an Integer / 144 \\ 4.5. Integral Representation of the Hypergeometric Function / 150 \\ 4.6. Barnes' Integral Representation of the Hypergeometric Function / 153 \\ 4.7. The Value of $F(\alpha, \beta, \gamma, 1)$ / 156 \\ 4.8. Connections between the Fundamental Solutions at the Singular Points $0, 1, \infty$. Analytic Continuation / 159 \\ 4.9. When $\gamma - \alpha - \beta$, $\alpha - \beta$ are Integers / 162 \\ 4.10. Jacobi Polynomials / 169 \\ 4.11. Chebyshev Polynomials / 173 \\ 4.12. Quadratic Transformations / 177 \\ 4.13. Kummer's Formula and Summation Formula Derived from It / 184 \\ 4.14. Asymptotic Expansions for Large Parameters / 186 \\ 4.15. Generalized Hypergeometric Series / 189 \\ 4.16. Hypergeometric Series with Two Variables / 191 \\ 4.17. The Transformation Formulae of $F_1$ and $F_2$ / 195 \\ 4.18. Reducible Cases / 197 \\ Exercise 4 / 202 \\ 5: LEGENDRE FUNCTIONS \\ 5.1. Legendre Equation / 210 \\ 5.2. Legendre Polynomials / 212 \\ 5.3. The Generating Function of $P_n(i)$. Rodrigues Formula / 215 \\ 5.4. Integral Representations of $P_n(x)$ / 216 \\ 5.5. Recurrence Relations of $P_n(x)$ / 218 \\ 5.6. Legendre Polynomials as a Complete Set of Orthonormal Functions / 219 \\ 5.7. Zeros of $P_n(x)$ / 223 \\ 5.8. Legendre Functions of the Second Kind, $Q_n(x)$ / 224 \\ 5.9. Recurrence Relations of $Q_n(x)$ / 230 \\ 5.10. Expansion of the Function $(x - t)^{-1}$ in Terms of Legendre Functions. Neumann Expansion / 231 \\ 5.11. Associate Legendre Functions $P_l^m(x)$ / 233 \\ 5.12. Orthogonality Relations of $P_l^m(x)$ / 235 \\ 5.13. Recurrence Relations for $P_l^m(x)$ and $Q_l^m(x)$ / 239 \\ 5.14. Addition Formula / 241 \\ 5.15. Spherical Surface Harmonics $Y_{lm}(\theta, \phi)$ / 244 \\ 5.16. The General Associate Legendre Functions $P_\nu^\mu(z)$ / 247 \\ 5.17. $Q_\nu^\mu(z)$ / 251 \\ 5.18. Definition of $P_\nu^\mu(x)$ on the Cut: $-\infty < x < 1$ / 255 \\ 5.19. Definition of $Q_\nu^\mu(x)$ on the Cut: $-\infty < x < 1$ / 258 \\ 5.20. Other Integral Expressions for $P_\nu(z)$ and $P_\nu^m(z)$ / 262 \\ 5.21. Addition Formulae / 267 \\ 5.22. Asymptotic Expansions of $P_\nu^\mu(\cos \theta)$ and $Q_\nu^\mu(\cos \theta)$ when $\nu \to \infty$ / 270 \\ 5.23. Ultra-Spherical Polynomials $C_n^\lambda(x)$ / 274 \\ Exercise 5 / 277 \\ 6: CONFLUENT HYPERGEOMETRIC FUNCTIONS \\ 6.1. Confluent Hypergeometric Functions / 296 \\ 6.2. Relations among the Consecutive Functions / 299 \\ 6.3. Whittaker Equation and Whittaker Functions $M_{k,m}(z)$ / 300 \\ 6.4. Integral Representations / 302 \\ 6.5. Whittaker Functions $W_{k,m}(z)$ / 305 \\ 6.6. Asymptotic Expansion of $W_{k,m}(z)$ when $z \to \infty$ / 307 \\ 6.7. Barnes' Integral Representation of $W_{k,m}(z)$ / 310 \\ 6.8. Relations between $W_{\pm k,m}(\pm z)$ and $M_{\pm k,m}(\pm z)$. Asymptotic Expansion of $F(\alpha, \gamma, z)$. Stokes Phenomenon / 313 \\ 6.9. The Case when $\gamma$ (or $2m$) is an Integer / 316 \\ 6.10. The Asymptotic Expansions of $F(\alpha, \gamma, z)$ for Large $|\alpha|$, $|\gamma|$ / 318 \\ 6.11. Differential Equations Reducible to the Confluent Hypergeometric Equation / 318 \\ 6.12. Weber Equation. Parabolic Cylinder Functions $D_n(z)$ / 320 \\ 6.13. Hermite Functions and Hermite Polynomials / 325 \\ 6.14. Laguerre Polynomials / 327 \\ 6.15. Other Special Functions Expressible by Whittaker Functions / 332 \\ Exercise 6 / 335 \\ 7: BESSEL FUNCTIONS \\ 7.1. Bessel Equation. Its Relation to the Confluent Hypergeometric Equation / 345 \\ 7.2. Bessel Functions of the First Kind: $J_{\pm \nu}(z)$, $2\nu \neq$ integer / 347 \\ 7.3. Bessel Functions of Order Half an Odd Integer: $J_{n + 1/2}(z)$ $(n = 0, \pm 1, \pm 2, \ldots{})$ / 350 \\ 7.4. Integral Representations of $J_\nu(z)$ / 351 \\ 7.5. Bessel Functions of Integral Order $J_n(z)$ $(n = 0, 1, 2, \ldots{})$ / 359 \\ 7.6. Bessel Functions of the Second Kind $Y_\nu(z)$ / 365 \\ 7.7. Bessel Functions of the Third Kind (Hankel Functions) $H_\nu^{(1)}(z)$, $H_\nu^{(2)}(z)$ / 368 \\ 7.8. Modified (or Imaginary Argument) Bessel Functions $I_\nu(z)$ and $K_\nu(z)$. Thomson Functions $\ber_\nu(z)$ and $\bei_\nu(z)$; etc. / 374 \\ 7.9. Spherical Bessel Functions $j_l(z)$, $n_l(z)$, $h_l^{(1)}(z), $h_l^{(2)}(z) / 376 \\ 7.10. Asymptotic Expansions for the Case $|z| \to \infty$ / 378 \\ 7.11. The Method of Steepest Descent / 381 \\ 7.12. Asymptotic Expansions of Bessel Functions of Order $\nu$ for Large $|\nu|$ and $|z|$ / 384 \\ 7.13. Addition Formulae / 395 \\ 7.14. Integrals Containing Bessel Functions. (1) Finite Integrals / 399 \\ 7.15. Integrals Containing Bessel Functions. (2) Infinite Integrals / 401 \\ 7.16. Neumann Expansion / 412 \\ 7.17. Kapteyn Expansion / 415 \\ 7.18. The Zeros of Bessel Functions / 420 \\ 7.19. Fourier--Bessel Expansion / 424 \\ Exercise 7 / 425 \\ 8: WEIERSTRASS ELLIPTIC FUNCTIONS \\ 8.1. Elliptic Integrals and Elliptic Functions / 456 \\ 8.2. The Periods of Elliptic Integrals / 460 \\ 8.3. The General Properties of Doubly-Periodic Functions and Elliptic Functions / 462 \\ 8.4. The Function $\wp(z)$ / 466 \\ 8.5. Algebraic Relation between $\wp(z)$ and $\wp'(z)$ / 468 \\ 8.6. The Function $\zeta(z)$ / 471 \\ 8.7. The Function $\sigma(z)$ / 473 \\ 8.8. Homogeneity of the Weierstrass Elliptic Function / 476 \\ 8.9. Representations of a General Elliptic Function / 476 \\ 8.10. Addition Formulae / 481 \\ 8.11. Expressing the Coordinates of a Cubic Curve by Elliptic Functions / 485 \\ 8.12. The Problem of a Quartic Polynomial / 486 \\ 8.13. Curves of Genus (Deficiency) 1 / 489 \\ Exercise 8 / 493 \\ 9: THETA FUNCTIONS \\ 9.1. The Theta Function $\theta(\nu)$ / 498 \\ 9.2. The Functions $\vartheta_k(\nu)$ / 500 \\ 9.3. Elliptic Functions Represented by Theta Functions / 502 \\ 9.4. Relations among the Squares of $\vartheta_k(\nu)$ / 503 \\ 9.5. Addition Formulae / 504 \\ 9.6. Differential Equations Satisfied by Theta Functions / 506 \\ 9.7. The Values of Some Constants / 508 \\ 9.8. Legendre's Elliptic Integral of the First Kind / 510 \\ 9.9. Jacobi's Imaginary Transformation / 514 \\ 9.10. Transformation of Landen-Type / 516 \\ 9.11. Representation of Theta Functions by Infinite Product / 517 \\ 9.12. Fourier Expansion of the Logarithmic Derivatives of Theta Functions / 521 \\ 9.13. The Functions $\Theta(u)$ and $H(u)$ / 522 \\ Exercise 9 / 523 \\ 10: JACOBIAN ELLIPTIC FUNCTIONS \\ 10.1. Jacobian Elliptic Functions $\sn u$, $\cn u$, $\dn u$ / 530 \\ 10.2. Geometric Representations of Jacobian Elliptic Functions / 532 \\ 10.3. Complete Elliptic Integrals / 535 \\ 10.4. Addition Formulae / 537 \\ 10.5. The Periodicity of Jacobian Elliptic Functions / 539 \\ 10.6. The Zeros and Poles of Jacobian Elliptic Functions / 540 \\ 10.7. Transformations of Elliptic Functions / 542 \\ 10.8. Reductions of Elliptic Integrals / 545 \\ 10.9. Elliptic Integral of the Second Kind / 552 \\ 10.10. Elliptic Integral of the Third Kind / 553 \\ 10.11. Properties of the Function $E(u)$ / 555 \\ 10.12. Differential Equations Satisfied by $K$ and $E$ with Respect to $k$ and Expansions of $K$ and $E$ with Respect to $k$ / 558 \\ 10.13. Relations between Jacobian Elliptic Functions and Theta Functions / 561 \\ 10.14. Expressing Jacobian Elliptic Functions in Infinite Products and Fourier Series / 566 \\ Exercise 10 / 569 \\ 11: LAM{\'E} FUNCTIONS \\ 11.1. Ellipsoidal Coordinates / 575 \\ 11.2. Representing the Coordinates with Elliptic Functions / 578 \\ 11.3. Lam{\'e} Equation / 580 \\ 11.4. Four Types of Lam{\'e} Functions / 583 \\ 11.5. Ellipsoidal Harmonics / 589 \\ 11.6. Niven's Representation / 591 \\ 11.7. On the Zeros of Lam{\'e} Polynomials / 595 \\ 11.8. Lam{\'e} Functions of the Second Kind / 597 \\ 11.9. Generalized Lam{\'e} Functions / 599 \\ 11.10. Integral Equations of Lam{\'e} Functions / 602 \\ 11.11. The Integral Representation of Ellipsoidal Harmonics / 604 \\ Exercise 11 / 607 \\ 12: MATHIEU FUNCTIONS \\ 12.1. Mathieu Equation / 610 \\ 12.2. General Properties of the Solution. Fundamental Solutions / 612 \\ 12.3. Floquet Solution / 614 \\ 12.4. Periodic Solutions of Mathieu Equation / 615 \\ 12.5. Fourier Expansion of the Floquet Solution / 617 \\ 12.6. Formulae for Computing Eigenvalues $\lambda(q)$ / 620 \\ 12.7. Mathieu Functions $\ce_m(z)$, $m = 0, 1, 2, \ldots{}$ and $\se_m(z)$, $m = 1, 2 \ldots{}$ / 624 \\ 12.8. Expansion of $\lambda_\nu(q)$ in Powers of $q$ / 627 \\ 12.9. Fourier Expansions of $\ce_m(z)$ and $\se_m(z)$ for Small $q$ / 630 \\ 12.10. Infinite Determinant / 632 \\ 12.11. Hill Equation / 633 \\ 12.12. Stable and Unstable Solutions of Mathieu Equation. Stable Region and Unstable Region / 637 \\ 12.13. Approximate Solutions of Mathieu Equation for $\lambda \gg q > 0$ / 640 \\ 12.14. Integral Equations for Mathieu Functions / 643 \\ Exercise 12 / 645 \\ Appendices \\ Appendix I. Roots of a Cubic Equation / 654 \\ Appendix II. Roots of the Quartic Equation / 656 \\ Appendix III. Orthogonal Curvilinear Coordinate Systems / 658 \\ Bibliography / 677 \\ Glossary / 679 \\ Index / 683

entry:
@Book{Wang:1989:SF,
  author =       "Z. X. Wang and D. R. Guo",
  title =        "Special Functions",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xvi + 695",
  year =         "1989",
  ISBN =         "1-283-63565-8, 661394811X, 981-277-936-1 (e-book),
                 9971-5-0659-9 (hardcover), 9971-5-0667-X (paperback)",
  ISBN-13 =      "978-1-283-63565-3, 661394811X, 978-981-277-936-6
                 (e-book), 978-9971-5-0659-9 (hardcover),
                 978-9971-5-0667-4 (paperback)",
  LCCN =         "QA331 .W296 1989",
  bibdate =      "Mon Sep 3 16:10:24 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translation to English by D.R. Guo and X. J. Xia.",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted in 2010. Library catalogs record two rather
                 different pages values. The one chosen here matches the
                 tableofcontents value.",
  shorttableofcontents = "1: The expansion of functions in infinite
                 series and infinite products \\
                 2: Linear ordinary differential equations of the second
                 order \\
                 3: The gamma function \\
                 4: Hypergeometric function \\
                 5: Legendre functions \\
                 6: Confluent hypergeometric functions \\
                 7: Bessel functions \\
                 8: Weierstrass elliptic functions \\
                 9: Theta functions \\
                 10: Jacobian elliptic functions \\
                 11: Lame functions \\
                 12: Mathieu functions",
  subject =      "Functions",
  tableofcontents = "1: THE EXPANSION OF FUNCTIONS IN INFINITE SERIES
                 AND INFINITE PRODUCTS \\
                 1.1. Bernoulli Polynomials and Bernoulli Numbers / 1
                 \\
                 1.2. Euler Polynomials and Euler Numbers / 5 \\
                 1.3. Euler--Maclaurin Formula / 8 \\
                 1.4. Lagrange's Expansion Formula / 14 \\
                 1.5. Expansion of Meromorphic Functions in Rational
                 Fractions / 17 \\
                 1.6. Infinite Product / 21 \\
                 1.7. The Expansion of a Function in Infinite Product
                 Weierstrass Theorem / 25 \\
                 1.8. Asymptotic Expansion / 29 \\
                 1.9. The Asymptotic Expansion of the Laplace Integral,
                 Watson's Lemma / 34 \\
                 1.10. Expansion in Terms of Functions of an Orthonormal
                 Set / 36 \\
                 Exercise 1 / 41 \\
                 2: LINEAR ORDINARY DIFFERENTIAL EQUATIONS OF THE SECOND
                 ORDER \\
                 2.1. Singular Points of Linear Ordinary Differential
                 Equations of the Second Order / 47 \\
                 2.2. Solution of the Equation in the Vicinity of an
                 Ordinary Point / 48 \\
                 2.3. Solutions of the Equation in the Vicinity of a
                 Singular Point / 51 \\
                 2.4. Regular Solution. Regular Singularities / 55 \\
                 2.5. Frobenius Method / 61 \\
                 2.6. Point at Infinity / 63 \\
                 2.7. Equations of Fuchsian Type / 64 \\
                 2.8. Equations of Fuchsian Type Having Five Regular
                 Singular Points / 66 \\
                 2.9. Equations of Fuchsian Type Having Three Regular
                 Singularities / 68 \\
                 2.10. Irregular Singularities. Formal Regular Solution
                 / 71 \\
                 2.11. Irregular Singularities. Normal Solutions and
                 Subnormal Solutions / 73 \\
                 2.12. Method of Solution by Integrals. Basic Principle
                 / 78 \\
                 2.13. Equations of Laplacian Type and Laplace Transform
                 / 81 \\
                 2.14. Euler Transform / 85 \\
                 Exercise 2 / 88 \\
                 3: THE GAMMA FUNCTION \\
                 3.1. Definition of the Gamma Function / 93 \\
                 3.2. Recurrence Relation / 94 \\
                 3.3. The Infinite-Product Expression of Euler / 95 \\
                 3.4. Weierstrass' Infinite Product / 97 \\
                 3.5. Relation between the $\Gamma$-Function and the
                 Trigonometric Function / 98 \\
                 3.6. Multiplication Formula / 99 \\
                 3.7. Contour Integral / 101 \\
                 3.8. Euler Integral of the First Kind. $B$-Function /
                 103 \\
                 3.9. Double-Contour Integral / 105 \\
                 3.10. Dirichlet Integral / 106 \\
                 3.11. Logarithmic Derivative of the $\Gamma$-Function /
                 107 \\
                 3.12. Asymptotic Expansions / 111 \\
                 3.13. Another Derivation of the Asymptotic Expansion /
                 112 \\
                 3.14. Riemann $\zeta$ Function / 114 \\
                 3.15. The Functional Equation of the $\zeta$-Function /
                 115 \\
                 3.16. The Value of $\zeta(s,a)$ when $s$ is an Integer
                 / 117 \\
                 3.17. Hermite Formula / 118 \\
                 3.18. Relation to the $\Gamma$-Function / 120 \\
                 3.19. Euler Product of the $\zeta$-Function / 123 \\
                 3.20. Riemann Integral of the $\zeta$-Function / 124
                 \\
                 3.21. Another Derivation of the Asymptotic Expansion of
                 the $\Gamma$-Function / 125 \\
                 3.22. Evaluation of the $\zeta$-Function / 128 \\
                 Exercise 3 / 128 \\
                 4: HYPERGEOMETRIC FUNCTION \\
                 4.1. Hypergeometric Series and Hypergeometric Function
                 / 135 \\
                 4.2. Recurrence Relations / 137 \\
                 4.3. Other Solutions of the Hypergeometric Equation
                 Expressed in Terms of Hypergeometric Functions / 139
                 \\
                 4.4. The Second Solution of the Hypergeometric Equation
                 when the Difference of the Exponents is an Integer /
                 144 \\
                 4.5. Integral Representation of the Hypergeometric
                 Function / 150 \\
                 4.6. Barnes' Integral Representation of the
                 Hypergeometric Function / 153 \\
                 4.7. The Value of $F(\alpha, \beta, \gamma, 1)$ / 156
                 \\
                 4.8. Connections between the Fundamental Solutions at
                 the Singular Points $0, 1, \infty$. Analytic
                 Continuation / 159 \\
                 4.9. When $\gamma - \alpha - \beta$, $\alpha - \beta$
                 are Integers / 162 \\
                 4.10. Jacobi Polynomials / 169 \\
                 4.11. Chebyshev Polynomials / 173 \\
                 4.12. Quadratic Transformations / 177 \\
                 4.13. Kummer's Formula and Summation Formula Derived
                 from It / 184 \\
                 4.14. Asymptotic Expansions for Large Parameters / 186
                 \\
                 4.15. Generalized Hypergeometric Series / 189 \\
                 4.16. Hypergeometric Series with Two Variables / 191
                 \\
                 4.17. The Transformation Formulae of $F_1$ and $F_2$ /
                 195 \\
                 4.18. Reducible Cases / 197 \\
                 Exercise 4 / 202 \\
                 5: LEGENDRE FUNCTIONS \\
                 5.1. Legendre Equation / 210 \\
                 5.2. Legendre Polynomials / 212 \\
                 5.3. The Generating Function of $P_n(i)$. Rodrigues
                 Formula / 215 \\
                 5.4. Integral Representations of $P_n(x)$ / 216 \\
                 5.5. Recurrence Relations of $P_n(x)$ / 218 \\
                 5.6. Legendre Polynomials as a Complete Set of
                 Orthonormal Functions / 219 \\
                 5.7. Zeros of $P_n(x)$ / 223 \\
                 5.8. Legendre Functions of the Second Kind, $Q_n(x)$ /
                 224 \\
                 5.9. Recurrence Relations of $Q_n(x)$ / 230 \\
                 5.10. Expansion of the Function $(x - t)^{-1}$ in Terms
                 of Legendre Functions. Neumann Expansion / 231 \\
                 5.11. Associate Legendre Functions $P_l^m(x)$ / 233 \\
                 5.12. Orthogonality Relations of $P_l^m(x)$ / 235 \\
                 5.13. Recurrence Relations for $P_l^m(x)$ and
                 $Q_l^m(x)$ / 239 \\
                 5.14. Addition Formula / 241 \\
                 5.15. Spherical Surface Harmonics $Y_{lm}(\theta,
                 \phi)$ / 244 \\
                 5.16. The General Associate Legendre Functions
                 $P_\nu^\mu(z)$ / 247 \\
                 5.17. $Q_\nu^\mu(z)$ / 251 \\
                 5.18. Definition of $P_\nu^\mu(x)$ on the Cut: $-\infty
                 < x < 1$ / 255 \\
                 5.19. Definition of $Q_\nu^\mu(x)$ on the Cut: $-\infty
                 < x < 1$ / 258 \\
                 5.20. Other Integral Expressions for $P_\nu(z)$ and
                 $P_\nu^m(z)$ / 262 \\
                 5.21. Addition Formulae / 267 \\
                 5.22. Asymptotic Expansions of $P_\nu^\mu(\cos \theta)$
                 and $Q_\nu^\mu(\cos \theta)$ when $\nu \to \infty$ /
                 270 \\
                 5.23. Ultra-Spherical Polynomials $C_n^\lambda(x)$ /
                 274 \\
                 Exercise 5 / 277 \\
                 6: CONFLUENT HYPERGEOMETRIC FUNCTIONS \\
                 6.1. Confluent Hypergeometric Functions / 296 \\
                 6.2. Relations among the Consecutive Functions / 299
                 \\
                 6.3. Whittaker Equation and Whittaker Functions
                 $M_{k,m}(z)$ / 300 \\
                 6.4. Integral Representations / 302 \\
                 6.5. Whittaker Functions $W_{k,m}(z)$ / 305 \\
                 6.6. Asymptotic Expansion of $W_{k,m}(z)$ when $z \to
                 \infty$ / 307 \\
                 6.7. Barnes' Integral Representation of $W_{k,m}(z)$ /
                 310 \\
                 6.8. Relations between $W_{\pm k,m}(\pm z)$ and $M_{\pm
                 k,m}(\pm z)$. Asymptotic Expansion of $F(\alpha,
                 \gamma, z)$. Stokes Phenomenon / 313 \\
                 6.9. The Case when $\gamma$ (or $2m$) is an Integer /
                 316 \\
                 6.10. The Asymptotic Expansions of $F(\alpha, \gamma,
                 z)$ for Large $|\alpha|$, $|\gamma|$ / 318 \\
                 6.11. Differential Equations Reducible to the Confluent
                 Hypergeometric Equation / 318 \\
                 6.12. Weber Equation. Parabolic Cylinder Functions
                 $D_n(z)$ / 320 \\
                 6.13. Hermite Functions and Hermite Polynomials / 325
                 \\
                 6.14. Laguerre Polynomials / 327 \\
                 6.15. Other Special Functions Expressible by Whittaker
                 Functions / 332 \\
                 Exercise 6 / 335 \\
                 7: BESSEL FUNCTIONS \\
                 7.1. Bessel Equation. Its Relation to the Confluent
                 Hypergeometric Equation / 345 \\
                 7.2. Bessel Functions of the First Kind: $J_{\pm
                 \nu}(z)$, $2\nu \neq$ integer / 347 \\
                 7.3. Bessel Functions of Order Half an Odd Integer:
                 $J_{n + 1/2}(z)$ $(n = 0, \pm 1, \pm 2, \ldots{})$ /
                 350 \\
                 7.4. Integral Representations of $J_\nu(z)$ / 351 \\
                 7.5. Bessel Functions of Integral Order $J_n(z)$ $(n =
                 0, 1, 2, \ldots{})$ / 359 \\
                 7.6. Bessel Functions of the Second Kind $Y_\nu(z)$ /
                 365 \\
                 7.7. Bessel Functions of the Third Kind (Hankel
                 Functions) $H_\nu^{(1)}(z)$, $H_\nu^{(2)}(z)$ / 368 \\
                 7.8. Modified (or Imaginary Argument) Bessel Functions
                 $I_\nu(z)$ and $K_\nu(z)$. Thomson Functions
                 $\ber_\nu(z)$ and $\bei_\nu(z)$; etc. / 374 \\
                 7.9. Spherical Bessel Functions $j_l(z)$, $n_l(z)$,
                 $h_l^{(1)}(z), $h_l^{(2)}(z) / 376 \\
                 7.10. Asymptotic Expansions for the Case $|z| \to
                 \infty$ / 378 \\
                 7.11. The Method of Steepest Descent / 381 \\
                 7.12. Asymptotic Expansions of Bessel Functions of
                 Order $\nu$ for Large $|\nu|$ and $|z|$ / 384 \\
                 7.13. Addition Formulae / 395 \\
                 7.14. Integrals Containing Bessel Functions. (1) Finite
                 Integrals / 399 \\
                 7.15. Integrals Containing Bessel Functions. (2)
                 Infinite Integrals / 401 \\
                 7.16. Neumann Expansion / 412 \\
                 7.17. Kapteyn Expansion / 415 \\
                 7.18. The Zeros of Bessel Functions / 420 \\
                 7.19. Fourier--Bessel Expansion / 424 \\
                 Exercise 7 / 425 \\
                 8: WEIERSTRASS ELLIPTIC FUNCTIONS \\
                 8.1. Elliptic Integrals and Elliptic Functions / 456
                 \\
                 8.2. The Periods of Elliptic Integrals / 460 \\
                 8.3. The General Properties of Doubly-Periodic
                 Functions and Elliptic Functions / 462 \\
                 8.4. The Function $\wp(z)$ / 466 \\
                 8.5. Algebraic Relation between $\wp(z)$ and $\wp'(z)$
                 / 468 \\
                 8.6. The Function $\zeta(z)$ / 471 \\
                 8.7. The Function $\sigma(z)$ / 473 \\
                 8.8. Homogeneity of the Weierstrass Elliptic Function /
                 476 \\
                 8.9. Representations of a General Elliptic Function /
                 476 \\
                 8.10. Addition Formulae / 481 \\
                 8.11. Expressing the Coordinates of a Cubic Curve by
                 Elliptic Functions / 485 \\
                 8.12. The Problem of a Quartic Polynomial / 486 \\
                 8.13. Curves of Genus (Deficiency) 1 / 489 \\
                 Exercise 8 / 493 \\
                 9: THETA FUNCTIONS \\
                 9.1. The Theta Function $\theta(\nu)$ / 498 \\
                 9.2. The Functions $\vartheta_k(\nu)$ / 500 \\
                 9.3. Elliptic Functions Represented by Theta Functions
                 / 502 \\
                 9.4. Relations among the Squares of $\vartheta_k(\nu)$
                 / 503 \\
                 9.5. Addition Formulae / 504 \\
                 9.6. Differential Equations Satisfied by Theta
                 Functions / 506 \\
                 9.7. The Values of Some Constants / 508 \\
                 9.8. Legendre's Elliptic Integral of the First Kind /
                 510 \\
                 9.9. Jacobi's Imaginary Transformation / 514 \\
                 9.10. Transformation of Landen-Type / 516 \\
                 9.11. Representation of Theta Functions by Infinite
                 Product / 517 \\
                 9.12. Fourier Expansion of the Logarithmic Derivatives
                 of Theta Functions / 521 \\
                 9.13. The Functions $\Theta(u)$ and $H(u)$ / 522 \\
                 Exercise 9 / 523 \\
                 10: JACOBIAN ELLIPTIC FUNCTIONS \\
                 10.1. Jacobian Elliptic Functions $\sn u$, $\cn u$,
                 $\dn u$ / 530 \\
                 10.2. Geometric Representations of Jacobian Elliptic
                 Functions / 532 \\
                 10.3. Complete Elliptic Integrals / 535 \\
                 10.4. Addition Formulae / 537 \\
                 10.5. The Periodicity of Jacobian Elliptic Functions /
                 539 \\
                 10.6. The Zeros and Poles of Jacobian Elliptic
                 Functions / 540 \\
                 10.7. Transformations of Elliptic Functions / 542 \\
                 10.8. Reductions of Elliptic Integrals / 545 \\
                 10.9. Elliptic Integral of the Second Kind / 552 \\
                 10.10. Elliptic Integral of the Third Kind / 553 \\
                 10.11. Properties of the Function $E(u)$ / 555 \\
                 10.12. Differential Equations Satisfied by $K$ and $E$
                 with Respect to $k$ and Expansions of $K$ and $E$ with
                 Respect to $k$ / 558 \\
                 10.13. Relations between Jacobian Elliptic Functions
                 and Theta Functions / 561 \\
                 10.14. Expressing Jacobian Elliptic Functions in
                 Infinite Products and Fourier Series / 566 \\
                 Exercise 10 / 569 \\
                 11: LAM{\'E} FUNCTIONS \\
                 11.1. Ellipsoidal Coordinates / 575 \\
                 11.2. Representing the Coordinates with Elliptic
                 Functions / 578 \\
                 11.3. Lam{\'e} Equation / 580 \\
                 11.4. Four Types of Lam{\'e} Functions / 583 \\
                 11.5. Ellipsoidal Harmonics / 589 \\
                 11.6. Niven's Representation / 591 \\
                 11.7. On the Zeros of Lam{\'e} Polynomials / 595 \\
                 11.8. Lam{\'e} Functions of the Second Kind / 597 \\
                 11.9. Generalized Lam{\'e} Functions / 599 \\
                 11.10. Integral Equations of Lam{\'e} Functions / 602
                 \\
                 11.11. The Integral Representation of Ellipsoidal
                 Harmonics / 604 \\
                 Exercise 11 / 607 \\
                 12: MATHIEU FUNCTIONS \\
                 12.1. Mathieu Equation / 610 \\
                 12.2. General Properties of the Solution. Fundamental
                 Solutions / 612 \\
                 12.3. Floquet Solution / 614 \\
                 12.4. Periodic Solutions of Mathieu Equation / 615 \\
                 12.5. Fourier Expansion of the Floquet Solution / 617
                 \\
                 12.6. Formulae for Computing Eigenvalues $\lambda(q)$ /
                 620 \\
                 12.7. Mathieu Functions $\ce_m(z)$, $m = 0, 1, 2,
                 \ldots{}$ and $\se_m(z)$, $m = 1, 2 \ldots{}$ / 624 \\
                 12.8. Expansion of $\lambda_\nu(q)$ in Powers of $q$ /
                 627 \\
                 12.9. Fourier Expansions of $\ce_m(z)$ and $\se_m(z)$
                 for Small $q$ / 630 \\
                 12.10. Infinite Determinant / 632 \\
                 12.11. Hill Equation / 633 \\
                 12.12. Stable and Unstable Solutions of Mathieu
                 Equation. Stable Region and Unstable Region / 637 \\
                 12.13. Approximate Solutions of Mathieu Equation for
                 $\lambda \gg q > 0$ / 640 \\
                 12.14. Integral Equations for Mathieu Functions / 643
                 \\
                 Exercise 12 / 645 \\
                 Appendices \\
                 Appendix I. Roots of a Cubic Equation / 654 \\
                 Appendix II. Roots of the Quartic Equation / 656 \\
                 Appendix III. Orthogonal Curvilinear Coordinate Systems
                 / 658 \\
                 Bibliography / 677 \\
                 Glossary / 679 \\
                 Index / 683",
  xxpages =      "xiii + 422",
}


bibtype: article
filename: elefunt.bib
label: Wasilkowski:1989:AIV
author: G. W. Wasilkowski
journal: j-J-COMPLEXITY
volume: 5
number: 3
pages: 363--368
month: sep
monthnumber: 9
year: 1989
CODEN: JOCOEH
ISSN: 0885-064X (print), 1090-2708 (electronic) OR 0885064X (print), 10902708 (electronic)
ISSNL: 0885-064X OR 0885064X
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of complexity
acknowledgement: ack-nhfb
affiliation: Univ. of Kentucky, Lexington, KY
journalURL: http://www.sciencedirect.com/science/journal/0885064X
rawauthor: G. W. Wasilkowski
title:
On adaptive information with varying cardinality for linear problems with elliptically contoured measures

subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES

rawtitle:
On adaptive information with varying cardinality for linear problems with elliptically contoured measures

entry:
@Article{Wasilkowski:1989:AIV,
  author =       "G. W. Wasilkowski",
  title =        "On adaptive information with varying cardinality for
                 linear problems with elliptically contoured measures",
  journal =      j-J-COMPLEXITY,
  volume =       "5",
  number =       "3",
  pages =        "363--368",
  month =        sep,
  year =         "1989",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X (print), 1090-2708 (electronic)",
  ISSN-L =       "0885-064X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Kentucky, Lexington, KY",
  bibno =        "68756",
  catcode =      "G.1.2; G.1.2; F.1.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  fjournal =     "Journal of complexity",
  genterm =      "algorithms; theory",
  guideno =      "1989-08045",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0885064X",
  journalabbrev = "J. Complexity",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES",
}


bibtype: article
filename: elefunt.bib
label: Weniger:1989:NST
author: Ernst Joachim Weniger
journal: j-COMPUT-PHYS-REP
volume: 10
number: 5--6
pages: 189--371
month: dec
monthnumber: 12
year: 1989
CODEN: CPHREF
DOI: https://doi.org/10.1016/0167-7977(89)90011-7
ISSN: 0167-7977 (print), 1878-1004 (electronic) OR 01677977 (print), 18781004 (electronic)
ISSNL: 0167-7977 OR 01677977
bibdate: Thu Dec 01 10:13:37 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:13:37 ???
note: Available as math.NA/0306302.
fjournal: Computer Physics Reports
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Ernst Joachim Weniger
rawnote: Available as math.NA/0306302.
title:
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series

rawtitle:
Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series

entry:
@Article{Weniger:1989:NST,
  author =       "Ernst Joachim Weniger",
  title =        "Nonlinear sequence transformations for the
                 acceleration of convergence and the summation of
                 divergent series",
  journal =      j-COMPUT-PHYS-REP,
  volume =       "10",
  number =       "5--6",
  pages =        "189--371",
  month =        dec,
  year =         "1989",
  CODEN =        "CPHREF",
  DOI =          "https://doi.org/10.1016/0167-7977(89)90011-7",
  ISSN =         "0167-7977 (print), 1878-1004 (electronic)",
  ISSN-L =       "0167-7977",
  bibdate =      "Thu Dec 01 10:13:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Available as math.NA/0306302.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Reports",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Yortsos:1989:LSI
author: Y. C. Yortsos and F. J. Hickernell
title: Linear stability of immiscible displacement in porous media
journal: j-SIAM-J-APPL-MATH
volume: 49
number: 3
pages: 730--748
month: jun
monthnumber: 6
year: 1989
CODEN: SMJMAP
ISSN: 0036-1399 (print), 1095-712X (electronic) OR 00361399 (print), 1095712X (electronic)
ISSNL: 0036-1399 OR 00361399
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: SIAM Journal on Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/siap
rawauthor: Y. C. Yortsos and F. J. Hickernell
rawtitle: Linear stability of immiscible displacement in porous media
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J. Computer Applications; J.2 PHYSICAL SCIENCES AND ENGINEERING

entry:
@Article{Yortsos:1989:LSI,
  author =       "Y. C. Yortsos and F. J. Hickernell",
  title =        "Linear stability of immiscible displacement in porous
                 media",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "730--748",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64942",
  catcode =      "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Parabolic
                 equations; G.1.0 General; G.1.0 Stability (and
                 instability); J.2 Earth and atmospheric sciences; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.4 Quadrature and Numerical Differentiation; G.1.4
                 Finite difference methods; G.1.8 Partial Differential
                 Equations; G.1.8 Difference methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Parabolic equations;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Stability (and instability); Computer Applications,
                 PHYSICAL SCIENCES AND ENGINEERING, Earth and
                 atmospheric sciences; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Finite difference methods; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Difference methods",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09711",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING",
}


bibtype: article
filename: elefunt.bib
label: Zalik:1989:NIE
author: R. A. Zalik
title: A new inequality for entire functions
journal: j-J-APPROX-THEORY
volume: 58
number: 3
pages: 281--283
month: sep
monthnumber: 9
year: 1989
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: R. A. Zalik
rawtitle: A new inequality for entire functions
entry:
@Article{Zalik:1989:NIE,
  author =       "R. A. Zalik",
  title =        "A new inequality for entire functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "3",
  pages =        "281--283",
  month =        sep,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72294",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1989-07871",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: book
filename: elefunt.bib
label: Ziemer:1989:WDF
author: William P. Ziemer
title: Weakly differentiable functions: Sobolev spaces and functions of bounded variation
volume: 120
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 308
year: 1989
ISBN: 0-387-97017-7 OR 0387970177
ISBN13: 978-0-387-97017-2 OR 9780387970172
LCCN: QA323 .Z53 1989
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
series: Graduate texts in mathematics
acknowledgement: ack-nhfb
affiliation: Indiana Univ., Bloomington
rawauthor: William P. Ziemer
rawtitle: Weakly differentiable functions: {Sobolev} spaces and functions of bounded variation
entry:
@Book{Ziemer:1989:WDF,
  author =       "William P. Ziemer",
  title =        "Weakly differentiable functions: {Sobolev} spaces and
                 functions of bounded variation",
  volume =       "120",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 308",
  year =         "1989",
  ISBN =         "0-387-97017-7",
  ISBN-13 =      "978-0-387-97017-2",
  LCCN =         "QA323 .Z53 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Graduate texts in mathematics",
  acknowledgement = ack-nhfb,
  affiliation =  "Indiana Univ., Bloomington",
  bibno =        "69369",
  catcode =      "G.1.2; G.1.8; G.1.5",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.8 Partial Differential Equations;
                 G.1.5 Roots of Nonlinear Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations",
  genterm =      "algorithms; theory",
  guideno =      "1989-01732",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Amos:1990:RPP
author: Donald E. Amos
journal: j-TOMS
volume: 16
number: 4
pages: 404--404
month: dec
monthnumber: 12
year: 1990
CODEN: ACMSCU
DOI: https://doi.org/10.1145/98267.98299
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 09 10:26:24 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:26:24 ???
note: See cite Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; theory
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Donald E. Amos
rawnote: See \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.
title:
Remark on ``Algorithm 644: a Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order''

subject:
bf F.2.2: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.

rawtitle:
Remark on ``{Algorithm 644}: a Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order''

entry:
@Article{Amos:1990:RPP,
  author =       "Donald E. Amos",
  title =        "Remark on ``{Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "404--404",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98299",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:26:24 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems.",
}


bibtype: article
filename: elefunt.bib
label: Anderson:1990:FIC
author: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
title: Functional Inequalities for Complete Elliptic Integrals and Their Ratios
journal: j-SIAM-J-MATH-ANA
volume: 21
number: 2
pages: 536--549
month: mar
monthnumber: 3
year: 1990
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33E05 (30C62 33C75)
MRnumber: 91d:33039
MRreviewer: K. C. Gupta
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: G. D. Anderson and M. K. Vamanamurthy and M. Vuorinen
rawtitle: Functional Inequalities for Complete Elliptic Integrals and Their Ratios
entry:
@Article{Anderson:1990:FIC,
  author =       "G. D. Anderson and M. K. Vamanamurthy and M.
                 Vuorinen",
  title =        "Functional Inequalities for Complete Elliptic
                 Integrals and Their Ratios",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "21",
  number =       "2",
  pages =        "536--549",
  month =        mar,
  year =         "1990",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05 (30C62 33C75)",
  MRnumber =     "91d:33039",
  MRreviewer =   "K. C. Gupta",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1990:BRPb
author: Anonymous
journal: j-MATH-COMPUT-SIMUL
volume: 32
number: 4
pages: 420--420
month: oct
monthnumber: 10
year: 1990
CODEN: MCSIDR
DOI: https://doi.org/10.1016/0378-4754(90)90150-H
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Mon Aug 18 12:50:00 MDT 2025
bibtimestamp: 2025.08.18 12:50:00 MDT
URL: https://www.sciencedirect.com/science/article/pii/037847549090150H
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: Anonymous
title:
Book Review: booktitle Properties of estimators for the gamma function: K. O. Bowman and L. R. Shenton, Marcel Dekker, New York, 1988. 268 pp., ISBN 0-8247-7556-2

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib

rawtitle:
Book Review: {{\booktitle{Properties of estimators for the gamma function}}: K. O. Bowman and L. R. Shenton, Marcel Dekker, New York, 1988. 268 pp., ISBN 0-8247-7556-2}

entry:
@Article{Anonymous:1990:BRPb,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Properties of estimators for
                 the gamma function}}: K. O. Bowman and L. R. Shenton,
                 Marcel Dekker, New York, 1988. 268 pp., ISBN
                 0-8247-7556-2}",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "32",
  number =       "4",
  pages =        "420--420",
  month =        oct,
  year =         "1990",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(90)90150-H",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 12:50:00 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/037847549090150H",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: article
filename: elefunt.bib
label: Bellalij:1990:SPC
author: M. Bellalij
title: A simultaneous process for convergence acceleration and error control
journal: j-J-COMPUT-APPL-MATH
volume: 33
number: 2
pages: 217--231
day: 21
month: dec
monthnumber: 12
year: 1990
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(90)90370-F
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65B99 (65G10)
MRnumber: 1090897 (92a:65029)
MRreviewer: Thomas A. Atchison
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Bellalij
rawtitle: A simultaneous process for convergence acceleration and error control
entry:
@Article{Bellalij:1990:SPC,
  author =       "M. Bellalij",
  title =        "A simultaneous process for convergence acceleration
                 and error control",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "33",
  number =       "2",
  pages =        "217--231",
  day =          "21",
  month =        dec,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90370-F",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B99 (65G10)",
  MRnumber =     "1090897 (92a:65029)",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Bronstein:1990:IEF
author: Manuel Bronstein
title: Integration of elementary functions
journal: j-J-SYMBOLIC-COMP
volume: 9
number: 2
pages: 117--173
month: feb
monthnumber: 2
year: 1990
CODEN: JSYCEH
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 12H05 (68Q40)
MRnumber: 91h:12017
MRreviewer: Alexandru Buium
bibdate: Sat May 10 15:54:09 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Theory/cathode.bib
bibtimestamp: 1997.05.10 15:54:09 MDT
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
classcodes: C1120 (Analysis); C4160 (Numerical integration and differentiation)
corpsource: Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
journalURL: http://www.sciencedirect.com/science/journal/07477171
treatment: T Theoretical or Mathematical
rawauthor: Manuel Bronstein
rawtitle: Integration of elementary functions
keywords:
algebraic extension; algebraic function; decision procedure; elementary function field; elementary functions; exponential; finite terms; indefinite; integration; integration Risch ODEs oderef; logarithm; proof; Trager

entry:
@Article{Bronstein:1990:IEF,
  author =       "Manuel Bronstein",
  title =        "Integration of elementary functions",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "9",
  number =       "2",
  pages =        "117--173",
  month =        feb,
  year =         "1990",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "12H05 (68Q40)",
  MRnumber =     "91h:12017",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Theory/cathode.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson
                 Res. Center, Yorktown Heights, NY, USA",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "algebraic extension; algebraic function; decision
                 procedure; elementary function field; elementary
                 functions; exponential; finite terms; indefinite;
                 integration; integration Risch ODEs oderef; logarithm;
                 proof; Trager",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Carre:1990:PEF
author: C. Carre
title: Plethysm of elementary functions
journal: Bayreuth. Math. Schr.
volume: 31
pages: 1--18
year: 1990
ISSN: 0172-1062 OR 01721062
MRclass: 20C30 (05E05 22E45)
MRnumber: 91f:20013
MRreviewer: John R. Stembridge
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: C. Carre
rawtitle: Plethysm of elementary functions
entry:
@Article{Carre:1990:PEF,
  author =       "C. Carre",
  title =        "Plethysm of elementary functions",
  journal =      "Bayreuth. Math. Schr.",
  volume =       "31",
  pages =        "1--18",
  year =         "1990",
  ISSN =         "0172-1062",
  MRclass =      "20C30 (05E05 22E45)",
  MRnumber =     "91f:20013",
  MRreviewer =   "John R. Stembridge",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ciminiera:1990:HRS
author: L. Ciminiera and P. Montuschi
title: Higher radix square rooting
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 10
pages: 1220--1231
month: oct
monthnumber: 10
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.59853
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:04 MDT 2011
bibtimestamp: 2011.07.07 14:20:04 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: L. Ciminiera and P. Montuschi
rawtitle: Higher radix square rooting
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Ciminiera:1990:HRS,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Higher radix square rooting",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "10",
  pages =        "1220--1231",
  month =        oct,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.59853",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A general discussion on nonrestoring square root
                 algorithms is presented, showing bounds and constraints
                 delimiting the space of feasible algorithms, for all
                 the choices of radix, digit set and representation of
                 the partial remainder. Two classes of \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cody:1990:PEP
author: W. J. Cody
title: Performance Evaluation of Programs for the Error and Complementary Error Functions
journal: j-TOMS
volume: 16
number: 1
pages: 29--37
month: mar
monthnumber: 3
year: 1990
CODEN: ACMSCU
DOI: https://doi.org/10.1145/77626.77628
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65-04 (65G05)
MRnumber: 1 073 407
bibdate: Tue Oct 09 09:29:47 2007
bibtimestamp: 2007.10.09 09:29:47 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
affiliation: Argonne Nat. Lab., IL, USA
journalURL: https://dl.acm.org/loi/toms
thesaurus: Error analysis; Function approximation; Performance evaluation
rawauthor: W. J. Cody
rawtitle: Performance Evaluation of Programs for the Error and Complementary Error Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/; http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html

abstract:
This paper presents methods for performance evaluation of computer programs for the functions $ textrm erf(x) $, $ textrm erfc(x) $, and $ ^x^2 textrm erfc(x) $. Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of $ textrm erfc(x) $. Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.

keywords:
Complementary error functions; Computer programs; FORTRAN; Power series expansions; Repeated integrals; Robustness; Test program

subject:
bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
This paper presents methods for performance evaluation of computer programs for the functions $ \textrm {erf}(x) $, $ \textrm {erfc}(x) $, and $ \e^{x^2} \textrm {erfc}(x) $. Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of $ \textrm {erfc}(x) $. Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.

entry:
@Article{Cody:1990:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs for the Error and
                 Complementary Error Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "29--37",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77628",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "1 073 407",
  bibdate =      "Tue Oct 09 09:29:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
  abstract =     "This paper presents methods for performance evaluation
                 of computer programs for the functions $ \textrm
                 {erf}(x) $, $ \textrm {erfc}(x) $, and $ \e^{x^2}
                 \textrm {erfc}(x) $. Accuracy estimates are based on
                 comparisons using power series expansions and an
                 expansion in the repeated integrals of $ \textrm
                 {erfc}(x) $. Some suggestions for checking robustness
                 are also given. Details of a specific implementation of
                 a test program are included.",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Complementary error functions; Computer programs;
                 FORTRAN; Power series expansions; Repeated integrals;
                 Robustness; Test program",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "Error analysis; Function approximation; Performance
                 evaluation",
}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1990:SDC
author: Armido R. DiDonato
title: Significant Digit Computation of the Elliptical Coverage Function
type: Technical Report
number: NAVSWC TR 90-513
institution: Naval Surface Warfare Center
address: Dahlgren, VA 22448-5000, USA and Silver Spring, MD 20903-5000, USA
pages: v + 13 + A-7 + B-9 + 5
month: sep
monthnumber: 9
year: 1990
bibdate: Sat Nov 15 10:55:35 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2014.11.15 10:55:35 ???
URL: http://www.dtic.mil/dtic/tr/fulltext/u2/a230523.pdf
acknowledgement: ack-nhfb
rawauthor: Armido R. DiDonato
rawtitle: Significant Digit Computation of the Elliptical Coverage Function
entry:
@TechReport{DiDonato:1990:SDC,
  author =       "Armido R. DiDonato",
  title =        "Significant Digit Computation of the Elliptical
                 Coverage Function",
  type =         "Technical Report",
  number =       "NAVSWC TR 90-513",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
                 20903-5000, USA",
  pages =        "v + 13 + A-7 + B-9 + 5",
  month =        sep,
  year =         "1990",
  bibdate =      "Sat Nov 15 10:55:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a230523.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dunham:1990:FPF
author: C. B. Dunham
title: Feasibility of ``perfect'' function evaluation
journal: j-SIGNUM
volume: 25
number: 4
pages: 25--26
month: oct
monthnumber: 10
year: 1990
CODEN: SNEWD6
DOI: https://doi.org/10.1145/122272.122276
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:19 MDT 2005
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 07:50:19 MDT
fjournal: ACM SIGNUM Newsletter
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: C. B. Dunham
rawtitle: Feasibility of ``perfect'' function evaluation
entry:
@Article{Dunham:1990:FPF,
  author =       "C. B. Dunham",
  title =        "Feasibility of ``perfect'' function evaluation",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "4",
  pages =        "25--26",
  month =        oct,
  year =         "1990",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/122272.122276",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:19 MDT 2005",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}


bibtype: article
filename: elefunt.bib
label: Dvorak:1990:NCI
author: Steven L. Dvorak and Edward F. Kuester
title: Numerical computation of the incomplete Lipschitz--Hankel integral $ rm Je_0 (a, z) $
journal: j-J-COMPUT-PHYS
volume: 87
number: 2
pages: 301--327
month: apr
monthnumber: 4
year: 1990
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(90)90255-Y
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:40 MST 2012
bibtimestamp: 2012.01.02 07:55:40 MST
URL: http://www.sciencedirect.com/science/article/pii/002199919090255Y
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Steven L. Dvorak and Edward F. Kuester
rawtitle: Numerical computation of the incomplete {Lipschitz--Hankel} integral {$ {\rm Je}_0 (a, z) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib

entry:
@Article{Dvorak:1990:NCI,
  author =       "Steven L. Dvorak and Edward F. Kuester",
  title =        "Numerical computation of the incomplete
                 {Lipschitz--Hankel} integral {$ {\rm Je}_0 (a, z) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "87",
  number =       "2",
  pages =        "301--327",
  month =        apr,
  year =         "1990",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(90)90255-Y",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:40 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919090255Y",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:1990:RSR
author: M. D. Ercegovac and T. Lang
title: Radix-$4$ square root without initial PLA
journal: j-IEEE-TRANS-COMPUT
volume: 39
number: 8
pages: 1016--1024
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57040
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Jul 7 14:20:03 MDT 2011
bibtimestamp: 2011.07.07 14:20:03 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. D. Ercegovac and T. Lang
rawtitle: Radix-$4$ square root without initial {PLA}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Ercegovac:1990:RSR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Radix-$4$ square root without initial {PLA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1016--1024",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57040",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Germain-Bonne:1990:CAN
author: B. Germain-Bonne
title: Convergence acceleration of number-machine sequences
journal: j-J-COMPUT-APPL-MATH
volume: 32
number: 1--2
pages: 83--88
day: 26
month: nov
monthnumber: 11
year: 1990
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(90)90419-Z
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65B05
MRnumber: 1091778 (91m:65007)
MRreviewer: W. Govaerts
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: Extrapolation and rational approximation (Luminy, 1989)
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. Germain-Bonne
rawnote: Extrapolation and rational approximation (Luminy, 1989)
rawtitle: Convergence acceleration of number-machine sequences
entry:
@Article{Germain-Bonne:1990:CAN,
  author =       "B. Germain-Bonne",
  title =        "Convergence acceleration of number-machine sequences",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "32",
  number =       "1--2",
  pages =        "83--88",
  day =          "26",
  month =        nov,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90419-Z",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B05",
  MRnumber =     "1091778 (91m:65007)",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Luminy,
                 1989)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Hashemian:1990:SRA
author: R. Hashemian
title: Square Rooting Algorithms for Integer and Floating-Point Numbers
journal: j-IEEE-TRANS-COMPUT
volume: C-39
number: 8
pages: 1025--1029
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57041
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
affiliation: Dept. of Electr. Eng., Northern Illinois Univ., Dekalb, IL, USA
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
thesaurus: Digital arithmetic; Iterative methods; Number theory
rawauthor: R. Hashemian
rawtitle: Square Rooting Algorithms for Integer and Floating-Point Numbers
abstract:
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

keywords:
Bit-shift operation; Close estimate; Division by 2; Fast converging iteration; Floating-point numbers; Initial value modification; Integer numbers; Precise root; Real numbers; Square rooting algorithms

rawabstract:
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

entry:
@Article{Hashemian:1990:SRA,
  author =       "R. Hashemian",
  title =        "Square Rooting Algorithms for Integer and
                 Floating-Point Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1025--1029",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57041",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise root is evaluated.
                 The major effort in this development has been
                 concentrated on two objectives: high speed and no
                 division operation other than division by 2. The first
                 objective is achieved through a simple two-step
                 procedure for getting the first estimate, and then
                 modifying it by employing a fast converging iteration
                 technique. The second objective is also fulfilled
                 through applying bit-shift operation rather than
                 division operation. The algorithm is simulated for both
                 integer and real numbers, and the results are compared
                 to two methods being widely used. The results
                 (tabulated) show considerable improvement in speed
                 compared to these other two methods.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Dept. of Electr. Eng., Northern Illinois Univ.,
                 Dekalb, IL, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Bit-shift operation; Close estimate; Division by 2;
                 Fast converging iteration; Floating-point numbers;
                 Initial value modification; Integer numbers; Precise
                 root; Real numbers; Square rooting algorithms",
  summary =      "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise \ldots{}",
  thesaurus =    "Digital arithmetic; Iterative methods; Number theory",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Holton:1990:IJE
author: P. G. W. Holton
title: An Introduction to the Jacobian Elliptic Functions with some Applications
type: Thesis (M.Sc.)
school: University of Newcastle upon Tyne
address: Newcastle upon Tyne, UK
pages: 117
year: 1990
bibdate: Wed Mar 15 06:50:49 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 06:50:49 MDT
acknowledgement: ack-nhfb
rawauthor: P. G. W. Holton
rawtitle: An Introduction to the {Jacobian} Elliptic Functions with some Applications
entry:
@MastersThesis{Holton:1990:IJE,
  author =       "P. G. W. Holton",
  title =        "An Introduction to the {Jacobian} Elliptic Functions
                 with some Applications",
  type =         "Thesis (M.Sc.)",
  school =       "University of Newcastle upon Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "117",
  year =         "1990",
  LCCN =         "????",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ifantis:1990:DIP
author: E. K. Ifantis and P. D. Siafarikas
title: Differential inequalities for the positive zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 30
number: 2
pages: 139--143
day: 28
month: may
monthnumber: 5
year: 1990
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:45 MST 2017
bibtimestamp: 2017.02.25 12:20:45 MST
URL: http://www.sciencedirect.com/science/article/pii/037704279090022R
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: E. K. Ifantis and P. D. Siafarikas
rawtitle: Differential inequalities for the positive zeros of {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib

entry:
@Article{Ifantis:1990:DIP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "Differential inequalities for the positive zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "139--143",
  day =          "28",
  month =        may,
  year =         "1990",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:45 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279090022R",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kiernan:1990:FAE
author: J. M. Kiernan and T. B. Blachowiak
title: Fast, Accurate Elementary Functions For the Cray Y-MP Computer
crossref: Cray:1990:PCU
pages: 243--252
year: 1990
bibdate: Thu Sep 1 10:15:30 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:30 ???
acknowledgement: ack-nj
rawauthor: J. M. Kiernan and T. B. Blachowiak
rawtitle: Fast, Accurate Elementary Functions For the {Cray Y-MP} Computer
entry:
@InProceedings{Kiernan:1990:FAE,
  author =       "J. M. Kiernan and T. B. Blachowiak",
  title =        "Fast, Accurate Elementary Functions For the {Cray
                 Y-MP} Computer",
  crossref =     "Cray:1990:PCU",
  pages =        "243--252",
  year =         "1990",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1990:BRC
author: K. S. Kolbig
journal: j-MATH-COMPUT
volume: 55
number: 191
pages: 395--397
month: jul
monthnumber: 7
year: 1990
CODEN: MCMPAF
DOI: https://doi.org/10.2307/2008818
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Jan 24 08:35:37 2017
bibtimestamp: 2017.01.24 08:35:37 ???
URL: http://www.jstor.org/stable/2008818
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: K. S. K{\"o}lbig
title:
Book Review: booktitle Computation of Functions on Electronic Computers --- Handbook (in Russian). Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S. Tesler

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

rawtitle:
Book Review: {{\booktitle{Computation of Functions on Electronic Computers --- Handbook}} (in Russian). Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S. Tesler}

entry:
@Article{Kolbig:1990:BRC,
  author =       "K. S. K{\"o}lbig",
  title =        "Book Review: {{\booktitle{Computation of Functions on
                 Electronic Computers --- Handbook}} (in Russian).
                 Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S.
                 Tesler}",
  journal =      j-MATH-COMPUT,
  volume =       "55",
  number =       "191",
  pages =        "395--397",
  month =        jul,
  year =         "1990",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008818",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jan 24 08:35:37 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.jstor.org/stable/2008818",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Koren:1990:EEF
author: I. Koren and O. Zinaty
title: Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
journal: j-IEEE-TRANS-COMPUT
volume: C-39
number: 8
pages: 1030--1037
month: aug
monthnumber: 8
year: 1990
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.57042
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Sep 1 10:15:30 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 10:15:30 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: I. Koren and O. Zinaty
rawtitle: Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational Approximations
entry:
@Article{Koren:1990:EEF,
  author =       "I. Koren and O. Zinaty",
  title =        "Evaluating Elementary Functions in a Numerical
                 Coprocessor Based on Rational Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1030--1037",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57042",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Lentz:1990:CFC
author: William J. Lentz
title: Continued fraction calculation of spherical Bessel functions
journal: j-COMPUT-PHYS
volume: 4
number: 4
pages: 403--407
month: jul
monthnumber: 7
year: 1990
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168382
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
MRnumber: 33C10 30B70 65-04
bibdate: Wed Mar 22 14:36:46 2017
bibtimestamp: 2017.03.22 14:36:46 ???
URL: https://aip.scitation.org/doi/10.1063/1.168382
fjournal: Computers in Physics
ZMnumber: 0703.33001
acknowledgement: ack-nhfb
ajournal: Comput. Phys.
journalURL: https://aip.scitation.org/journal/cip
rawauthor: William J. Lentz
rawtitle: Continued fraction calculation of spherical {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/computphys.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
An efficient new method of calculating spherical Bessel functions of complex argument based on continued fractions is developed. The method does not depend on recurrence relations, and it allows accurate calculations on computers with differing word lengths. The method may be easily extended to other types of Bessel functions and to complex orders.

rawabstract:
An efficient new method of calculating spherical Bessel functions of complex argument based on continued fractions is developed. The method does not depend on recurrence relations, and it allows accurate calculations on computers with differing word lengths. The method may be easily extended to other types of Bessel functions and to complex orders.

entry:
@Article{Lentz:1990:CFC,
  author =       "William J. Lentz",
  title =        "Continued fraction calculation of spherical {Bessel}
                 functions",
  journal =      j-COMPUT-PHYS,
  volume =       "4",
  number =       "4",
  pages =        "403--407",
  month =        jul,
  year =         "1990",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168382",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  MRnumber =     "33C10 30B70 65-04",
  bibdate =      "Wed Mar 22 14:36:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168382",
  ZMnumber =     "0703.33001",
  abstract =     "An efficient new method of calculating spherical
                 Bessel functions of complex argument based on continued
                 fractions is developed. The method does not depend on
                 recurrence relations, and it allows accurate
                 calculations on computers with differing word lengths.
                 The method may be easily extended to other types of
                 Bessel functions and to complex orders.",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys.",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


