# bibtab

bibtype: article
filename: elefunt.bib
label: Frenzen:1985:NAE
author: C. L. Frenzen and R. Wong
title: A note on asymptotic evaluation of some Hankel transforms
journal: j-MATH-COMPUT
volume: 45
number: 172
pages: 537--548
month: oct
monthnumber: 10
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 41A60 (44A15 65R10)
MRnumber: 87c:41024
MRreviewer: F. W. J. Olver
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 Math., British Columbia Univ., Vancouver, BC, Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: C. L. Frenzen and R. Wong
rawtitle: A note on asymptotic evaluation of some {Hankel} transforms
keywords:
asymptotic expansion; Bessel function; Bessel functions; growth condition; Hankel transforms; meromorphic function; transforms

classcodes:
B0230 (Integral transforms); B0290Z (Other numerical methods)C1130 (Integral transforms); C4190 (Other numerical methods)

entry:
@Article{Frenzen:1985:NAE,
  author =       "C. L. Frenzen and R. Wong",
  title =        "A note on asymptotic evaluation of some {Hankel}
                 transforms",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "537--548",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A60 (44A15 65R10)",
  MRnumber =     "87c:41024",
  MRreviewer =   "F. W. J. Olver",
  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 =   "B0230 (Integral transforms); B0290Z (Other numerical
                 methods)C1130 (Integral transforms); C4190 (Other
                 numerical methods)",
  corpsource =   "Dept. of Math., British Columbia Univ., Vancouver, BC,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansion; Bessel function; Bessel
                 functions; growth condition; Hankel transforms;
                 meromorphic function; transforms",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gal:1985:CEF
author: Shmuel Gal
title: Computing Elementary Functions: a New Approach for Achieving High Accuracy and Good Performance
crossref: Miranker:1985:ASC
pages: 1--16
year: 1985
DOI: https://doi.org/10.1007/3-540-16798-6_1
bibdate: Thu Sep 01 12:27:23 1994
bibtimestamp: 1994.09.01 12:27:23 ???
acknowledgement: ack-nj
rawauthor: Shmuel Gal
rawtitle: Computing Elementary Functions: a New Approach for Achieving High Accuracy and Good Performance
bibsource:
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Gal:1985:CEF,
  author =       "Shmuel Gal",
  title =        "Computing Elementary Functions: a New Approach for
                 Achieving High Accuracy and Good Performance",
  crossref =     "Miranker:1985:ASC",
  pages =        "1--16",
  year =         "1985",
  DOI =          "https://doi.org/10.1007/3-540-16798-6_1",
  bibdate =      "Thu Sep 01 12:27:23 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: elefunt.bib
label: Gustafson:1985:SCA
author: Sven-AA ke Gustafson
title: Stable convergence acceleration using Laplace transforms
journal: j-NUM-MATH
volume: 47
number: 3
pages: 387--394
month: nov
monthnumber: 11
year: 1985
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65B10 (65D30)
MRnumber: 86m:65009
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Dept. of Numerical Anal. and Comput. Sci., R. Inst. of Technol., Stockholm, Sweden
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Sven-{\AA}ke Gustafson
rawtitle: Stable convergence acceleration using {Laplace} transforms
keywords:
convergence acceleration; Laplace transforms; power series; quadrature schemes; series (mathematics); stable convergence acceleration

entry:
@Article{Gustafson:1985:SCA,
  author =       "Sven-{\AA}ke Gustafson",
  title =        "Stable convergence acceleration using {Laplace}
                 transforms",
  journal =      j-NUM-MATH,
  volume =       "47",
  number =       "3",
  pages =        "387--394",
  month =        nov,
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B10 (65D30)",
  MRnumber =     "86m:65009",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Dept. of Numerical Anal. and Comput. Sci., R. Inst. of
                 Technol., Stockholm, Sweden",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration; Laplace transforms; power
                 series; quadrature schemes; series (mathematics);
                 stable convergence acceleration",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Hill:1985:RCS
author: I. D. Hill and M. C. Pike
title: Remark on ``Algorithm 299: Chi-Squared Integral''
journal: j-TOMS
volume: 11
number: 2
pages: 185--185
month: jun
monthnumber: 6
year: 1985
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Feb 06 05:28:22 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.06 05:28:22 ???
note: See cite Hill:1967:ACS,elLozy:1976:RAC,elLozy:1979:RAS.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: I. D. Hill and M. C. Pike
rawnote: See \cite{Hill:1967:ACS,elLozy:1976:RAC,elLozy:1979:RAS}.
rawtitle: Remark on ``{Algorithm 299: Chi-Squared Integral}''
entry:
@Article{Hill:1985:RCS,
  author =       "I. D. Hill and M. C. Pike",
  title =        "Remark on ``{Algorithm 299: Chi-Squared Integral}''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "185--185",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:22 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1967:ACS,elLozy:1976:RAC,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Hull:1985:PRV
author: T. E. Hull and A. Abrham
title: Properly Rounded Variable Precision Square Root
journal: j-TOMS
volume: 11
number: 3
pages: 229--237
month: sep
monthnumber: 9
year: 1985
CODEN: ACMSCU
DOI: https://doi.org/10.1145/214408.214413
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15 (65G05)
MRnumber: 87a:65041
bibdate: Fri Nov 8 18:01:57 MST 2002
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms; decimal floating-point arithmetic; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: T. E. Hull and A. Abrham
rawtitle: Properly Rounded Variable Precision Square Root
bibsource:
ACM Computing Archive CD-ROM database (1991); 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/1985-11-3/p229-hull/; http://www.acm.org/pubs/toc/Abstracts/toms/214413.html

abstract:
The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. em Properly rounded means rounded to the nearest, or to nearest even in case of a tie. It is em variable precision in that it is designed to return a $p$-digit approximation to a $p$-digit argument, for any $ p > 0 $. (Precision $p$ means $p$ decimal digits.) The program and the analysis are valid for all $ p > 0 $, but current implementations place some restrictions on $p$.

subject:
bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.

rawabstract:
The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. {\em Properly rounded} means rounded to the nearest, or to nearest even in case of a tie. It is {\em variable precision} in that it is designed to return a $p$-digit approximation to a $p$-digit argument, for any $ p > 0 $. (Precision $p$ means $p$ decimal digits.) The program and the analysis are valid for all $ p > 0 $, but current implementations place some restrictions on $p$.

entry:
@Article{Hull:1985:PRV,
  author =       "T. E. Hull and A. Abrham",
  title =        "Properly Rounded Variable Precision Square Root",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "229--237",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214413",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65G05)",
  MRnumber =     "87a:65041",
  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;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/214413.html",
  abstract =     "The square root function presented here returns a
                 properly rounded approximation to the square root of
                 its argument, or it raises an error condition if the
                 argument is negative. {\em Properly rounded} means
                 rounded to the nearest, or to nearest even in case of a
                 tie. It is {\em variable precision} in that it is
                 designed to return a $p$-digit approximation to a
                 $p$-digit argument, for any $ p > 0 $. (Precision $p$
                 means $p$ decimal digits.) The program and the analysis
                 are valid for all $ p > 0 $, but current
                 implementations place some restrictions on $p$.",
  acknowledgement = ack-nhfb,
  catcode =      "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0",
  CRclass =      "G.4 Algorithm analysis; G.4 Verification; G.1.0
                 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.4 Certification and testing; G.1.0 General; G.1.0
                 Error analysis",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Verification; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Error
                 analysis",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "algorithms; verification",
  guideno =      "02789",
  journal-URL =  "https://dl.acm.org/loi/toms",
  jrldate =      "Sept. 1985",
  keywords =     "algorithms; decimal floating-point arithmetic;
                 verification",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Error analysis. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}


bibtype: article
filename: elefunt.bib
label: Humblet:1985:BFE
author: J. Humblet
title: Bessel function expansions of Coulomb wave functions
journal: j-J-MATH-PHYS
volume: 26
number: 4
pages: 656--659
month: apr
monthnumber: 4
year: 1985
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.526602
ISSNL: 0022-2488 OR 00222488
MRclass: 81C05 (33A40 81G45)
MRnumber: 87c:81034
bibdate: Mon Oct 31 11:57:19 MDT 2011
bibtimestamp: 2011.10.31 11:57:19 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v26/i4/p656_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: J. Humblet
rawtitle: {Bessel} function expansions of {Coulomb} wave functions
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

entry:
@Article{Humblet:1985:BFE,
  author =       "J. Humblet",
  title =        "{Bessel} function expansions of {Coulomb} wave
                 functions",
  journal =      j-J-MATH-PHYS,
  volume =       "26",
  number =       "4",
  pages =        "656--659",
  month =        apr,
  year =         "1985",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.526602",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "81C05 (33A40 81G45)",
  MRnumber =     "87c:81034",
  bibdate =      "Mon Oct 31 11:57:19 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/v26/i4/p656_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "4",
}


bibtype: article
filename: elefunt.bib
label: Jones:1985:CIG
author: William B. Jones and W. J. Thron
title: On the computation of incomplete gamma functions in the complex domain
journal: j-J-COMPUT-APPL-MATH
volume: 12--13
pages: 401--417
month: may
monthnumber: 5
year: 1985
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:12 MST 2017
bibtimestamp: 2017.02.25 12:27:12 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042785900342
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: William B. Jones and W. J. Thron
rawtitle: On the computation of incomplete gamma functions in the complex domain
entry:
@Article{Jones:1985:CIG,
  author =       "William B. Jones and W. J. Thron",
  title =        "On the computation of incomplete gamma functions in
                 the complex domain",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "12--13",
  number =       "??",
  pages =        "401--417",
  month =        may,
  year =         "1985",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:12 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042785900342",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:1985:EFK
author: William Kahan
title: Elementary Functions from Kernels and Elementary Inequalities among Elementary Functions
institution: inst-BERKELEY-CS
address: inst-BERKELEY-CS:adr
pages: 5
day: 24
month: oct
monthnumber: 10
year: 1985
bibdate: Sat Aug 23 06:12:44 2025
bibtimestamp: 2025.08.23 06:12:44 ???
URL: https://ieeemilestones.ethw.org/w/images/1/16/Wk_elems_from_kernels_oct85.pdf
acknowledgement: ack-nhfb
rawauthor: William Kahan
rawtitle: Elementary Functions from Kernels and Elementary Inequalities among Elementary Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Given binary floating-point subprograms to calculate the ``Kernels'' $ ln (x) $ for $ x ge 0 $ and $ ln 1 p(x) = ln (1 + x) $ for $ x ge - 1 $, $ exp (x) $ and $ expmone (x) = exp (x) - 1 $ for all $x$, and $ tan (x)$ for $ |x] < pi / 8$ and $ arctan (x)$ for $ |x| < sqrt 2 - 1$, to nearly full working accuracy, we may calculate all the other elementary transcendental functions almost as accurately, and with no violation of (weak) monotonicity,

rawabstract:
Given binary floating-point subprograms to calculate the ``Kernels'' $ \ln (x) $ for $ x \ge 0 $ and $ \ln 1 p(x) = \ln (1 + x) $ for $ x \ge - 1 $, $ \exp (x) $ and $ \expmone (x) = \exp (x) - 1 $ for all $x$, and $ \tan (x)$ for $ |x] < \pi / 8$ and $ \arctan (x)$ for $ |x| < \sqrt {2} - 1$, to nearly full working accuracy, we may calculate all the other elementary transcendental functions almost as accurately, and with no violation of (weak) monotonicity,

entry:
@Unpublished{Kahan:1985:EFK,
  author =       "William Kahan",
  title =        "Elementary Functions from Kernels and Elementary
                 Inequalities among Elementary Functions",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "5",
  day =          "24",
  month =        oct,
  year =         "1985",
  bibdate =      "Sat Aug 23 06:12:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/1/16/Wk_elems_from_kernels_oct85.pdf",
  abstract =     "Given binary floating-point subprograms to calculate
                 the ``Kernels'' $ \ln (x) $ for $ x \ge 0 $ and $ \ln 1
                 p(x) = \ln (1 + x) $ for $ x \ge - 1 $, $ \exp (x) $
                 and $ \expmone (x) = \exp (x) - 1 $ for all $x$, and $
                 \tan (x)$ for $ |x] < \pi / 8$ and $ \arctan (x)$ for $
                 |x| < \sqrt {2} - 1$, to nearly full working accuracy,
                 we may calculate all the other elementary
                 transcendental functions almost as accurately, and with
                 no violation of (weak) monotonicity,",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kravchuk:1985:ACE
author: V. R. Kravchuk
title: Approximation of certain elementary functions by rational functions of order $ (n, 2) $. (Russian)
journal: Akad. Nauk Ukrain. SSR Inst. Mat. Preprint
volume: 18
pages: 7--40
year: 1985
MRclass: 41A25 (41A10)
MRnumber: 87b:41017
MRreviewer: R. Smarzewski
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. R. Kravchuk
rawtitle:
Approximation of certain elementary functions by rational functions of order $ (n, 2) $. ({Russian})

entry:
@Article{Kravchuk:1985:ACE,
  author =       "V. R. Kravchuk",
  title =        "Approximation of certain elementary functions by
                 rational functions of order $ (n, 2) $. ({Russian})",
  journal =      "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
  volume =       "18",
  pages =        "7--40",
  year =         "1985",
  MRclass =      "41A25 (41A10)",
  MRnumber =     "87b:41017",
  MRreviewer =   "R. Smarzewski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Kravchuk:1985:EAE
author: V. R. Kravchuk
journal: j-UKR-MAT-Z
volume: 37
number: 2
pages: 175--180, 270
year: 1985
CODEN: UMZHAA
ISSN: 0041-6053 OR 00416053
MRclass: 41A20 (41A25)
MRnumber: 86h:41013
MRreviewer: Miguel A. Jim{\'e}nez Pozo
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: Ukrainskii matematicheskii zhurnal
language: Russian
acknowledgement: ack-nhfb
rawauthor: V. R. Kravchuk
title:
Effective approximation of elementary functions by rational polynomials of order $ (n, 1) $. (Russian)

rawtitle:
Effective approximation of elementary functions by rational polynomials of order $ (n, 1) $. ({Russian})

entry:
@Article{Kravchuk:1985:EAE,
  author =       "V. R. Kravchuk",
  title =        "Effective approximation of elementary functions by
                 rational polynomials of order $ (n, 1) $. ({Russian})",
  journal =      j-UKR-MAT-Z,
  volume =       "37",
  number =       "2",
  pages =        "175--180, 270",
  year =         "1985",
  CODEN =        "UMZHAA",
  ISSN =         "0041-6053",
  MRclass =      "41A20 (41A25)",
  MRnumber =     "86h:41013",
  MRreviewer =   "Miguel A. Jim{\'e}nez Pozo",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ukrainskii matematicheskii zhurnal",
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Lazard:1985:PFD
author: Daniel Lazard
journal: Asterisque
volume: 121--122
pages: 295--308
year: 1985
MRclass: 12H05 (12-04)
MRnumber: 86k:12010
MRreviewer: J. H. Davenport
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: French
acknowledgement: ack-nhfb
rawauthor: Daniel Lazard
title:
Primitives des fonctions elementaires (d'apres Risch et Davenport). (French) [Primitives of elementary functions (following Risch and Davenport)] Seminar Bourbaki, Vol. 1983/84, No. 121-122

rawtitle:
Primitives des fonctions {\'e}l{\'e}mentaires (d'apr{\`e}s {Risch} et {Davenport}). ({French}) [Primitives of elementary functions (following {Risch} and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No. 121-122}

entry:
@Article{Lazard:1985:PFD,
  author =       "Daniel Lazard",
  title =        "Primitives des fonctions {\'e}l{\'e}mentaires
                 (d'apr{\`e}s {Risch} et {Davenport}). ({French})
                 [Primitives of elementary functions (following {Risch}
                 and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No.
                 121-122}",
  journal =      "Ast{\'e}risque",
  volume =       "121--122",
  pages =        "295--308",
  year =         "1985",
  MRclass =      "12H05 (12-04)",
  MRnumber =     "86k:12010",
  MRreviewer =   "J. H. Davenport",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: article
filename: elefunt.bib
label: Lewanowicz:1985:RRH
author: Stanislaw Lewanowicz
title: Recurrence relations for hypergeometric functions of unit argument
journal: j-MATH-COMPUT
volume: 45
number: 172
pages: 521--535
month: oct
monthnumber: 10
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A35 (65Q05)
MRnumber: 86m:33004
MRreviewer: S. Conde
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
classcodes: B0290 (Numerical analysis); C4100 (Numerical analysis)
corpsource: Inst. of Comput. Sci., Wroclaw Univ., Poland
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Stanis{\l}aw Lewanowicz
rawtitle: Recurrence relations for hypergeometric functions of unit argument
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database

keywords:
(mathematics); convergence of numerical methods; hypergeometric function; numerical analysis; recurrence relation; series; unit argument

entry:
@Article{Lewanowicz:1985:RRH,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "Recurrence relations for hypergeometric functions of
                 unit argument",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "521--535",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A35 (65Q05)",
  MRnumber =     "86m:33004",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "(mathematics); convergence of numerical methods;
                 hypergeometric function; numerical analysis; recurrence
                 relation; series; unit argument",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Lo:1985:GPB
author: Hao-Yung Lo and Y. Aoki
title: Generation of a Precise Binary Logarithm with Difference Grouping Programmable Logic Array
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 8
pages: 681--691
month: aug
monthnumber: 8
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676614
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:33:17 MDT 2011
bibtimestamp: 2011.07.10 08:33:17 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676614
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Hao-Yung Lo and Y. Aoki
rawtitle: Generation of a Precise Binary Logarithm with Difference Grouping Programmable Logic Array
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Lo:1985:GPB,
  author =       "Hao-Yung Lo and Y. Aoki",
  title =        "Generation of a Precise Binary Logarithm with
                 Difference Grouping Programmable Logic Array",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "681--691",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676614",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676614",
  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: Majerski:1985:SRA
author: S. Majerski
title: Square-Rooting Algorithms for High-Speed Digital Circuits
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 8
pages: 724--733
month: aug
monthnumber: 8
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676618
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sun Jul 10 08:33:17 MDT 2011
bibtimestamp: 2011.07.10 08:33:17 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: S. Majerski
rawtitle: Square-Rooting Algorithms for High-Speed Digital Circuits
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/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Majerski:1985:SRA,
  author =       "S. Majerski",
  title =        "Square-Rooting Algorithms for High-Speed Digital
                 Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "724--733",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676618",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
  acknowledgement = ack-nj # "\slash " # 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: Martin:1985:FAB
author: Pablo Martin and Antonio L. Guerrero
title: Fractional approximations to the Bessel function $ J_0 (x) $
journal: j-J-MATH-PHYS
volume: 26
number: 4
pages: 705--707
month: apr
monthnumber: 4
year: 1985
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.526610
ISSNL: 0022-2488 OR 00222488
MRclass: 41A21 (33A40)
MRnumber: 86g:41031
MRreviewer: Hans-J{\"u}rgen Albrand
bibdate: Mon Oct 31 11:57:19 MDT 2011
bibtimestamp: 2011.10.31 11:57:19 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v26/i4/p705_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Pablo Mart{\'\i}n and Antonio L. Guerrero
rawtitle: Fractional approximations to the {Bessel} function {$ J_0 (x) $}
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

entry:
@Article{Martin:1985:FAB,
  author =       "Pablo Mart{\'\i}n and Antonio L. Guerrero",
  title =        "Fractional approximations to the {Bessel} function {$
                 J_0 (x) $}",
  journal =      j-J-MATH-PHYS,
  volume =       "26",
  number =       "4",
  pages =        "705--707",
  month =        apr,
  year =         "1985",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.526610",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A21 (33A40)",
  MRnumber =     "86g:41031",
  MRreviewer =   "Hans-J{\"u}rgen Albrand",
  bibdate =      "Mon Oct 31 11:57:19 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/v26/i4/p705_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "3",
}


bibtype: article
filename: elefunt.bib
label: Milgram:1985:GIE
author: M. S. Milgram
title: The Generalized Integro-Exponential Function
journal: j-MATH-COMPUT
volume: 44
number: 170
pages: 443--458
month: apr
monthnumber: 4
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A70 (65D15)
MRnumber: 86c:33024
MRreviewer: S. Conde
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: AECL, Chalk River, Ont., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. S. Milgram
rawtitle: The Generalized Integro-Exponential Function
keywords:
exponential function; exponential integral; first-order functions; function; function approximation; function evaluation; generalized integro-; incomplete gamma; minimax; rational minimax approximations; techniques

classcodes:
B0290D (Functional analysis); B0290F (Interpolation and function approximation); C4120 (Functional analysis); C4130 (Interpolation and function approximation)

entry:
@Article{Milgram:1985:GIE,
  author =       "M. S. Milgram",
  title =        "The Generalized Integro-Exponential Function",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "443--458",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A70 (65D15)",
  MRnumber =     "86c:33024",
  MRreviewer =   "S. Conde",
  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 =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "AECL, Chalk River, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "exponential function; exponential integral;
                 first-order functions; function; function
                 approximation; function evaluation; generalized
                 integro-; incomplete gamma; minimax; rational minimax
                 approximations; techniques",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Muller:1985:DBC
author: Jean-Michel Muller
title: Discrete basis and computation of elementary functions
journal: j-IEEE-TRANS-COMPUT
volume: C-34
number: 9
pages: 857--862
month: sep
monthnumber: 9
year: 1985
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1985.1676643
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 65D20 (65V05)
MRnumber: 87e:65016
MRreviewer: D. Zwick
bibdate: Sun Jul 10 08:33:33 MDT 2011
bibtimestamp: 2011.07.10 08:33:33 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Jean-Michel Muller
rawtitle: Discrete basis and computation of elementary functions
abstract:
We give necessary and sufficient conditions in order that the infinite product or sum of the terms of a positive decreasing sequence generates the reals in a given interval.

rawabstract:
We give necessary and sufficient conditions in order that the infinite product or sum of the terms of a positive decreasing sequence generates the reals in a given interval.

entry:
@Article{Muller:1985:DBC,
  author =       "Jean-Michel Muller",
  title =        "Discrete basis and computation of elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "857--862",
  month =        sep,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676643",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D20 (65V05)",
  MRnumber =     "87e:65016",
  MRreviewer =   "D. Zwick",
  bibdate =      "Sun Jul 10 08:33:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
  abstract =     "We give necessary and sufficient conditions in order
                 that the infinite product or sum of the terms of a
                 positive decreasing sequence generates the reals in a
                 given interval.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: incollection
filename: elefunt.bib
label: Muller:1985:RNR
author: Jean-Michel Muller
booktitle: Seminar on number theory, 1984--1985 (Talence, 1984/1985)
volume: 12
publisher: Univ. Bordeaux I
address: Talence, France
pages: 22
year: 1985
MRclass: 26-04 (11B13 11B34 26A09)
MRnumber: 87k:26001
MRreviewer: S. L. Segal
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: French
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller
rawbooktitle: Seminar on number theory, 1984--1985 (Talence, 1984/1985)
title:
Representation des nombres reels et calcul des fonctions elementaires. (French) [Representation of real numbers and calculation of elementary functions]

remark:
From the MRreview: ``About one third of the paper is devoted to algorithms for calculating quantities like square root, exponential, logarithm, or trigonometric funtions, using discrete bases. Indeed, the major motivation for the present paper is obtaining simple algorithms which can easily be realized by hardware.''

rawtitle:
Repr{\'e}sentation des nombres r{\'e}els et calcul des fonctions {\'e}l{\'e}mentaires. ({French}) [Representation of real numbers and calculation of elementary functions]

entry:
@InCollection{Muller:1985:RNR,
  author =       "Jean-Michel Muller",
  booktitle =    "Seminar on number theory, 1984--1985 (Talence,
                 1984/1985)",
  title =        "Repr{\'e}sentation des nombres r{\'e}els et calcul des
                 fonctions {\'e}l{\'e}mentaires. ({French})
                 [Representation of real numbers and calculation of
                 elementary functions]",
  volume =       "12",
  publisher =    "Univ. Bordeaux {I}",
  address =      "Talence, France",
  pages =        "22",
  year =         "1985",
  MRclass =      "26-04 (11B13 11B34 26A09)",
  MRnumber =     "87k:26001",
  MRreviewer =   "S. L. Segal",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "From the MRreview: ``About one third of the paper is
                 devoted to algorithms for calculating quantities like
                 square root, exponential, logarithm, or trigonometric
                 funtions, using discrete bases. Indeed, the major
                 motivation for the present paper is obtaining simple
                 algorithms which can easily be realized by
                 hardware.''",
}


bibtype: techreport
filename: elefunt.bib
label: Parlett:1985:DAA
author: Beresford N. Parlett and K. C. Ng
title: Development of an accurate algorithm for $ exp (B t) $
type: Technical Report
number: PAM-294
institution: inst-CPAM-UCB
address: inst-CPAM-UCB:adr
pages: 22
month: aug
monthnumber: 8
year: 1985
bibdate: Fri Nov 11 09:06:19 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.11.11 09:06:19 ???
acknowledgement: ack-nhfb
rawauthor: Beresford N. Parlett and K. C. Ng
rawtitle: Development of an accurate algorithm for {$ \exp (B t) $}
entry:
@TechReport{Parlett:1985:DAA,
  author =       "Beresford N. Parlett and K. C. Ng",
  title =        "Development of an accurate algorithm for {$ \exp (B t)
                 $}",
  type =         "Technical Report",
  number =       "PAM-294",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        aug,
  year =         "1985",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: phdthesis
filename: elefunt.bib
label: Peralta:1985:TRN
author: Rene Caupolican Peralta
type: Thesis (Ph.D.)
school: Department of Computer Science, University of California, Berkeley
address: Berkeley, CA, USA
pages: 52
month: dec
monthnumber: 12
year: 1985
bibdate: Sat Oct 17 16:25:07 MDT 1998
bibtimestamp: 1998.10.17 16:25:07 MDT
acknowledgement: ack-nhfb
rawauthor: Rene Caupolican Peralta
title:
Three results in number theory and cryptography: a new algorithm to compute square roots modulo a prime number; On the bit complexity of the discrete logarithm; a framework for the study of cryptoprotocols

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

keywords:
dissertations; dissertations, academic --- UCB --- computer science --- 1981--1990; University of California, Berkeley. computer science division --

rawtitle:
Three results in number theory and cryptography: a new algorithm to compute square roots modulo a prime number; On the bit complexity of the discrete logarithm; a framework for the study of cryptoprotocols

entry:
@PhdThesis{Peralta:1985:TRN,
  author =       "Rene Caupolican Peralta",
  title =        "Three results in number theory and cryptography: a new
                 algorithm to compute square roots modulo a prime
                 number; On the bit complexity of the discrete
                 logarithm; a framework for the study of
                 cryptoprotocols",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "52",
  month =        dec,
  year =         "1985",
  LCCN =         "????",
  bibdate =      "Sat Oct 17 16:25:07 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations; dissertations, academic --- UCB ---
                 computer science --- 1981--1990; University of
                 California, Berkeley. computer science division --",
}


bibtype: article
filename: elefunt.bib
label: Pereira:1985:ECF
author: N. Costa Pereira
title: Estimates for the Chebyshev function $ psi (x) - theta (x) $
journal: j-MATH-COMPUT
volume: 44
number: 169
pages: 211--221
month: jan
monthnumber: 1
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11A25 (11N45 11Y35 33A70)
MRnumber: 86k:11005
bibdate: Thu Jun 15 07:26:46 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 2000.06.15 07:26:46 ???
note: See corrigendum cite Pereira:1987:CEC.
fjournal: Mathematics of Computation
keywords: Chebyshev approximation; Chebyshev function
acknowledgement: ack-nhfb
classcodes: B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: N. Costa Pereira
rawnote: See corrigendum \cite{Pereira:1987:CEC}.
rawtitle: Estimates for the {Chebyshev} function $ \psi (x) - \theta (x) $
entry:
@Article{Pereira:1985:ECF,
  author =       "N. Costa Pereira",
  title =        "Estimates for the {Chebyshev} function $ \psi (x) -
                 \theta (x) $",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "169",
  pages =        "211--221",
  month =        jan,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11A25 (11N45 11Y35 33A70)",
  MRnumber =     "86k:11005",
  bibdate =      "Thu Jun 15 07:26:46 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See corrigendum \cite{Pereira:1987:CEC}.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; Chebyshev function",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Schoof:1985:ECF
author: Rene Schoof
title: Elliptic Curves Over Finite Fields and the Computation of Square Roots $ operatorname mod p $
journal: j-MATH-COMPUT
volume: 44
number: 170
pages: 483--494
month: apr
monthnumber: 4
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y16 (11G20 14G15)
MRnumber: 86e:11122
MRreviewer: Karl Rubin
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Amsterdam Univ., Netherlands
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Ren{\'e} Schoof
rawtitle: Elliptic Curves Over Finite Fields and the Computation of Square Roots $ \operatorname {mod} p $
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/mathcomp1980.bib; JSTOR database

keywords:
computational complexity; deterministic algorithm; elliptic curve; F/sub q/-points; finite fields; function evaluation; number theory; square roots mod p; Weierstrass equation

classcodes:
B0250 (Combinatorial mathematics); B0290D (Functional analysis); C1160 (Combinatorial mathematics); C4120 (Functional analysis); C4240 (Programming and algorithm theory)

entry:
@Article{Schoof:1985:ECF,
  author =       "Ren{\'e} Schoof",
  title =        "Elliptic Curves Over Finite Fields and the Computation
                 of Square Roots $ \operatorname {mod} p $",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "483--494",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y16 (11G20 14G15)",
  MRnumber =     "86e:11122",
  MRreviewer =   "Karl Rubin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0250 (Combinatorial mathematics); B0290D (Functional
                 analysis); C1160 (Combinatorial mathematics); C4120
                 (Functional analysis); C4240 (Programming and algorithm
                 theory)",
  corpsource =   "Amsterdam Univ., Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; deterministic algorithm;
                 elliptic curve; F/sub q/-points; finite fields;
                 function evaluation; number theory; square roots mod p;
                 Weierstrass equation",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Shah:1985:SAA
author: Arvind K. Shah
title: A Simpler Approximation for Areas Under the Standard Normal Curve
journal: j-AMER-STAT
volume: 39
number: 1
pages: 80--80
month: feb
monthnumber: 2
year: 1985
CODEN: ASTAAJ
ISSN: 0003-1305 (print), 1537-2731 (electronic) OR 00031305 (print), 15372731 (electronic)
ISSNL: 0003-1305 OR 00031305
bibdate: Fri Jan 27 12:40:28 MST 2012
bibtimestamp: 2012.01.27 12:40:28 MST
URL: http://www.jstor.org/stable/2683918
fjournal: The American Statistician
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/utas20
rawauthor: Arvind K. Shah
rawtitle: A Simpler Approximation for Areas Under the Standard Normal Curve
bibsource:
http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326426; https://www.math.utah.edu/pub/tex/bib/amstat1980.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Shah:1985:SAA,
  author =       "Arvind K. Shah",
  title =        "A Simpler Approximation for Areas Under the Standard
                 Normal Curve",
  journal =      j-AMER-STAT,
  volume =       "39",
  number =       "1",
  pages =        "80--80",
  month =        feb,
  year =         "1985",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 12:40:28 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326426;
                 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/2683918",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}


bibtype: article
filename: elefunt.bib
label: Spijker:1985:SRS
author: M. N. Spijker
journal: j-MATH-COMPUT
volume: 45
number: 172
pages: 377--392
month: oct
monthnumber: 10
year: 1985
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65L20 (65M10)
MRnumber: 86j:65106
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: Inst. of Appl. Math. and Comput. Sci., Leiden Univ., Netherlands
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: M. N. Spijker
title:
Stepsize restrictions for stability of one-step methods in the numerical solution of initial value problems

keywords:
convection; convergence of numerical methods; differential equations; diffusion; diffusion-convection; error growth; initial value problems; iterative methods; numerical solution; partial; problem; stability of one-step methods; stepsize restrictions

classcodes:
A0260 (Numerical approximation and analysis); A0560 (Transport processes: theory); B0290F (Interpolation and function approximation); B0290P (Differential equations); C4130 (Interpolation and function approximation); C4170 (Differential equations); C7320 (Physics and chemistry computing)

rawtitle:
Stepsize restrictions for stability of one-step methods in the numerical solution of initial value problems

entry:
@Article{Spijker:1985:SRS,
  author =       "M. N. Spijker",
  title =        "Stepsize restrictions for stability of one-step
                 methods in the numerical solution of initial value
                 problems",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "377--392",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L20 (65M10)",
  MRnumber =     "86j:65106",
  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); A0560
                 (Transport processes: theory); B0290F (Interpolation
                 and function approximation); B0290P (Differential
                 equations); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations); C7320
                 (Physics and chemistry computing)",
  corpsource =   "Inst. of Appl. Math. and Comput. Sci., Leiden Univ.,
                 Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "convection; convergence of numerical methods;
                 differential equations; diffusion;
                 diffusion-convection; error growth; initial value
                 problems; iterative methods; numerical solution;
                 partial; problem; stability of one-step methods;
                 stepsize restrictions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Sreedharan:1985:ASS
author: J. Sreedharan and A. Dhurkadas
title: 8086 algorithm solves square roots
journal: j-EDN
volume: 30
number: 7
pages: 272
month: apr
monthnumber: 4
year: 1985
CODEN: EDNSBH
ISSN: 0012-7515, 0364-6637 OR 00127515, 03646637
bibdate: Thu Sep 1 10:15:42 1994
bibtimestamp: 1994.09.01 10:15:42 ???
fjournal: EDN
acknowledgement: ack-nj
rawauthor: J. Sreedharan and A. Dhurkadas
rawtitle: 8086 algorithm solves square roots
entry:
@Article{Sreedharan:1985:ASS,
  author =       "J. Sreedharan and A. Dhurkadas",
  title =        "8086 algorithm solves square roots",
  journal =      j-EDN,
  volume =       "30",
  number =       "7",
  pages =        "272",
  month =        apr,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  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;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}


bibtype: article
filename: elefunt.bib
label: Temme:1985:LTI
author: N. M. Temme
title: Laplace type integrals: transformation to standard form and uniform asymptotic expansions
journal: j-QUART-APPL-MATH
volume: 43
number: 1
pages: 103--123
year: 1985
CODEN: QAMAAY
DOI: https://doi.org/10.1090/qam/782260
ISSN: 0033-569x (print), 1552-4485 (electronic) OR 0033569x (print), 15524485 (electronic)
ISSNL: 0033-569X OR 0033569X
MRclass: 44A10 (41A60)
MRnumber: 782260
MRreviewer: I. Feny{\H{o}}
bibdate: Tue Feb 6 11:42:02 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.02.06 11:42:02 ???
fjournal: Quarterly of Applied Mathematics
acknowledgement: ack-nhfb
ajournal: Q. Appl. Math.
journalURL: http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam
rawauthor: N. M. Temme
rawtitle: {Laplace} type integrals: transformation to standard form and uniform asymptotic expansions
entry:
@Article{Temme:1985:LTI,
  author =       "N. M. Temme",
  title =        "{Laplace} type integrals: transformation to standard
                 form and uniform asymptotic expansions",
  journal =      j-QUART-APPL-MATH,
  volume =       "43",
  number =       "1",
  pages =        "103--123",
  year =         "1985",
  CODEN =        "QAMAAY",
  DOI =          "https://doi.org/10.1090/qam/782260",
  ISSN =         "0033-569x (print), 1552-4485 (electronic)",
  ISSN-L =       "0033-569X",
  MRclass =      "44A10 (41A60)",
  MRnumber =     "782260",
  MRreviewer =   "I. Feny{\H{o}}",
  bibdate =      "Tue Feb 6 11:42:02 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Q. Appl. Math.",
  fjournal =     "Quarterly of Applied Mathematics",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J641;
                 http://www.ams.org/journals/qam",
}


bibtype: article
filename: elefunt.bib
label: Agarwal:1986:NSV
title: New Scalar and Vector Elementary Functions for the IBM System / 370
journal: j-IBM-JRD
volume: 30
number: 2
pages: 126--144
month: mar
monthnumber: 3
year: 1986
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.302.0126
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 76W05
MRnumber: 840 341
bibdate: Sat Jan 11 17:44:01 MST 1997
bibtimestamp: 1997.01.11 17:44:01 MST
note: See clarification cite Agarwal:1987:CNS.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
ajournal: IBM J. Res. Develop.
classcodes: C6140D (High level languages); C7310 (Mathematics computing)
corpsource: IBM Res. Div., Yorktown Heights, NY, USA
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalabr: IBM J Res Dev
treatment: N New Development; P Practical
rawnote: See clarification \cite{Agarwal:1987:CNS}.
rawtitle: New Scalar and Vector Elementary Functions for the {IBM System\slash 370}
author:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

bibsource:
Compendex database; 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/ibmjrd.bib

abstract:
Algorithms have been developed to compute short-and long-precision elementary functions: SIN, COS, TAN, COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS, ATAN2, and CABS, in scalar (28 functions) and vector (22 functions) mode. They have been implemented as part of the new VS FORTRAN library recently announced along with the IBM 3090 Vector Facility. These algorithms are essentially table-based algorithms. An important feature of these algorithms is that they produce bitwise-identical results on scalar and vector System / 370 machines. Of these, for five functions the computed value result is always the correctly rounded value of the infinite-precision result. For the rest of the functions, the value returned is one of the two floating-point neighbors bordering the infinite-precision result, which implies exact results if they are machine-representable. For the five correctly rounded elementary functions, scalar and vector algorithms are designed independently to optimize performance in each case.

keywords:
ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2; bitwise-identical results; CABS; computer metatheory; computer programming; computer programming languages --- fortran; COS; COTAN; design; elementary functions; EXP; FORTRAN; fortran library; functions; IBM computers; IBM System/370; infinite-precision result; LOG; LOG10; mainframes; measurement; performance; POWER; scalar elementary functions; SIN; SQRT; subroutines; table-based algorithms; TAN; vector elementary; VS FORTRAN library

subject:
C.4 Computer Systems Organization, PERFORMANCE OF SYSTEMS I.1.2 Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms F.3.3 Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies of Program Constructs, Functional constructs C.1.2 Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors

rawabstract:
Algorithms have been developed to compute short-and long-precision elementary functions: SIN, COS, TAN, COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS, ATAN2, and CABS, in scalar (28 functions) and vector (22 functions) mode. They have been implemented as part of the new VS FORTRAN library recently announced along with the IBM 3090 Vector Facility. These algorithms are essentially table-based algorithms. An important feature of these algorithms is that they produce bitwise-identical results on scalar and vector System\slash 370 machines. Of these, for five functions the computed value result is always the correctly rounded value of the infinite-precision result. For the rest of the functions, the value returned is one of the two floating-point neighbors bordering the infinite-precision result, which implies exact results if they are machine-representable. For the five correctly rounded elementary functions, scalar and vector algorithms are designed independently to optimize performance in each case.

rawauthor:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

entry:
@Article{Agarwal:1986:NSV,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "New Scalar and Vector Elementary Functions for the
                 {IBM System\slash 370}",
  journal =      j-IBM-JRD,
  volume =       "30",
  number =       "2",
  pages =        "126--144",
  month =        mar,
  year =         "1986",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.302.0126",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "840 341",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "Compendex database;
                 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/ibmjrd.bib",
  note =         "See clarification \cite{Agarwal:1987:CNS}.",
  abstract =     "Algorithms have been developed to compute short-and
                 long-precision elementary functions: SIN, COS, TAN,
                 COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
                 ATAN2, and CABS, in scalar (28 functions) and vector
                 (22 functions) mode. They have been implemented as part
                 of the new VS FORTRAN library recently announced along
                 with the IBM 3090 Vector Facility. These algorithms are
                 essentially table-based algorithms. An important
                 feature of these algorithms is that they produce
                 bitwise-identical results on scalar and vector
                 System\slash 370 machines. Of these, for five functions
                 the computed value result is always the correctly
                 rounded value of the infinite-precision result. For the
                 rest of the functions, the value returned is one of the
                 two floating-point neighbors bordering the
                 infinite-precision result, which implies exact results
                 if they are machine-representable. For the five
                 correctly rounded elementary functions, scalar and
                 vector algorithms are designed independently to
                 optimize performance in each case.",
  accepted =     "2 December 1985",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  classcodes =   "C6140D (High level languages); C7310 (Mathematics
                 computing)",
  classification = "723",
  corpsource =   "IBM Res. Div., Yorktown Heights, NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2;
                 bitwise-identical results; CABS; computer metatheory;
                 computer programming; computer programming languages
                 --- fortran; COS; COTAN; design; elementary functions;
                 EXP; FORTRAN; fortran library; functions; IBM
                 computers; IBM System/370; infinite-precision result;
                 LOG; LOG10; mainframes; measurement; performance;
                 POWER; scalar elementary functions; SIN; SQRT;
                 subroutines; table-based algorithms; TAN; vector
                 elementary; VS FORTRAN library",
  received =     "5 November 1985",
  remark-1 =     "Numerous figures show errors in ulps, in either linear
                 or logarithmic scales, as dot plots over a range of
                 arguments, an idea that the authors credit to a
                 suggestion by Cleve Moler, then consulting with IBM
                 Palo Alto labs; such plots are used extensively in
                 \cite{Beebe:2017:MFC}.",
  remark-2 =     "From pages 128--129: ``A great deal of satisfaction
                 was obtained from the fact that five of the intrinsic
                 functions reported here always deliver correctly
                 rounded results; these are SQRT, DSQRT, CABS, CDABS,
                 and EXP. One important aspect of this is that correctly
                 rounded results were obtained with surprisingly little
                 sacrifice in performance.''",
  remark-3 =     "From page 132: ``Our CABS and CDABS functions satisfy
                 $\e/u < 0.5$ (this can also be called a half-ulp
                 criterion). They have best-possible rounding, except
                 that unavoidably there are cases when $| e/u | = 0.5$,
                 in which case it would be equally correct to round
                 downward or upward; we choose to round upward. This is
                 consistent with the System/370 definition of
                 rounding.''",
  remark-4 =     "From pages 134--135: ``Tuckerman's condition is of
                 historic significance, as its use allowed us to produce
                 IBM's first elementary function that delivered
                 correctly rounded results for all arguments.''",
  remark-5 =     "From page 137: ``X**2.0 usually produces a correctly
                 rounded value, while X*X always produces the truncated
                 value of $X^2$ .''",
  remark-6 =     "From page 139: ``Generating precise times is
                 difficult, since seemingly inconsequential changes in
                 the timing procedure may have a noticeable effect on
                 the measured times. For example, on the 3081KX the
                 performance of the STM [store multiple] and LM [load
                 multiple] instructions is severely degraded near page
                 boundaries. This means that in the rare event that the
                 save area of a subroutine is near a page boundary, the
                 speed of execution of the subroutine will be
                 substantially decreased.''",
  subject =      "C.4 Computer Systems Organization, PERFORMANCE OF
                 SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms \\ F.3.3 Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Functional constructs \\ C.1.2
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Array and vector processors",
  treatment =    "N New Development; P Practical",
}


bibtype: article
filename: elefunt.bib
label: Amos:1986:APP
author: D. E. Amos
title: Algorithm 644: a Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order
journal: j-TOMS
volume: 12
number: 3
pages: 265--273
month: sep
monthnumber: 9
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/7921.214331
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D20
MRnumber: 889 069
bibdate: Tue Mar 09 10:26:27 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1999.03.09 10:26:27 ???
note: See also cite Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA.
URL: http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: D. E. Amos
rawnote: See also \cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.
abstract:
This algorithm is a package of subroutines for Computing Bessel functions $ H_v^(1)(z) $, $ H_v^(2)(z) $, $ I_v(z) $, $ J_v(z) $, $ K_v(z) $, $ Y_v(z) $ and Airy functions $ mbox Ai(z) $, $ mbox Ai'(z) $, $ mbox Bi(z) $, $ mbox Bi'(z) $ for orders $ v geq 0 $ and complex $z$ in $ - pi < mbox arg z leq pi $. Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options.

subject:
bf G.1.0: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf G.1.m: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. bf G.m: Mathematics of Computing, MISCELLANEOUS.

rawabstract:
This algorithm is a package of subroutines for Computing Bessel functions $ H_v^{(1)}(z) $, $ H_v^{(2)}(z) $, $ I_v(z) $, $ J_v(z) $, $ K_v(z) $, $ Y_v(z) $ and Airy functions $ \mbox {Ai}(z) $, $ \mbox {Ai}'(z) $, $ \mbox {Bi}(z) $, $ \mbox {Bi}'(z) $ for orders $ v \geq 0 $ and complex $z$ in $ - \pi < \mbox {arg} z \leq \pi $. Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options.

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

entry:
@Article{Amos:1986:APP,
  author =       "D. E. Amos",
  title =        "{Algorithm 644}: a Portable Package for {Bessel}
                 Functions of a Complex Argument and Nonnegative Order",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "265--273",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.214331",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "889 069",
  bibdate =      "Tue Mar 09 10:26:27 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/",
  abstract =     "This algorithm is a package of subroutines for
                 Computing Bessel functions $ H_v^{(1)}(z) $, $
                 H_v^{(2)}(z) $, $ I_v(z) $, $ J_v(z) $, $ K_v(z) $, $
                 Y_v(z) $ and Airy functions $ \mbox {Ai}(z) $, $ \mbox
                 {Ai}'(z) $, $ \mbox {Bi}(z) $, $ \mbox {Bi}'(z) $ for
                 orders $ v \geq 0 $ and complex $z$ in $ - \pi < \mbox
                 {arg} z \leq \pi $. Eight callable subroutines and
                 their double-precision counterparts are provided.
                 Exponential scaling and sequence generation are
                 auxiliary options.",
  acknowledgement = ack-nhfb,
  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, Numerical algorithms. {\bf G.1.m}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Miscellaneous. {\bf G.m}: Mathematics of Computing,
                 MISCELLANEOUS.",
}


bibtype: article
filename: elefunt.bib
label: Andrews:1986:SCA
author: George E. Andrews and Ian P. Goulden and David M. Jackson
title: Shanks' convergence acceleration transform, Pade approximants and partitions
journal: j-J-COMB-THEORY-A
volume: 43
number: 1
pages: 70--84
year: 1986
CODEN: JCBTA7
DOI: https://doi.org/10.1016/0097-3165(86)90024-5
ISSN: 0097-3165 (print), 1096-0899 (electronic) OR 00973165 (print), 10960899 (electronic)
ISSNL: 0097-3165 OR 00973165
MRclass: 65B99 (11N99 11Y35)
MRnumber: 859298 (88c:65005)
MRreviewer: Kenneth A. Jukes
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 Combinatorial Theory (Series A)
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00973165
rawauthor: George E. Andrews and Ian P. Goulden and David M. Jackson
rawtitle: {Shanks}' convergence acceleration transform, {Pad{\'e}} approximants and partitions
entry:
@Article{Andrews:1986:SCA,
  author =       "George E. Andrews and Ian P. Goulden and David M.
                 Jackson",
  title =        "{Shanks}' convergence acceleration transform,
                 {Pad{\'e}} approximants and partitions",
  journal =      j-J-COMB-THEORY-A,
  volume =       "43",
  number =       "1",
  pages =        "70--84",
  year =         "1986",
  CODEN =        "JCBTA7",
  DOI =          "https://doi.org/10.1016/0097-3165(86)90024-5",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  MRclass =      "65B99 (11N99 11Y35)",
  MRnumber =     "859298 (88c:65005)",
  MRreviewer =   "Kenneth A. Jukes",
  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 Combinatorial Theory (Series A)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Bustoz:1986:GFI
author: Joaquin Bustoz and Mourad E. H. Ismail
title: On Gamma Function Inequalities
journal: j-MATH-COMPUT
volume: 47
number: 176
pages: 659--667
month: oct
monthnumber: 10
year: 1986
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A15 (26D20)
MRnumber: 87m:33002
MRreviewer: G. Gasper
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: C1130 (Integral transforms); C1140Z (Other and miscellaneous)
corpsource: Dept. of Math., Arizona State Univ., Tempe, AZ, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Joaquin Bustoz and Mourad E. H. Ismail
rawtitle: On Gamma Function Inequalities
keywords:
gamma function inequalities; infinite divisibility; Laplace; Laplace transforms; monotonic functions; probability; probability distributions; quotients; transforms

entry:
@Article{Bustoz:1986:GFI,
  author =       "Joaquin Bustoz and Mourad E. H. Ismail",
  title =        "On Gamma Function Inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "659--667",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A15 (26D20)",
  MRnumber =     "87m:33002",
  MRreviewer =   "G. Gasper",
  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 =   "C1130 (Integral transforms); C1140Z (Other and
                 miscellaneous)",
  corpsource =   "Dept. of Math., Arizona State Univ., Tempe, AZ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "gamma function inequalities; infinite divisibility;
                 Laplace; Laplace transforms; monotonic functions;
                 probability; probability distributions; quotients;
                 transforms",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Campbell:1986:NSR
author: R. A. Campbell
title: NS32000 Square Roots
journal: j-DDJ
volume: 11
number: 3
pages: 122--123, 106
month: mar
monthnumber: 3
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Fri Dec 08 13:05:56 1995
bibtimestamp: 1995.12.08 13:05:56 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: R. A. Campbell
rawtitle: {NS32000} Square Roots
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Campbell:1986:NSR,
  author =       "R. A. Campbell",
  title =        "{NS32000} Square Roots",
  journal =      j-DDJ,
  volume =       "11",
  number =       "3",
  pages =        "122--123, 106",
  month =        mar,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Dec 08 13:05:56 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: elefunt.bib
label: Cathey:1986:LEI
author: J. Cathey
title: Letter to the editor [Integer Square Root]
journal: j-DDJ
volume: 11
number: 8
pages: 14, 82--85
month: aug
monthnumber: 8
year: 1986
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Thu Sep 08 07:59:25 1994
bibtimestamp: 1994.09.08 07:59:25 ???
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nj
rawauthor: J. Cathey
rawtitle: Letter to the editor [Integer Square Root]
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Cathey:1986:LEI,
  author =       "J. Cathey",
  title =        "Letter to the editor [Integer Square Root]",
  journal =      j-DDJ,
  volume =       "11",
  number =       "8",
  pages =        "14, 82--85",
  month =        aug,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 08 07:59:25 1994",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1986:GEL
author: C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver and P. R. Turner
title: Generalized Exponential and Logarithmic Functions
journal: j-COMPUT-MATH-APPL
volume: 12
number: 5--6
pages: 1091--1101
month: sep
monthnumber: 9
year: 1986
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(86)90233-6
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
MRclass: 33A70 (39B10 65G05)
MRnumber: MR0871348 (88a:33027)
bibdate: Fri Jul 09 06:27:26 2004
bibtimestamp: 2004.07.09 06:27:26 ???
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver and P. R. Turner
rawtitle: Generalized Exponential and Logarithmic Functions
abstract:
Generalizations of the exponential and logarithmic functions are defined and an investigation is made of two possible versions of these functions. Some applications are described, including computer arithmetic, properties of very large and very small numbers, and the determination of functional roots.

rawabstract:
Generalizations of the exponential and logarithmic functions are defined and an investigation is made of two possible versions of these functions. Some applications are described, including computer arithmetic, properties of very large and very small numbers, and the determination of functional roots.

entry:
@Article{Clenshaw:1986:GEL,
  author =       "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
                 and P. R. Turner",
  title =        "Generalized Exponential and Logarithmic Functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "12",
  number =       "5--6",
  pages =        "1091--1101",
  month =        sep # "\slash " # dec,
  year =         "1986",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(86)90233-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "33A70 (39B10 65G05)",
  MRnumber =     "MR0871348 (88a:33027)",
  bibdate =      "Fri Jul 09 06:27:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generalizations of the exponential and logarithmic
                 functions are defined and an investigation is made of
                 two possible versions of these functions. Some
                 applications are described, including computer
                 arithmetic, properties of very large and very small
                 numbers, and the determination of functional roots.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1986:UAR
author: C. W. Clenshaw and F. W. J. Olver
title: Unrestricted algorithms for reciprocals and square roots
journal: j-BIT
volume: 26
number: 4
pages: 475--492
month: dec
monthnumber: 12
year: 1986
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01935054
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D20
MRnumber: 87k:65019
MRreviewer: Luciano Biasini
bibdate: Wed Jan 4 18:52:19 MST 2006
bibtimestamp: 2006.01.04 18:52:19 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: C. W. Clenshaw and F. W. J. Olver
rawtitle: Unrestricted algorithms for reciprocals and square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Clenshaw:1986:UAR,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Unrestricted algorithms for reciprocals and square
                 roots",
  journal =      j-BIT,
  volume =       "26",
  number =       "4",
  pages =        "475--492",
  month =        dec,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01935054",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20",
  MRnumber =     "87k:65019",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Wed Jan 4 18:52:19 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  xxpages =      "476--492??",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1986:CIG
author: Armido R. DiDonato and Alfred H. Morris, Jr.
title: Computation of the Incomplete Gamma Function Ratios and Their Inverse
journal: j-TOMS
volume: 12
number: 4
pages: 377--393
month: dec
monthnumber: 12
year: 1986
CODEN: ACMSCU
DOI: https://doi.org/10.1145/22721.23109
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 04 21:31:03 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
bibtimestamp: 1994.09.04 21:31:03 ???
URL: http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p377-didonato/
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
subject: bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Armido R. DiDonato and Alfred H. {Morris, Jr.}
rawtitle: Computation of the Incomplete Gamma Function Ratios and Their Inverse
abstract:
An algorithm is given for computing the incomplete gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $ a geq 0 $, $ x geq 0 $, $ a + x neq 0 $. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An extensive set of coefficients for the Temme expansions is included.par An algorithm, employing third-order Schroder iteration supported by Newton-Raphson iteration, is provided for computing $x$ when $a$, $ P(a, x) $, and $ Q(a, x) $ are given. Three iterations at most are required to obtain 10 significant digit accuracy for $x$.

rawabstract:
An algorithm is given for computing the incomplete gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $ a \geq 0 $, $ x \geq 0 $, $ a + x \neq 0 $. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An extensive set of coefficients for the Temme expansions is included.\par An algorithm, employing third-order Schr{\"o}der iteration supported by Newton-Raphson iteration, is provided for computing $x$ when $a$, $ P(a, x) $, and $ Q(a, x) $ are given. Three iterations at most are required to obtain 10 significant digit accuracy for $x$.

entry:
@Article{DiDonato:1986:CIG,
  author =       "Armido R. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "Computation of the Incomplete Gamma Function Ratios
                 and Their Inverse",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "377--393",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.23109",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:31:03 1994",
  bibsource =    "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/1986-12-4/p377-didonato/",
  abstract =     "An algorithm is given for computing the incomplete
                 gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $
                 a \geq 0 $, $ x \geq 0 $, $ a + x \neq 0 $. Temme's
                 uniform asymptotic expansions are used. The algorithm
                 is robust; results accurate to 14 significant digits
                 can be obtained. An extensive set of coefficients for
                 the Temme expansions is included.\par

                 An algorithm, employing third-order Schr{\"o}der
                 iteration supported by Newton-Raphson iteration, is
                 provided for computing $x$ when $a$, $ P(a, x) $, and $
                 Q(a, x) $ are given. Three iterations at most are
                 required to obtain 10 significant digit accuracy for
                 $x$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8709-0775",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}


bibtype: article
filename: elefunt.bib
label: DiMarzio:1986:IPA
author: F. Di Marzio
journal: j-COMP-PHYS-COMM
volume: 39
number: 3
pages: 343--345
month: apr
monthnumber: 4
year: 1986
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(86)90095-0
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 10:28:13 MST 2012
bibtimestamp: 2012.02.13 10:28:13 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465586900950
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: F. {Di Marzio}
title:
An improved procedure for the accurate evaluation of polygamma functions with integer and half-integer argument

rawtitle:
An improved procedure for the accurate evaluation of polygamma functions with integer and half-integer argument

entry:
@Article{DiMarzio:1986:IPA,
  author =       "F. {Di Marzio}",
  title =        "An improved procedure for the accurate evaluation of
                 polygamma functions with integer and half-integer
                 argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "39",
  number =       "3",
  pages =        "343--345",
  month =        apr,
  year =         "1986",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(86)90095-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:13 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465586900950",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Dutka:1986:SRT
author: Jacques Dutka
title: On square roots and their representations
journal: j-ARCH-HIST-EXACT-SCI
volume: 36
number: 1
pages: 21--39
month: mar
monthnumber: 3
year: 1986
CODEN: AHESAN
DOI: https://doi.org/10.1007/BF00357439
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A05 (11-03 11A63)
MRnumber: 863340 (87m:01003)
MRreviewer: Donald Cook
bibdate: Fri Feb 4 21:50:24 MST 2011
bibtimestamp: 2011.02.04 21:50:24 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21
fjournal: Archive for History of Exact Sciences
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: Jacques Dutka
rawtitle: On square roots and their representations
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1; https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Dutka:1986:SRT,
  author =       "Jacques Dutka",
  title =        "On square roots and their representations",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "36",
  number =       "1",
  pages =        "21--39",
  month =        mar,
  year =         "1986",
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  ISSN-L =       "0003-9519",
  MRclass =      "01A05 (11-03 11A63)",
  MRnumber =     "863340 (87m:01003)",
  MRreviewer =   "Donald Cook",
  bibdate =      "Fri Feb 4 21:50:24 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "On square roots and their representations",
}


bibtype: article
filename: elefunt.bib
label: Evans:1986:RIU
author: D. J. Evans and G. M. Megson
title: Romberg integration using systolic arrays
journal: j-PARALLEL-COMPUTING
volume: 3
number: 4
pages: 289--304
month: oct
monthnumber: 10
year: 1986
CODEN: PACOEJ
ISSN: 0167-8191 (print), 1872-7336 (electronic) OR 01678191 (print), 18727336 (electronic)
ISSNL: 0167-8191 OR 01678191
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: Parallel Computing
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01678191
rawauthor: D. J. Evans and G. M. Megson
rawtitle: {Romberg} integration using systolic arrays
entry:
@Article{Evans:1986:RIU,
  author =       "D. J. Evans and G. M. Megson",
  title =        "{Romberg} integration using systolic arrays",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "3",
  number =       "4",
  pages =        "289--304",
  month =        oct,
  year =         "1986",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  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 =        "11019",
  catcode =      "G.1.1; G.1.2",
  CRclass =      "G.1.1 Interpolation; G.1.1 Extrapolation; G.1.2
                 Approximation; G.1.2 Elementary function
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  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
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                 approximation",
  fjournal =     "Parallel Computing",
  genterm =      "theory; design; algorithms",
  guideno =      "1986-10554",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
  journalabbrev = "Parallel Comput.",
  jrldate =      "Oct. 1986",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
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}


bibtype: article
filename: elefunt.bib
label: FernandezVelicia:1986:HPA
author: F. J. Fernandez Velicia
journal: j-PHYS-REV-A-3
volume: 34
number: 5
pages: 4387--4395
year: 1986
CODEN: PLRAAN
MRclass: 33A70 (82A05)
MRnumber: MR869021 (88b:33024)
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Physical Review. A. Third Series
acknowledgement: ack-nhfb
journalURL: http://pra.aps.org/browse
rawauthor: F. J. {Fern{\'a}ndez Velicia}
title:
High-precision analytic approximations for the Fermi--Dirac functions by means of elementary functions

ISSN:
1050-2947 (print), 1094-1622, 1538-4446, 1538-4519 OR 10502947 (print), 10941622, 15384446, 15384519

rawtitle:
High-precision analytic approximations for the {Fermi--Dirac} functions by means of elementary functions

entry:
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  author =       "F. J. {Fern{\'a}ndez Velicia}",
  title =        "High-precision analytic approximations for the
                 {Fermi--Dirac} functions by means of elementary
                 functions",
  journal =      j-PHYS-REV-A-3,
  volume =       "34",
  number =       "5",
  pages =        "4387--4395",
  year =         "1986",
  CODEN =        "PLRAAN",
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  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review. A. Third Series",
  journal-URL =  "http://pra.aps.org/browse",
}


bibtype: article
filename: elefunt.bib
label: Froman:1986:PIF
author: Per Olof Froman and Finn Karlsson and Staffan Yngve
journal: j-J-MATH-PHYS
volume: 27
number: 11
pages: 2738--2747
month: nov
monthnumber: 11
year: 1986
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.527296
ISSNL: 0022-2488 OR 00222488
MRclass: 41A60 (33A40 81C12)
MRnumber: 87j:41073
bibdate: Mon Oct 31 11:57:50 MDT 2011
bibtimestamp: 2011.10.31 11:57:50 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v27/i11/p2738_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Per Olof Fr{\"o}man and Finn Karlsson and Staffan Yngve
title:
Phase-integral formulas for Bessel functions and their relation to already existing asymptotic formulas

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

rawtitle:
Phase-integral formulas for {Bessel} functions and their relation to already existing asymptotic formulas

entry:
@Article{Froman:1986:PIF,
  author =       "Per Olof Fr{\"o}man and Finn Karlsson and Staffan
                 Yngve",
  title =        "Phase-integral formulas for {Bessel} functions and
                 their relation to already existing asymptotic
                 formulas",
  journal =      j-J-MATH-PHYS,
  volume =       "27",
  number =       "11",
  pages =        "2738--2747",
  month =        nov,
  year =         "1986",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.527296",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A60 (33A40 81C12)",
  MRnumber =     "87j:41073",
  bibdate =      "Mon Oct 31 11:57:50 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/v27/i11/p2738_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "10",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gal:1986:CEF
author: Shmuel Gal
title: Computing elementary functions: a new approach for achieving high accuracy and good performance
crossref: Miranker:1986:ASC
pages: 1--16
year: 1986
MRclass: 65D20
MRnumber: 868 283
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: Shmuel Gal
rawtitle: Computing elementary functions: a new approach for achieving high accuracy and good performance
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Gal:1986:CEF,
  author =       "Shmuel Gal",
  title =        "Computing elementary functions: a new approach for
                 achieving high accuracy and good performance",
  crossref =     "Miranker:1986:ASC",
  pages =        "1--16",
  year =         "1986",
  MRclass =      "65D20",
  MRnumber =     "868 283",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Gustavson:1986:FEF
author: F. G. Gustavson
title: Fast Elementary Function Algorithms for 370 Machines
crossref: Miranker:1986:ASC
pages: 17--17
year: 1986
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: F. G. Gustavson
rawtitle: Fast Elementary Function Algorithms for 370 Machines
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Gustavson:1986:FEF,
  author =       "F. G. Gustavson",
  title =        "Fast Elementary Function Algorithms for 370 Machines",
  crossref =     "Miranker:1986:ASC",
  pages =        "17--17",
  year =         "1986",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Hochstadt:1986:FMP
author: Harry Hochstadt
title: The Functions of Mathematical Physics
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xi + 322
year: 1986
ISBN: 0-486-65214-9 (paperback), 0-486-16878-6 (e-book) OR 0486652149 (paperback), 0486168786 (ebook)
LCCN: QA351 .H68 1986
bibdate: Tue Dec 5 10:51:16 MST 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.12.05 10:51:16 MST
acknowledgement: ack-nhfb
rawauthor: Harry Hochstadt
rawtitle: The Functions of Mathematical Physics
ISBN13:
978-0-486-65214-6 (paperback), 978-0-486-16878-4 (e-book) OR 9780486652146 (paperback), 9780486168784 (ebook)

TOC:
1: Orthogonal Polynomials 1 Linear Spaces / 1 2 Orthogonal Polynomials / 6 3 The Recurrence Formula / 8 4 The Christoffel--Darboux Formula / 9 5 The Weierstrass Approximation Theorem / 11 6 The Zeros of the Orthogonal Polynomials / 14 7 Approximation Theory / 16 8 More about the Zeros of the Orthonormal Polynomials / 23 9 The completeness of the Orthonormal Polynomials in the Space of Square-Integrable Functions / 27 10 Generalizations and an Application to Conformal Mappings / 32 2: The Classical Orthogonal Polynomials 1 Rodrigues' Formula and the Classical Orthogonal Polynomials / 39 2 The Differential Equations Satisfied by the Classical Orthogonal Polynomials / 43 3 On the Zeros of the Jacobi Polynomials / 45 4 An Alternative Approach to the Tchebicheff Polynomials / 46 5 An Application of the Hermite Polynomials to Quantum Mechanics / 49 6 The Completeness of the Hermite and Laguerre Polynomials / 53 7 Generating Functions / 57 3: The Gamma Function 1 Definitions and Basic Properties / 61 2 Analytic Continuation and Integral Representations / 65 3 Asymptotic Expansions / 69 4 Beta Functions / 75 5 The Logarithmic Derivative of the Gamma Function / 77 6 Mellin--Barnes Integrals / 78 7 Mellin Transforms / 80 8 Applications to Algebraic Equations / 81 4: Hypergeometric Functions 1 Review of Linear Differential Equations with Regular Singular Points / 88 2 The Hypergeometric Differential Equation / 90 3 The Hypergeometric Function / 93 4 A General Method for Finding Integral Representations / 100 5 Integral Representations for the Hypergeometric Function / 105 6 The Twenty-four Solutions of the Hypergeometric / Equation / 106 7 The Schwarz--Christoffel Transformation / 112 8 Mappings of Curvilinear Triangles / 119 9 Group Theoretic Discussion of the Case $ pi (alpha _1 + alpha _2 + alpha _3) > pi $ / 130 10 Nonlinear Transformations of Hypergeometric Functions / 132 5: The Legendre Functions 1 Laplace's Differential Equation / 138 2 Maxwell's Theory of Poles / 140 3 Relationship to the Hypergeometric Functions / 141 4 Expansion Formulas / 147 5 The Addition Theorem / 149 6 Green's Functions / 153 7 The Complete Solution of Legendre's Differential Equation / 156 8 Asymptotic Formulas / 161 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous Polynomials / 168 2 Orthogonality of Spherical Harmonics / 171 3 Legendre Polynomials / 175 4 Applications to Boundary Value Problems / 183 7: Confluent Hypergeometric Functions 1 Relationship to the Hypergeometric Functions / 189 2 Applications of These Functions in Mathematical Physics / 191 3 Integral Representations / 195 4 Asymptotic Representations / 198 8: Bessel Functions 1 Basic Definitions / 200 2 Integral Representations / 203 3 Relationship to the Legendre Functions / 205 4 The Generating Function of the Bessel Function / 207 5 More Integral Representations / 210 6 Addition Theorems / 216 7 The Complete Solution of Bessel's Equation / 223 8 Asymptotic Expansions for Large Argument / 225 9 Airy Functions / 230 10 Asymptotic Expansions for Large Indices and Large Arguments / 235 11 Some Applications of Bessel Functions in Physical Optics / 241 12 The Zeros of Bessel Functions / 249 13 Fourier--Bessel Expansions / 257 14 Applications in Mathematical Physics / 266 15 Discontinuous Integrals / 269 9: Hill's Equation 1 Mathieu's Equation / 281 2 Hill's Equation / 282 3 The Discriminant / 287 4 Expansion Theorems / 299 5 Inverse Problems / 305 6 Hill's Equations with Even Coefficients / 309 7 Mathieu's Equation Revisited / 310 8 Energy Bands in Crystals / 313 Appendix / 314 Bibliography / 318 Index / 321

rawTOC:
1: Orthogonal Polynomials \\ 1 Linear Spaces / 1 \\ 2 Orthogonal Polynomials / 6 \\ 3 The Recurrence Formula / 8 \\ 4 The Christoffel--Darboux Formula / 9 \\ 5 The Weierstrass Approximation Theorem / 11 \\ 6 The Zeros of the Orthogonal Polynomials / 14 \\ 7 Approximation Theory / 16 \\ 8 More about the Zeros of the Orthonormal Polynomials / 23 \\ 9 The completeness of the Orthonormal Polynomials in the Space of Square-Integrable Functions / 27 \\ 10 Generalizations and an Application to Conformal Mappings / 32 \\ \\ 2: The Classical Orthogonal Polynomials 1 Rodrigues' Formula and the Classical Orthogonal Polynomials / 39 \\ 2 The Differential Equations Satisfied by the Classical Orthogonal Polynomials / 43 \\ 3 On the Zeros of the Jacobi Polynomials / 45 \\ 4 An Alternative Approach to the Tchebicheff Polynomials / 46 \\ 5 An Application of the Hermite Polynomials to Quantum Mechanics / 49 \\ 6 The Completeness of the Hermite and Laguerre Polynomials / 53 \\ 7 Generating Functions / 57 \\ \\ 3: The Gamma Function 1 Definitions and Basic Properties / 61 \\ 2 Analytic Continuation and Integral Representations / 65 \\ 3 Asymptotic Expansions / 69 \\ 4 Beta Functions / 75 \\ 5 The Logarithmic Derivative of the Gamma Function / 77 \\ 6 Mellin--Barnes Integrals / 78 \\ 7 Mellin Transforms / 80 \\ 8 Applications to Algebraic Equations / 81 \\ \\ 4: Hypergeometric Functions 1 Review of Linear Differential Equations with Regular Singular Points / 88 \\ 2 The Hypergeometric Differential Equation / 90 \\ 3 The Hypergeometric Function / 93 \\ 4 A General Method for Finding Integral Representations / 100 \\ 5 Integral Representations for the Hypergeometric Function / 105 \\ 6 The Twenty-four Solutions of the Hypergeometric / Equation / 106 \\ 7 The Schwarz--Christoffel Transformation / 112 \\ 8 Mappings of Curvilinear Triangles / 119 \\ 9 Group Theoretic Discussion of the Case $ \pi(\alpha_1 + \alpha_2 + \alpha_3) > \pi$ / 130 \\ 10 Nonlinear Transformations of Hypergeometric Functions / 132 \\ \\ 5: The Legendre Functions 1 Laplace's Differential Equation / 138 \\ 2 Maxwell's Theory of Poles / 140 \\ 3 Relationship to the Hypergeometric Functions / 141 \\ 4 Expansion Formulas / 147 \\ 5 The Addition Theorem / 149 \\ 6 Green's Functions / 153 \\ 7 The Complete Solution of Legendre's Differential Equation / 156 \\ 8 Asymptotic Formulas / 161 \\ \\ 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous Polynomials / 168 \\ 2 Orthogonality of Spherical Harmonics / 171 \\ 3 Legendre Polynomials / 175 \\ 4 Applications to Boundary Value Problems / 183 \\ \\ 7: Confluent Hypergeometric Functions 1 Relationship to the Hypergeometric Functions / 189 \\ 2 Applications of These Functions in Mathematical Physics / 191 \\ 3 Integral Representations / 195 \\ 4 Asymptotic Representations / 198 \\ \\ 8: Bessel Functions 1 Basic Definitions / 200 \\ 2 Integral Representations / 203 \\ 3 Relationship to the Legendre Functions / 205 \\ 4 The Generating Function of the Bessel Function / 207 \\ 5 More Integral Representations / 210 \\ 6 Addition Theorems / 216 \\ 7 The Complete Solution of Bessel's Equation / 223 \\ 8 Asymptotic Expansions for Large Argument / 225 \\ 9 Airy Functions / 230 \\ 10 Asymptotic Expansions for Large Indices and Large Arguments / 235 \\ 11 Some Applications of Bessel Functions in Physical Optics / 241 \\ 12 The Zeros of Bessel Functions / 249 \\ 13 Fourier--Bessel Expansions / 257 \\ 14 Applications in Mathematical Physics / 266 \\ 15 Discontinuous Integrals / 269 \\ \\ 9: Hill's Equation 1 Mathieu's Equation / 281 \\ 2 Hill's Equation / 282 \\ 3 The Discriminant / 287 \\ 4 Expansion Theorems / 299 \\ 5 Inverse Problems / 305 \\ 6 Hill's Equations with Even Coefficients / 309 \\ 7 Mathieu's Equation Revisited / 310 \\ 8 Energy Bands in Crystals / 313 \\ Appendix / 314 \\ \\ Bibliography / 318 \\ \\ Index / 321

entry:
@Book{Hochstadt:1986:FMP,
  author =       "Harry Hochstadt",
  title =        "The Functions of Mathematical Physics",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 322",
  year =         "1986",
  ISBN =         "0-486-65214-9 (paperback), 0-486-16878-6 (e-book)",
  ISBN-13 =      "978-0-486-65214-6 (paperback), 978-0-486-16878-4
                 (e-book)",
  LCCN =         "QA351 .H68 1986",
  bibdate =      "Tue Dec 5 10:51:16 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Orthogonal Polynomials \\
                 1 Linear Spaces / 1 \\
                 2 Orthogonal Polynomials / 6 \\
                 3 The Recurrence Formula / 8 \\
                 4 The Christoffel--Darboux Formula / 9 \\
                 5 The Weierstrass Approximation Theorem / 11 \\
                 6 The Zeros of the Orthogonal Polynomials / 14 \\
                 7 Approximation Theory / 16 \\
                 8 More about the Zeros of the Orthonormal Polynomials /
                 23 \\
                 9 The completeness of the Orthonormal Polynomials in
                 the Space of Square-Integrable Functions / 27 \\
                 10 Generalizations and an Application to Conformal
                 Mappings / 32 \\
                 \\
                 2: The Classical Orthogonal Polynomials 1 Rodrigues'
                 Formula and the Classical Orthogonal Polynomials / 39
                 \\
                 2 The Differential Equations Satisfied by the Classical
                 Orthogonal Polynomials / 43 \\
                 3 On the Zeros of the Jacobi Polynomials / 45 \\
                 4 An Alternative Approach to the Tchebicheff
                 Polynomials / 46 \\
                 5 An Application of the Hermite Polynomials to Quantum
                 Mechanics / 49 \\
                 6 The Completeness of the Hermite and Laguerre
                 Polynomials / 53 \\
                 7 Generating Functions / 57 \\
                 \\
                 3: The Gamma Function 1 Definitions and Basic
                 Properties / 61 \\
                 2 Analytic Continuation and Integral Representations /
                 65 \\
                 3 Asymptotic Expansions / 69 \\
                 4 Beta Functions / 75 \\
                 5 The Logarithmic Derivative of the Gamma Function / 77
                 \\
                 6 Mellin--Barnes Integrals / 78 \\
                 7 Mellin Transforms / 80 \\
                 8 Applications to Algebraic Equations / 81 \\
                 \\
                 4: Hypergeometric Functions 1 Review of Linear
                 Differential Equations with Regular Singular Points /
                 88 \\
                 2 The Hypergeometric Differential Equation / 90 \\
                 3 The Hypergeometric Function / 93 \\
                 4 A General Method for Finding Integral Representations
                 / 100 \\
                 5 Integral Representations for the Hypergeometric
                 Function / 105 \\
                 6 The Twenty-four Solutions of the Hypergeometric /
                 Equation / 106 \\
                 7 The Schwarz--Christoffel Transformation / 112 \\
                 8 Mappings of Curvilinear Triangles / 119 \\
                 9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
                 + \alpha_2 + \alpha_3) > \pi$ / 130 \\
                 10 Nonlinear Transformations of Hypergeometric
                 Functions / 132 \\
                 \\
                 5: The Legendre Functions 1 Laplace's Differential
                 Equation / 138 \\
                 2 Maxwell's Theory of Poles / 140 \\
                 3 Relationship to the Hypergeometric Functions / 141
                 \\
                 4 Expansion Formulas / 147 \\
                 5 The Addition Theorem / 149 \\
                 6 Green's Functions / 153 \\
                 7 The Complete Solution of Legendre's Differential
                 Equation / 156 \\
                 8 Asymptotic Formulas / 161 \\
                 \\
                 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
                 Polynomials / 168 \\
                 2 Orthogonality of Spherical Harmonics / 171 \\
                 3 Legendre Polynomials / 175 \\
                 4 Applications to Boundary Value Problems / 183 \\
                 \\
                 7: Confluent Hypergeometric Functions 1 Relationship to
                 the Hypergeometric Functions / 189 \\
                 2 Applications of These Functions in Mathematical
                 Physics / 191 \\
                 3 Integral Representations / 195 \\
                 4 Asymptotic Representations / 198 \\
                 \\
                 8: Bessel Functions 1 Basic Definitions / 200 \\
                 2 Integral Representations / 203 \\
                 3 Relationship to the Legendre Functions / 205 \\
                 4 The Generating Function of the Bessel Function / 207
                 \\
                 5 More Integral Representations / 210 \\
                 6 Addition Theorems / 216 \\
                 7 The Complete Solution of Bessel's Equation / 223 \\
                 8 Asymptotic Expansions for Large Argument / 225 \\
                 9 Airy Functions / 230 \\
                 10 Asymptotic Expansions for Large Indices and Large
                 Arguments / 235 \\
                 11 Some Applications of Bessel Functions in Physical
                 Optics / 241 \\
                 12 The Zeros of Bessel Functions / 249 \\
                 13 Fourier--Bessel Expansions / 257 \\
                 14 Applications in Mathematical Physics / 266 \\
                 15 Discontinuous Integrals / 269 \\
                 \\
                 9: Hill's Equation 1 Mathieu's Equation / 281 \\
                 2 Hill's Equation / 282 \\
                 3 The Discriminant / 287 \\
                 4 Expansion Theorems / 299 \\
                 5 Inverse Problems / 305 \\
                 6 Hill's Equations with Even Coefficients / 309 \\
                 7 Mathieu's Equation Revisited / 310 \\
                 8 Energy Bands in Crystals / 313 \\
                 Appendix / 314 \\
                 \\
                 Bibliography / 318 \\
                 \\
                 Index / 321",
}


bibtype: article
filename: elefunt.bib
label: Hull:1986:VPE
author: T. E. Hull and A. Abrham
title: Variable Precision Exponential Function
journal: j-TOMS
volume: 12
number: 2
pages: 79--91
month: jun
monthnumber: 6
year: 1986
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15 (65D20)
MRnumber: 863 786
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; verification
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: T. E. Hull and A. Abrham
rawtitle: Variable Precision Exponential Function
URL:
http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/; http://www.acm.org/pubs/toc/Abstracts/toms/6498.html

subject:
bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification.

entry:
@Article{Hull:1986:VPE,
  author =       "T. E. Hull and A. Abrham",
  title =        "Variable Precision Exponential Function",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "79--91",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "863 786",
  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/1986-12-2/p79-hull/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/6498.html",
  acknowledgement = ack-nhfb,
  bibno =        "91",
  content =      "algorithms; verification; THEORY",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Algorithm analysis; G.4
                 Certification and testing; G.4 Verification",
  CRnumber =     "1986-02428",
  descriptor =   "mathematics of computing, numerical analysis,
                 approximation, elementary function approximation;
                 mathematics of computing, mathematical software,
                 algorithm analysis; mathematics of computing,
                 mathematical software, certification and testing;
                 mathematics of computing, mathematical software,
                 verification",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  fortitle =     "ACM Trans. Math. Softw.",
  genterm =      "June 1986",
  guideno =      "2",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  review =       "ACM CR 8702-0091",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification.",
}


bibtype: article
filename: elefunt.bib
label: Jacobsen:1986:FRC
author: Lisa Jacobsen and William B. Jones and Haakon Waadeland
title: Further results on the computation of incomplete gamma functions
journal: j-LECT-NOTES-MATH
volume: 1199
pages: 67--89
year: 1986
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0075936
ISBN: 3-540-16768-4 (print), 3-540-38817-6 (e-book) OR 3540167684 (print), 3540388176 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
MRclass: 40A15 (33A10 33A15)
MRnumber: 870245 (88f:40004)
MRreviewer: Marietta J. Tretter
bibdate: Thu May 15 18:46:23 MDT 2014
bibtimestamp: 2014.05.15 18:46:23 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0075936/
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0075930
bookURL: http://www.springerlink.com/content/978-3-540-38817-3
journalURL: http://link.springer.com/bookseries/304
rawauthor: Lisa Jacobsen and William B. Jones and Haakon Waadeland
rawtitle: Further results on the computation of incomplete gamma functions
ISBN13:
978-3-540-16768-6 (print), 978-3-540-38817-3 (e-book) OR 9783540167686 (print), 9783540388173 (ebook)

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

entry:
@Article{Jacobsen:1986:FRC,
  author =       "Lisa Jacobsen and William B. Jones and Haakon
                 Waadeland",
  title =        "Further results on the computation of incomplete gamma
                 functions",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1199",
  pages =        "67--89",
  year =         "1986",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0075936",
  ISBN =         "3-540-16768-4 (print), 3-540-38817-6 (e-book)",
  ISBN-13 =      "978-3-540-16768-6 (print), 978-3-540-38817-3
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "40A15 (33A10 33A15)",
  MRnumber =     "870245 (88f:40004)",
  MRreviewer =   "Marietta J. Tretter",
  bibdate =      "Thu May 15 18:46:23 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/BFb0075936/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0075930",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38817-3",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: elefunt.bib
label: Kushner:1986:ECC
author: Ed Kushner and Rick Broussard
title: Efficient computation of the cylindrical Bessel functions of complex argument
journal: j-COMP-PHYS-COMM
volume: 42
number: 3
pages: 345--349
month: nov
monthnumber: 11
year: 1986
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(86)90004-4
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 10:28:16 MST 2012
bibtimestamp: 2012.02.13 10:28:16 MST
URL: http://www.sciencedirect.com/science/article/pii/0010465586900044
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Ed Kushner and Rick Broussard
rawtitle: Efficient computation of the cylindrical {Bessel} functions of complex argument
abstract:
An algorithm that generates the cylindrical Bessel function very accurately for a wide range of complex arguments has been developed by Mason. The Mason algorithm consists of four different methods that apply to different portions of the complex plane. Experience with the Floating Point Systems FPS-364 minisupercomputer indicates several ways by which these methods can be made more efficient. Specific improvements relate to: (1) the method for determination of the point where backward recursion is initiated for the Bessel functions of the first kind; (2) the way that the Bessel functions of the first and second kind are normalized when $ |y| < 5 $ and $ |x| leq 20 $; and (3) the extent that asymptotic expansions are used when $ |x| > 20 $ and $ |y| < 5 $. The first and third modifications will result in increased efficiency for all architectures. The second modification will be of value for many, but probably not all, architectures.

rawabstract:
An algorithm that generates the cylindrical Bessel function very accurately for a wide range of complex arguments has been developed by Mason. The Mason algorithm consists of four different methods that apply to different portions of the complex plane. Experience with the Floating Point Systems FPS-364 minisupercomputer indicates several ways by which these methods can be made more efficient. Specific improvements relate to: (1) the method for determination of the point where backward recursion is initiated for the Bessel functions of the first kind; (2) the way that the Bessel functions of the first and second kind are normalized when $ |y| < 5 $ and $ |x| \leq 20 $; and (3) the extent that asymptotic expansions are used when $ |x| > 20 $ and $ |y| < 5 $. The first and third modifications will result in increased efficiency for all architectures. The second modification will be of value for many, but probably not all, architectures.

entry:
@Article{Kushner:1986:ECC,
  author =       "Ed Kushner and Rick Broussard",
  title =        "Efficient computation of the cylindrical {Bessel}
                 functions of complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "42",
  number =       "3",
  pages =        "345--349",
  month =        nov,
  year =         "1986",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(86)90004-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:16 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465586900044",
  abstract =     "An algorithm that generates the cylindrical Bessel
                 function very accurately for a wide range of complex
                 arguments has been developed by Mason. The Mason
                 algorithm consists of four different methods that apply
                 to different portions of the complex plane. Experience
                 with the Floating Point Systems FPS-364
                 minisupercomputer indicates several ways by which these
                 methods can be made more efficient. Specific
                 improvements relate to: (1) the method for
                 determination of the point where backward recursion is
                 initiated for the Bessel functions of the first kind;
                 (2) the way that the Bessel functions of the first and
                 second kind are normalized when $ |y| < 5 $ and $ |x|
                 \leq 20 $; and (3) the extent that asymptotic
                 expansions are used when $ |x| > 20 $ and $ |y| < 5 $.
                 The first and third modifications will result in
                 increased efficiency for all architectures. The second
                 modification will be of value for many, but probably
                 not all, architectures.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Laforgia:1986:IBF
author: Andrea Laforgia
title: Inequalities for Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 15
number: 1
pages: 75--81
month: may
monthnumber: 5
year: 1986
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:55 MST 2017
bibtimestamp: 2017.02.25 11:59:55 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042786902396
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Andrea Laforgia
rawtitle: Inequalities for {Bessel} functions
entry:
@Article{Laforgia:1986:IBF,
  author =       "Andrea Laforgia",
  title =        "Inequalities for {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "1",
  pages =        "75--81",
  month =        may,
  year =         "1986",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902396",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lavoie:1986:SEG
author: J. L. Lavoie
title: Some evaluations for the generalized hypergeometric series
journal: j-MATH-COMPUT
volume: 46
number: 173
pages: 215--218
month: jan
monthnumber: 1
year: 1986
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A35 (65D20)
MRnumber: 87c:33007
MRreviewer: S. D. Bajpai
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
corpsource: Laval Univ., Que., Canada
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: J. L. Lavoie
rawtitle: Some evaluations for the generalized hypergeometric series
keywords:
evaluation formulae; generalized hypergeometric series; series (mathematics); summation formulae; unit argument; Whipple's theorem

classcodes:
B0200 (Engineering mathematics and mathematical techniques); B0290Z (Other numerical methods); C1100 (Mathematical techniques); C4190 (Other numerical methods)

entry:
@Article{Lavoie:1986:SEG,
  author =       "J. L. Lavoie",
  title =        "Some evaluations for the generalized hypergeometric
                 series",
  journal =      j-MATH-COMPUT,
  volume =       "46",
  number =       "173",
  pages =        "215--218",
  month =        jan,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A35 (65D20)",
  MRnumber =     "87c:33007",
  MRreviewer =   "S. D. Bajpai",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0200 (Engineering mathematics and mathematical
                 techniques); B0290Z (Other numerical methods); C1100
                 (Mathematical techniques); C4190 (Other numerical
                 methods)",
  corpsource =   "Laval Univ., Que., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "evaluation formulae; generalized hypergeometric
                 series; series (mathematics); summation formulae; unit
                 argument; Whipple's theorem",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Marsaglia:1986:CIG
author: John C. W. Marsaglia
title: C249. The incomplete gamma function and Ramanujan's rational approximation to $ e^x $
journal: j-J-STAT-COMPUT-SIMUL
volume: 24
number: 2
pages: 163--168
year: 1986
CODEN: JSCSAJ
DOI: https://doi.org/10.1080/00949658608810899
ISSNL: 0094-9655 OR 00949655
bibdate: Tue Apr 22 09:11:07 MDT 2014
bibtimestamp: 2014.04.22 09:11:07 MDT
fjournal: Journal of Statistical Computation and Simulation
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/gscs20
rawauthor: John C. W. Marsaglia
rawtitle: {C249}. {The} incomplete gamma function and {Ramanujan}'s rational approximation to $ e^x $
ISSN:
0094-9655 (print), 1026-7778 (electronic), 1563-5163 OR 00949655 (print), 10267778 (electronic), 15635163

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

entry:
@Article{Marsaglia:1986:CIG,
  author =       "John C. W. Marsaglia",
  title =        "{C249}. {The} incomplete gamma function and
                 {Ramanujan}'s rational approximation to $ e^x $",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "24",
  number =       "2",
  pages =        "163--168",
  year =         "1986",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949658608810899",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:11:07 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}


bibtype: article
filename: elefunt.bib
label: Muller:1986:MDC
author: Jean-Michel Muller
journal: j-MATH-MODEL-NUM-ANA
volume: 20
number: 4
pages: 667--695
year: 1986
CODEN: RMMAEV
ISSN: 0764-583X (print), 1290-3841 (electronic) OR 0764583X (print), 12903841 (electronic)
ISSNL: 0764-583X OR 0764583X
MRclass: 65D20 (41-04)
MRnumber: 88h:65043
MRreviewer: E. W. Cheney
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
journalURL: http://journals.cambridge.org/action/displayJournal?jid=MZA
rawauthor: Jean-Michel Muller
title:
Une methodologie du calcul hardware des fonctions elementaires. (French) [A methodology for the hardware computation of elementary functions]

fjournal:
Mathematical modelling and numerical analysis = Modelisation mathematique et analyse numerique: $M^2AN$

rawtitle:
Une m{\'e}thodologie du calcul hardware des fonctions {\'e}l{\'e}mentaires. ({French}) [{A} methodology for the hardware computation of elementary functions]

entry:
@Article{Muller:1986:MDC,
  author =       "Jean-Michel Muller",
  title =        "Une m{\'e}thodologie du calcul hardware des fonctions
                 {\'e}l{\'e}mentaires. ({French}) [{A} methodology for
                 the hardware computation of elementary functions]",
  journal =      j-MATH-MODEL-NUM-ANA,
  volume =       "20",
  number =       "4",
  pages =        "667--695",
  year =         "1986",
  CODEN =        "RMMAEV",
  ISSN =         "0764-583X (print), 1290-3841 (electronic)",
  ISSN-L =       "0764-583X",
  MRclass =      "65D20 (41-04)",
  MRnumber =     "88h:65043",
  MRreviewer =   "E. W. Cheney",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical modelling and numerical analysis =
                 Modelisation math{\'e}matique et analyse num{\'e}rique:
                 $M^2AN$",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=MZA",
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Petkovic:1986:SIS
author: M. S. Petkovic and L. V. Stefanovic
title: On some improvements of square root iteration for polynomial complex zeros
journal: j-J-COMPUT-APPL-MATH
volume: 15
number: 1
pages: 13--25
month: may
monthnumber: 5
year: 1986
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(86)90235-9
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:55 MST 2017
bibtimestamp: 2017.02.25 11:59:55 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042786902359
fjournal: Journal of Computational and Applied Mathematics
keywords: polynomial root finding
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}
rawtitle: On some improvements of square root iteration for polynomial complex zeros
entry:
@Article{Petkovic:1986:SIS,
  author =       "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
  title =        "On some improvements of square root iteration for
                 polynomial complex zeros",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "1",
  pages =        "13--25",
  month =        may,
  year =         "1986",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(86)90235-9",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902359",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "polynomial root finding",
}


bibtype: article
filename: elefunt.bib
label: Piessens:1986:ATP
author: Robert Piessens and Shafique Ahmed
title: Approximation for the turning points of Bessel functions
journal: j-J-COMPUT-PHYS
volume: 64
number: 1
pages: 253--257
month: may
monthnumber: 5
year: 1986
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(86)90029-X
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:29 MST 2012
bibtimestamp: 2012.01.01 15:59:29 MST
URL: http://www.sciencedirect.com/science/article/pii/002199918690029X
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Robert Piessens and Shafique Ahmed
rawtitle: Approximation for the turning points of {Bessel} functions
entry:
@Article{Piessens:1986:ATP,
  author =       "Robert Piessens and Shafique Ahmed",
  title =        "Approximation for the turning points of {Bessel}
                 functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "64",
  number =       "1",
  pages =        "253--257",
  month =        may,
  year =         "1986",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(86)90029-X",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:29 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/002199918690029X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: book
filename: elefunt.bib
label: Prudnikov:1986:ISE
author: Anatolij P. Prudnikov and Jurij A. Bryckov and Oleg I. Maricev
title: Integrals and series. Elementary functions
volume: 1
publisher: Gordon and Breach Science Publishers
address: New York, NY, USA
pages: 798
year: 1986
ISBN: 2-88124-089-5 OR 2881240895
ISBN13: 978-2-88124-089-8 OR 9782881240898
LCCN: QA308.P7813 1986
bibdate: Thu Nov 2 15:40:35 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.11.02 15:40:35 MDT
remark: Translated from the Russian by N. M. Queen.
subject: Integrals; Series
acknowledgement: ack-nhfb
authordates: 1927--
rawauthor: Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and Oleg I. Mari{\v{c}}ev
rawtitle: Integrals and series. {Elementary} functions
entry:
@Book{Prudnikov:1986:ISE,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {Elementary} functions",
  volume =       "1",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "798",
  year =         "1986",
  ISBN =         "2-88124-089-5",
  ISBN-13 =      "978-2-88124-089-8",
  LCCN =         "QA308.P7813 1986",
  bibdate =      "Thu Nov 2 15:40:35 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1927--",
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Integrals; Series",
}


bibtype: book
filename: elefunt.bib
label: Prudnikov:1986:ISS
author: Anatolij P. Prudnikov and Jurij A. Bryckov and Oleg I. Maricev
title: Integrals and series. Special functions
volume: 2
publisher: Gordon and Breach Science Publishers
address: New York, NY, USA
pages: 750
year: 1986
ISBN: 2-88124-090-9 OR 2881240909
ISBN13: 978-2-88124-090-4 OR 9782881240904
LCCN: QA308.P7813 1986
MRclass: 26A33, 26A36, 26A39, 26A42, 26B15, 26B20, 26B25
bibdate: Thu Nov 2 15:43:13 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.11.02 15:43:13 MDT
remark: Translated from the Russian by N. M. Queen.
subject: Integrals; Series
acknowledgement: ack-nhfb
rawauthor: Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and Oleg I. Mari{\v{c}}ev
rawtitle: Integrals and series. {Special} functions
entry:
@Book{Prudnikov:1986:ISS,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {Special} functions",
  volume =       "2",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "750",
  year =         "1986",
  ISBN =         "2-88124-090-9",
  ISBN-13 =      "978-2-88124-090-4",
  LCCN =         "QA308.P7813 1986",
  MRclass =      "26A33, 26A36, 26A39, 26A42, 26B15, 26B20, 26B25",
  bibdate =      "Thu Nov 2 15:43:13 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Integrals; Series",
}


bibtype: article
filename: elefunt.bib
label: Reichel:1986:PAU
author: L. Reichel
title: On polynomial approximation in the uniform norm by the discrete least squares method
journal: j-BIT
volume: 26
number: 3
pages: 350--368
month: jan
monthnumber: 1
year: 1986
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
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: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: L. Reichel
rawtitle: On polynomial approximation in the uniform norm by the discrete least squares method
entry:
@Article{Reichel:1986:PAU,
  author =       "L. Reichel",
  title =        "On polynomial approximation in the uniform norm by the
                 discrete least squares method",
  journal =      j-BIT,
  volume =       "26",
  number =       "3",
  pages =        "350--368",
  month =        jan,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  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 =        "12404",
  catcode =      "G.1.2; G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Least squares
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation, Spline
                 and piecewise polynomial approximation",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  genterm =      "algorithms",
  guideno =      "1986-03278",
  journal-URL =  "http://link.springer.com/journal/10543",
  jrldate =      "Jan. 1986",
  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: Ronning:1986:CTF
author: Gerd Ronning
title: On the curvature of the trigamma function
journal: j-J-COMPUT-APPL-MATH
volume: 15
number: 3
pages: 397--399
month: jul
monthnumber: 7
year: 1986
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:56 MST 2017
bibtimestamp: 2017.02.25 11:59:56 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042786902311
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Gerd Ronning
rawtitle: On the curvature of the trigamma function
entry:
@Article{Ronning:1986:CTF,
  author =       "Gerd Ronning",
  title =        "On the curvature of the trigamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "3",
  pages =        "397--399",
  month =        jul,
  year =         "1986",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902311",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: S:1986:CEF
author: A. S. Kuz'menko and K. I. Rogozin
journal: Prace Nauk. Inst. Cybernet. Tech. Politech. Wroclaw. Ser. Konfer.
volume: 74
number: 31
pages: 259--262
year: 1986
MRclass: 65G99 (65D20)
MRnumber: 894 691
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. S. Kuz'menko and K. I. Rogozin
title:
Calculation of elementary functions in a number system with arbitrary basis on the basis of order-differential transformations. (Russian)

rawtitle:
Calculation of elementary functions in a number system with arbitrary basis on the basis of order-differential transformations. ({Russian})

entry:
@Article{S:1986:CEF,
  author =       "A. S. Kuz'menko and K. I. Rogozin",
  title =        "Calculation of elementary functions in a number system
                 with arbitrary basis on the basis of order-differential
                 transformations. ({Russian})",
  journal =      "Prace Nauk. Inst. Cybernet. Tech. Politech.
                 Wroc{\l}aw. Ser. Konfer.",
  volume =       "74",
  number =       "31",
  pages =        "259--262",
  year =         "1986",
  MRclass =      "65G99 (65D20)",
  MRnumber =     "894 691",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Shore:1986:AID
author: Haim Shore
journal: j-J-STAT-COMPUT-SIMUL
volume: 23
number: 3
pages: 157--181
year: 1986
CODEN: JSCSAJ
ISSN: 0094-9655 (print), 1563-5163 (electronic) OR 00949655 (print), 15635163 (electronic)
ISSNL: 0094-9655 OR 00949655
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 Statistical Computation and Simulation
acknowledgement: ack-nhfb
affiliation: Ban-llan University, Israel
journalURL: http://www.tandfonline.com/loi/gscs20
reviewer: M. Snyder
rawauthor: Haim Shore
title:
An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres

subject:
G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS; G. Mathematics of Computing; G.m MISCELLANEOUS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; J. Computer Applications; J.3 LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing; G.3 PROBABILITY AND STATISTICS

rawtitle:
An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres

entry:
@Article{Shore:1986:AID,
  author =       "Haim Shore",
  title =        "An approximation for the inverse distribution function
                 of a combination of random variables, with an
                 application to operating theatres",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "23",
  number =       "3",
  pages =        "157--181",
  year =         "1986",
  CODEN =        "JSCSAJ",
  ISSN =         "0094-9655 (print), 1563-5163 (electronic)",
  ISSN-L =       "0094-9655",
  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 =  "Ban-llan University, Israel",
  bibno =        "5358",
  catcode =      "G.3; G.m; G.1.2; G.2.1; J.3; G.3",
  content =      "The author worked on a project to predict the
                 percentage of time that operations are carried out
                 relative to the time that the operating theater is
                 available. The numerator of the percentage is a
                 weighted sum of the times required to carry out
                 different kinds of operations, where the weights are
                 the numbers of operations of each kind to be performed.
                 Since different kinds of operations have different mean
                 times, this sum has a skewed distribution.\par

                 Based on the Central Limit Theorem, the normal
                 distribution is the most widely used approximation to
                 the distribution of a weighted sum of random variables.
                 However, this approximation is not very good if the sum
                 has a skewed distribution.\par

                 In a separate paper [1], the author derived an
                 alternative approximation based on the first four
                 moments of the sum. In the present paper, he applies
                 this approximation to the operating theater problem by
                 estimating the moments of the times of the different
                 kinds of operations. The paper also contains a Monte
                 Carlo comparison of the normal approximation with the
                 proposed approximation for four underlying
                 distributions of the sum.",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.2.1 Combinatorics;
                 G.2.1 Generating functions; J.3 Health; G.3
                 Probabilistic algorithms (including Monte Carlo)",
  CRnumber =     "8612-1109",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 MISCELLANEOUS; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions;
                 Computer Applications, LIFE AND MEDICAL SCIENCES,
                 Health; Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo)",
  fjournal =     "Journal of Statistical Computation and Simulation",
  genterm =      "algorithms; measurement",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  journalabbrev = "J. Stat. Comput. Simul.",
  jrldate =      "1986",
  reviewer =     "M. Snyder",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.m
                 MISCELLANEOUS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
                 DISCRETE MATHEMATICS; J. Computer Applications; J.3
                 LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing;
                 G.3 PROBABILITY AND STATISTICS",
}


bibtype: article
filename: elefunt.bib
label: Skeel:1986:CVS
author: Robert D. Skeel
title: Construction of Variable-Stepsize Multistep Formulas
journal: j-MATH-COMPUT
volume: 47
number: 176
pages: 503--510, S45--S52
month: oct
monthnumber: 10
year: 1986
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65L05
MRnumber: 87j:65080
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: C4110 (Error analysis in numerical methods); C4170 (Differential equations)
corpsource: Dept. of Comput. Sci., Illnois Univ., Urbana, IL, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Robert D. Skeel
rawtitle: Construction of Variable-Stepsize Multistep Formulas
keywords:
Adams formula; adaptable multistep methods; backward-differentiation; differential equations; error analysis; estimation; first Dahlquist barrier; fixed leading coefficient method; fixed-coefficient methods; fixed-stepsize; formula; formula changing; initial value; interpolatory methods; local error; minimum storage variable-stepsize; multistep formula; Nordsieck stepsize changing technique; problems; step methods; variable; variable coefficient methods; variable-order family of variable-coefficient formulas

entry:
@Article{Skeel:1986:CVS,
  author =       "Robert D. Skeel",
  title =        "Construction of Variable-Stepsize Multistep Formulas",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "503--510, S45--S52",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L05",
  MRnumber =     "87j:65080",
  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 =   "C4110 (Error analysis in numerical methods); C4170
                 (Differential equations)",
  corpsource =   "Dept. of Comput. Sci., Illnois Univ., Urbana, IL,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Adams formula; adaptable multistep methods;
                 backward-differentiation; differential equations; error
                 analysis; estimation; first Dahlquist barrier; fixed
                 leading coefficient method; fixed-coefficient methods;
                 fixed-stepsize; formula; formula changing; initial
                 value; interpolatory methods; local error; minimum
                 storage variable-stepsize; multistep formula; Nordsieck
                 stepsize changing technique; problems; step methods;
                 variable; variable coefficient methods; variable-order
                 family of variable-coefficient formulas",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Skeel:1986:SCV
author: Robert D. Skeel
title: Supplement to Construction of Variable-Stepsize Multistep Formulas
journal: j-MATH-COMPUT
volume: 47
number: 176
pages: S45--S52
month: oct
monthnumber: 10
year: 1986
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Robert D. Skeel
rawtitle: Supplement to Construction of Variable-Stepsize Multistep Formulas
entry:
@Article{Skeel:1986:SCV,
  author =       "Robert D. Skeel",
  title =        "Supplement to Construction of Variable-Stepsize
                 Multistep Formulas",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "S45--S52",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Temme:1986:DIC
author: N. M. Temme
title: A double integral containing the modified Bessel function: asymptotics and computation
journal: j-MATH-COMPUT
volume: 47
number: 176
pages: 683--691
month: oct
monthnumber: 10
year: 1986
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A40 (41A60 65D30)
MRnumber: 87m:33006
MRreviewer: S. D. Bajpai
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: Centre for Math. and Comput. Sci., Amsterdam, Netherlands
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: N. M. Temme
rawtitle: A double integral containing the modified {Bessel} function: asymptotics and computation
keywords:
distribution function; double integral; error analysis; error function; integral; integration; modified Bessel function; normal; polynomials; probability; series (mathematics); series expansions; two-dimensional

classcodes:
C4110 (Error analysis in numerical methods); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)

entry:
@Article{Temme:1986:DIC,
  author =       "N. M. Temme",
  title =        "A double integral containing the modified {Bessel}
                 function: asymptotics and computation",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "683--691",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (41A60 65D30)",
  MRnumber =     "87m:33006",
  MRreviewer =   "S. D. Bajpai",
  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 =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Centre for Math. and Comput. Sci., Amsterdam,
                 Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "distribution function; double integral; error
                 analysis; error function; integral; integration;
                 modified Bessel function; normal; polynomials;
                 probability; series (mathematics); series expansions;
                 two-dimensional",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Thompson:1986:CBF
author: I. J. Thompson and A. R. Barnett
title: Coulomb and Bessel functions of complex arguments and order
journal: j-J-COMPUT-PHYS
volume: 64
number: 2
pages: 490--509
month: jun
monthnumber: 6
year: 1986
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(86)90046-X
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:30 MST 2012
bibtimestamp: 2012.01.01 15:59:30 MST
URL: http://www.sciencedirect.com/science/article/pii/002199918690046X
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: I. J. Thompson and A. R. Barnett
rawtitle: {Coulomb} and {Bessel} functions of complex arguments and order
abstract:
The Coulomb wavefunctions, originally constructed for real $ varrho > 0 $, real $ eta $ and integer $ lambda geq 0 $ are defined for $ varrho $, $ eta $, and $ lambda $ all complex. We examine the complex continuation of a variety of series and continued-fraction expansions for the Coulomb functions and their logarithmic derivatives, and then see how these expansions may be selectively combined to calculate both the regular and irregular functions and their derivatives. The resulting algorithm [46] is a complex generalisation of Steed's method [6, 7] as it appears in the real procedure COULFG [10]. Complex Whittaker, confluent hypergeometric and Bessel functions can also be calculated.

rawabstract:
The Coulomb wavefunctions, originally constructed for real $ \varrho > 0 $, real $ \eta $ and integer $ \lambda \geq 0 $ are defined for $ \varrho $, $ \eta $, and $ \lambda $ all complex. We examine the complex continuation of a variety of series and continued-fraction expansions for the Coulomb functions and their logarithmic derivatives, and then see how these expansions may be selectively combined to calculate both the regular and irregular functions and their derivatives. The resulting algorithm [46] is a complex generalisation of Steed's method [6, 7] as it appears in the real procedure COULFG [10]. Complex Whittaker, confluent hypergeometric and Bessel functions can also be calculated.

entry:
@Article{Thompson:1986:CBF,
  author =       "I. J. Thompson and A. R. Barnett",
  title =        "{Coulomb} and {Bessel} functions of complex arguments
                 and order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "64",
  number =       "2",
  pages =        "490--509",
  month =        jun,
  year =         "1986",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(86)90046-X",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:30 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/002199918690046X",
  abstract =     "The Coulomb wavefunctions, originally constructed for
                 real $ \varrho > 0 $, real $ \eta $ and integer $
                 \lambda \geq 0 $ are defined for $ \varrho $, $ \eta $,
                 and $ \lambda $ all complex. We examine the complex
                 continuation of a variety of series and
                 continued-fraction expansions for the Coulomb functions
                 and their logarithmic derivatives, and then see how
                 these expansions may be selectively combined to
                 calculate both the regular and irregular functions and
                 their derivatives. The resulting algorithm [46] is a
                 complex generalisation of Steed's method [6, 7] as it
                 appears in the real procedure COULFG [10]. Complex
                 Whittaker, confluent hypergeometric and Bessel
                 functions can also be calculated.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: book
filename: elefunt.bib
label: Varshalovich:1986:QTA
author: D. A. Varshalovich and A. N. Moskalev and V. K. Khersonskii
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: x + 514
year: 1986
ISBN: 9971-5-0107-4 OR 9971501074
ISBN13: 978-9971-5-0107-5 OR 9789971501075
LCCN: QC793.3.A5 V3713 1986
bibdate: Tue Aug 5 06:20:04 MDT 2025
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.08.05 06:20:04 MDT
acknowledgement: ack-nhfb
rawauthor: D. A. Varshalovich and A. N. Moskalev and V. K. Khersonskii
title:
Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, $ 3 n j $ Symbols

subject:
Angular momentum (Nuclear physics); Quantum theory; Moment angulaire (Physique nucleaire); Theorie quantique; Angular momentum (Nuclear physics); Quantum theory.

TOC:
Preface / v Introduction: Basic Concepts / 1 1: Elements of Vector and Tensor Theory / 3 1.1. Coordinate Systems. Basis Vectors / 3 1.2. Vectors. Tensors / 11 1.3. Differential Operations / 17 1.4. Rotations of Coordinate System / 21 2: Angular Momentum Operators / 36 2.1. Total Angular Momentum Operator / 36 2.2. Orbital Angular Momentum Operator / 39 2.3. Spin Angular Momentum Operator / 42 2.4. Polarization Operators / 44 2.5. Spin Matrices for $S = 1/2$ / 47 2.6. Spin Matrices and Polarization Operators for $S = 1$ / 51 3: Irreducible Tensors / 61 3.1. Definition and Properties of Irreducible Tensors / 61 3.2. Relation Between the Irreducible Tensor Algebra and Vector and Tensor Theory / 65 3.3. Recoupling in Irreducible Tensor Products / 69 4: Wigner $D$-Functions / 72 4.1. Definition of $D^J_M M'(alpha , beta , gamma )$ / 72 4.2. Differential Equations for $D^J_M M'(alpha , beta , gamma )$ / 74 4.3. Explicit Forms of the Wigner $D$-Functions / 76 4.4. Symmetries of $d^J_M M'(beta )$ and $D^J_M M'(alpha , beta , gamma )$ / 79 4.5. Rotation Matrix $U^J_M M'$, in Terms of Angles $omega , Theta , Phi $ / 80 4.6. Sums Involving $D$-Functions / 84 4.7. Addition of Rotations / 87 4.8. Recursion Relations for $D^J_M M'(alpha , beta , gamma )$ / 90 4.9. Differential Relations for $D^J_M M'(alpha , beta , gamma )$ / 94 4.10. Orthogonality and Completeness of the $D$-Functions / 94 4.11. Integrals Involving the $D$-Functions / 96 4.12. Invariant Summation of Integrals Involving $D^J_M M'(alpha , beta , gamma )$ / 97 4.13. Generating Functions for $d^J_M M'(beta )$ / 98 4.14. Characters $chi ^J(R)$ of Irreducible Representations of Rotation Group / 99 4.15. Generalized Characters, $chi ^J_lambda (R)$ of Irreducible Representations of the Rotation Group / 106 4.16. $D^J_M M'(alpha , beta , gamma )$ for Particular Values of the Arguments / 112 4.17. Special Cases of $D^J_M M'(alpha , beta , gamma )$ for Particular $M$ or $M'$ / 113 4.18. Asymptotics of $D^J_M M'(alpha , beta , gamma )$ / 115 4.19. Definitions of $D^J_M M'(alpha , beta , gamma )$ by Other Authors / 117 4.20. Special Cases of $d^J_M M'(beta )$ for Particular $J$, $M$ and $M'$ / 117 4.21. Tables of $d^J_M M'(beta )$ for $beta = pi /2$ / 117 4.22. Special Cases of $U^J_M M'(omega ; Theta , Phi )$ / 117 5: Spherical Harmonics / 130 5.1. Definition / 130 5.2. Explicit Forms of the Spherical Harmonics and Their Relations to Other Functions / 133 5.3. Integral Representations of the Spherical Harmonics [4, 22, 27] / 139 5.4. Symmetry Properties / 140 5.5. Behaviour of $Y_l m(theta , phi )$ under Transformations of Coordinate Systems / 141 5.6. Expansions in Series of the Spherical Harmonics / 143 5.7. Recursion Relations / 145 5.8. Differential Relations / 146 5.9. Some Integrals Involving Spherical Harmonics / 148 5.10. Sums Involving Spherical Harmonics / 150 5.11. Generating Functions for $Y_l m(theta , phi )$ / 151 5.12. Asymptotic Expressions for $Y_l m(theta , phi )$ / 152 5.13. $Y_l m(theta , phi )$ for Special Values of $l$ and $m$ / 155 5.14. $Y_l m(theta , phi )$ and $(partial / partial theta ) Y_l m(theta , phi )$ for Special $theta $ / 158 5.15. Zeros of $Y_l m(theta , phi )$ and $(partial / partial theta ) Y_l m(theta , phi )$ / 158 5.16. Bipolar and Tripolar Spherical Harmonics / 160 5.17. Expansions of Functions Which Depend on Two Vectors / 163 6: Spin Functions / 170 6.1. Spin Functions of Particles with Arbitrary Spin / 170 6.2. Spin Functions for $S = 1/2$ / 178 6.3. Spin Functions for $S = 1$ / 185 7: Tensor Spherical Harmonics / 196 7.1. General Properties of Tensor Spherical Harmonics / 196 7.2. Spinor Spherical Harmonics / 202 7.3. Vector Spherical Harmonics / 208 7.4. Other Notations for Tensor Spherical Harmonics / 234 8: Clebsch--Gordan Coefficients and $3jm$ Symbols / 235 8.1. Definition / 235 8.2. Explicit Forms of the Clebsch--Gordan Coefficients and Their Relations to Other Functions / 237 8.3. Integral Representations / 243 8.4. Symmetry Properties / 244 8.5. Explicit Forms of the Clebsch--Gordan Coefficients for Special Values of the Arguments / 248 8.6. Recursion Relations for the Clebsch--Gordan Coefficients / 252 8.7. Sums of Products of the Clebsch--Gordan Coefficients / 259 8.8. Generating Functions / 263 8.9. Classical Limit and Asymptotic Expressions for the Clebsch--Gordan Coefficients / 264 8.10. Zeros of the Vector-Addition Coefficients / 268 8.11. Connection of the Clebsch--Gordan Coefficients and the $3jm$ Symbols with Analogous Functions of Other Authors / 268 8.12. Algebraic Tables of the Clebsch--Gordan Coefficients / 270 8.13. Numerical Tables of the Clebsch--Gordan Coefficients / 270 9: $6j$ Symbols and the Racah Coefficients / 290 9.1. Definition / 290 9.2. General Expressions for the $6j$ Symbols. Relations Between the $6j$ Symbols and Other Functions / 293 9.3. Integral Representations of the $6j$ Symbols / 297 9.4. Symmetries of the $6j$ Symbols and the Racah Coefficients / 298 9.5. Explicit Forms of the &j Symbols for Certain Arguments / 299 9.6. Recursion Relations / 303 9.7. Generating Function / 305 9.8. Sums Involving the $6j$ Symbols / 305 9.9. Asymptotics of the $6j$ Symbols for Large Angular Momenta / 306 9.10. Relations Between the Wigner $6j$ Symbols and Analogous Functions of Other Authors / 310 9.11. Tables of Algebraic Expressions for the $6j$ Symbols / 310 9.12. Numerical Values of the $6j$ Symbols / 310 10: $9j$ and $12j$ Symbols / 333 10.1. Definition of the $9j$ Symbols / 333 10.2. Explicit Forms of the $9j$ Symbols and Their Relations to Other Functions / 336 10.3. Integral Representations of the $9j$ Symbols / 340 10.4. Symmetry Properties of the $9j$ Symbols / 342 10.5. Recursion Relations for the $9j$ Symbols / 345 10.6. Generating Function of the $9j$ Symbols / 351 10.7. Asymptotic Expression for a $9j$ Symbol / 351 10.8. Explicit Forms of the $9j$ Symbols at Some Relations Between Arguments / 352 10.9. Explicit Forms of the $9j$ Symbols for Special Values of the Arguments / 357 10.10. Relations Between the Wigner $9j$ Symbols and Analogous Functions of Other Authors / 359 10.11. Tables of Algebraic Formulas of the $9j$ Symbols / 359 10.12. Tables of Numerical Values of the $9j$ Symbols / 360 10.13. $12j$ Symbols / 361 11: The Graphical Method in Angular Momentum Theory / 412 11.1. Graphical Representation of Functions / 412 11.2. Graphical Representation of the Main Operations of the Theory / 419 11.3. Rules of the Graphical Technique / 424 11.4. Summary of the Graphical Technique / 446 12: Sums Involving Vector Addition and Recoupling Coefficients / 452 12.1. Summation of Products of $3jm$ Symbols / 452 12.2. Summation of Products of $6j$ and $9j$ Symbols / 462 13: Matrix Elements of Irreducible Tensor Operators / 475 13.1. The Wigner--Eckart Theorem and the Evaluation of Matrix Elements / 475 13.2. Matrix Elements of Basic Tensor Operators / 485 Glossary of Symbols and Notation / 505 References / 509

rawtitle:
Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, $ 3 n j $ Symbols

shortTOC:
1: Elements of vector and tensor theory 2: Angular momentum operators 3: Irreducible tensors 4: Wigner D-functions 5: Spherical harmonics 6: Spin functions 7: Tensor spherical harmonics 8: Clebsch--Gordan coefficients and $3jm$ symbols 9: $6j$ symbols and the Racah coefficients 10: $9j$ and $12j$ symbols 11: The graphical method in angular momentum theory 12: Sums involving vector addition and recoupling coefficients 13: Matrix elements of irreducible tensor operators

rawshortTOC:
1: Elements of vector and tensor theory \\ 2: Angular momentum operators \\ 3: Irreducible tensors \\ 4: Wigner D-functions \\ 5: Spherical harmonics \\ 6: Spin functions \\ 7: Tensor spherical harmonics \\ 8: Clebsch--Gordan coefficients and $3jm$ symbols \\ 9: $6j$ symbols and the Racah coefficients \\ 10: $9j$ and $12j$ symbols \\ 11: The graphical method in angular momentum theory \\ 12: Sums involving vector addition and recoupling coefficients \\ 13: Matrix elements of irreducible tensor operators

rawTOC:
Preface / v \\ Introduction: Basic Concepts / 1 \\ 1: Elements of Vector and Tensor Theory / 3 \\ 1.1. Coordinate Systems. Basis Vectors / 3 \\ 1.2. Vectors. Tensors / 11 \\ 1.3. Differential Operations / 17 \\ 1.4. Rotations of Coordinate System / 21 \\ 2: Angular Momentum Operators / 36 \\ 2.1. Total Angular Momentum Operator / 36 \\ 2.2. Orbital Angular Momentum Operator / 39 \\ 2.3. Spin Angular Momentum Operator / 42 \\ 2.4. Polarization Operators / 44 \\ 2.5. Spin Matrices for $S = 1/2$ / 47 \\ 2.6. Spin Matrices and Polarization Operators for $S = 1$ / 51 \\ 3: Irreducible Tensors / 61 \\ 3.1. Definition and Properties of Irreducible Tensors / 61 \\ 3.2. Relation Between the Irreducible Tensor Algebra and Vector and Tensor Theory / 65 \\ 3.3. Recoupling in Irreducible Tensor Products / 69 \\ 4: Wigner $D$-Functions / 72 \\ 4.1. Definition of $D^J_{M M'}(\alpha, \beta, \gamma)$ / 72 \\ 4.2. Differential Equations for $D^J_{M M'}(\alpha, \beta, \gamma)$ / 74 \\ 4.3. Explicit Forms of the Wigner $D$-Functions / 76 \\ 4.4. Symmetries of $d^J_{M M'}(\beta)$ and $D^J_{M M'}(\alpha, \beta, \gamma)$ / 79 \\ 4.5. Rotation Matrix $U^J_{M M'}$, in Terms of Angles $\omega, \Theta, \Phi$ / 80 \\ 4.6. Sums Involving $D$-Functions / 84 \\ 4.7. Addition of Rotations / 87 \\ 4.8. Recursion Relations for $D^J_{M M'}(\alpha, \beta, \gamma)$ / 90 \\ 4.9. Differential Relations for $D^J_{M M'}(\alpha, \beta, \gamma)$ / 94 \\ 4.10. Orthogonality and Completeness of the $D$-Functions / 94 \\ 4.11. Integrals Involving the $D$-Functions / 96 \\ 4.12. Invariant Summation of Integrals Involving $D^J_{M M'}(\alpha, \beta, \gamma)$ / 97 \\ 4.13. Generating Functions for $d^J_{M M'}(\beta)$ / 98 \\ 4.14. Characters $\chi^J(R)$ of Irreducible Representations of Rotation Group / 99 \\ 4.15. Generalized Characters, $\chi^J_\lambda(R)$ of Irreducible Representations of the Rotation Group / 106 \\ 4.16. $D^J_{M M'}(\alpha, \beta, \gamma)$ for Particular Values of the Arguments / 112 \\ 4.17. Special Cases of $D^J_{M M'}(\alpha, \beta, \gamma)$ for Particular $M$ or $M'$ / 113 \\ 4.18. Asymptotics of $D^J_{M M'}(\alpha, \beta, \gamma)$ / 115 \\ 4.19. Definitions of $D^J_{M M'}(\alpha, \beta, \gamma)$ by Other Authors / 117 \\ 4.20. Special Cases of $d^J_{M M'}(\beta)$ for Particular $J$, $M$ and $M'$ / 117 \\ 4.21. Tables of $d^J_{M M'}(\beta)$ for $\beta = \pi/2$ / 117 \\ 4.22. Special Cases of $U^J_{M M'}(\omega; \Theta, \Phi)$ / 117 \\ 5: Spherical Harmonics / 130 \\ 5.1. Definition / 130 \\ 5.2. Explicit Forms of the Spherical Harmonics and Their Relations to Other Functions / 133 \\ 5.3. Integral Representations of the Spherical Harmonics [4, 22, 27] / 139 \\ 5.4. Symmetry Properties / 140 \\ 5.5. Behaviour of $Y_{l m}(\theta, \phi)$ under Transformations of Coordinate Systems / 141 \\ 5.6. Expansions in Series of the Spherical Harmonics / 143 \\ 5.7. Recursion Relations / 145 \\ 5.8. Differential Relations / 146 \\ 5.9. Some Integrals Involving Spherical Harmonics / 148 \\ 5.10. Sums Involving Spherical Harmonics / 150 \\ 5.11. Generating Functions for $Y_{l m}(\theta, \phi)$ / 151 \\ 5.12. Asymptotic Expressions for $Y_{l m}(\theta, \phi)$ / 152 \\ 5.13. $Y_{l m}(\theta, \phi)$ for Special Values of $l$ and $m$ / 155 \\ 5.14. $Y_{l m}(\theta, \phi)$ and $(\partial / \partial \theta) Y_{l m}(\theta, \phi)$ for Special $\theta$ / 158 \\ 5.15. Zeros of $Y_{l m}(\theta, \phi)$ and $(\partial / \partial \theta) Y_{l m}(\theta, \phi)$ / 158 \\ 5.16. Bipolar and Tripolar Spherical Harmonics / 160 \\ 5.17. Expansions of Functions Which Depend on Two Vectors / 163 \\ 6: Spin Functions / 170 \\ 6.1. Spin Functions of Particles with Arbitrary Spin / 170 \\ 6.2. Spin Functions for $S = 1/2$ / 178 \\ 6.3. Spin Functions for $S = 1$ / 185 \\ 7: Tensor Spherical Harmonics / 196 \\ 7.1. General Properties of Tensor Spherical Harmonics / 196 \\ 7.2. Spinor Spherical Harmonics / 202 \\ 7.3. Vector Spherical Harmonics / 208 \\ 7.4. Other Notations for Tensor Spherical Harmonics / 234 \\ 8: Clebsch--Gordan Coefficients and $3jm$ Symbols / 235 \\ 8.1. Definition / 235 \\ 8.2. Explicit Forms of the Clebsch--Gordan Coefficients and Their Relations to Other Functions / 237 \\ 8.3. Integral Representations / 243 \\ 8.4. Symmetry Properties / 244 \\ 8.5. Explicit Forms of the Clebsch--Gordan Coefficients for Special Values of the Arguments / 248 \\ 8.6. Recursion Relations for the Clebsch--Gordan Coefficients / 252 \\ 8.7. Sums of Products of the Clebsch--Gordan Coefficients / 259 \\ 8.8. Generating Functions / 263 \\ 8.9. Classical Limit and Asymptotic Expressions for the Clebsch--Gordan Coefficients / 264 \\ 8.10. Zeros of the Vector-Addition Coefficients / 268 \\ 8.11. Connection of the Clebsch--Gordan Coefficients and the $3jm$ Symbols with Analogous Functions of Other Authors / 268 \\ 8.12. Algebraic Tables of the Clebsch--Gordan Coefficients / 270 \\ 8.13. Numerical Tables of the Clebsch--Gordan Coefficients / 270 \\ 9: $6j$ Symbols and the Racah Coefficients / 290 \\ 9.1. Definition / 290 \\ 9.2. General Expressions for the $6j$ Symbols. Relations Between the $6j$ Symbols and Other Functions / 293 \\ 9.3. Integral Representations of the $6j$ Symbols / 297 \\ 9.4. Symmetries of the $6j$ Symbols and the Racah Coefficients / 298 \\ 9.5. Explicit Forms of the &j Symbols for Certain Arguments / 299 \\ 9.6. Recursion Relations / 303 \\ 9.7. Generating Function / 305 \\ 9.8. Sums Involving the $6j$ Symbols / 305 \\ 9.9. Asymptotics of the $6j$ Symbols for Large Angular Momenta / 306 \\ 9.10. Relations Between the Wigner $6j$ Symbols and Analogous Functions of Other Authors / 310 \\ 9.11. Tables of Algebraic Expressions for the $6j$ Symbols / 310 \\ 9.12. Numerical Values of the $6j$ Symbols / 310 \\ 10: $9j$ and $12j$ Symbols / 333 \\ 10.1. Definition of the $9j$ Symbols / 333 \\ 10.2. Explicit Forms of the $9j$ Symbols and Their Relations to Other Functions / 336 \\ 10.3. Integral Representations of the $9j$ Symbols / 340 \\ 10.4. Symmetry Properties of the $9j$ Symbols / 342 \\ 10.5. Recursion Relations for the $9j$ Symbols / 345 \\ 10.6. Generating Function of the $9j$ Symbols / 351 \\ 10.7. Asymptotic Expression for a $9j$ Symbol / 351 \\ 10.8. Explicit Forms of the $9j$ Symbols at Some Relations Between Arguments / 352 \\ 10.9. Explicit Forms of the $9j$ Symbols for Special Values of the Arguments / 357 \\ 10.10. Relations Between the Wigner $9j$ Symbols and Analogous Functions of Other Authors / 359 \\ 10.11. Tables of Algebraic Formulas of the $9j$ Symbols / 359 \\ 10.12. Tables of Numerical Values of the $9j$ Symbols / 360 \\ 10.13. $12j$ Symbols / 361 \\ 11: The Graphical Method in Angular Momentum Theory / 412 \\ 11.1. Graphical Representation of Functions / 412 \\ 11.2. Graphical Representation of the Main Operations of the Theory / 419 \\ 11.3. Rules of the Graphical Technique / 424 \\ 11.4. Summary of the Graphical Technique / 446 \\ 12: Sums Involving Vector Addition and Recoupling Coefficients / 452 \\ 12.1. Summation of Products of $3jm$ Symbols / 452 \\ 12.2. Summation of Products of $6j$ and $9j$ Symbols / 462 \\ 13: Matrix Elements of Irreducible Tensor Operators / 475 \\ 13.1. The Wigner--Eckart Theorem and the Evaluation of Matrix Elements / 475 \\ 13.2. Matrix Elements of Basic Tensor Operators / 485 \\ Glossary of Symbols and Notation / 505 \\ References / 509

entry:
@Book{Varshalovich:1986:QTA,
  author =       "D. A. Varshalovich and A. N. Moskalev and V. K.
                 Khersonskii",
  title =        "Quantum Theory of Angular Momentum: Irreducible
                 Tensors, Spherical Harmonics, Vector Coupling
                 Coefficients, $ 3 n j $ Symbols",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "x + 514",
  year =         "1986",
  ISBN =         "9971-5-0107-4",
  ISBN-13 =      "978-9971-5-0107-5",
  LCCN =         "QC793.3.A5 V3713 1986",
  bibdate =      "Tue Aug 5 06:20:04 MDT 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Elements of vector and tensor theory \\
                 2: Angular momentum operators \\
                 3: Irreducible tensors \\
                 4: Wigner D-functions \\
                 5: Spherical harmonics \\
                 6: Spin functions \\
                 7: Tensor spherical harmonics \\
                 8: Clebsch--Gordan coefficients and $3jm$ symbols \\
                 9: $6j$ symbols and the Racah coefficients \\
                 10: $9j$ and $12j$ symbols \\
                 11: The graphical method in angular momentum theory \\
                 12: Sums involving vector addition and recoupling
                 coefficients \\
                 13: Matrix elements of irreducible tensor operators",
  subject =      "Angular momentum (Nuclear physics); Quantum theory;
                 Moment angulaire (Physique nucl{\'e}aire); Th{\'e}orie
                 quantique; Angular momentum (Nuclear physics); Quantum
                 theory.",
  tableofcontents = "Preface / v \\
                 Introduction: Basic Concepts / 1 \\
                 1: Elements of Vector and Tensor Theory / 3 \\
                 1.1. Coordinate Systems. Basis Vectors / 3 \\
                 1.2. Vectors. Tensors / 11 \\
                 1.3. Differential Operations / 17 \\
                 1.4. Rotations of Coordinate System / 21 \\
                 2: Angular Momentum Operators / 36 \\
                 2.1. Total Angular Momentum Operator / 36 \\
                 2.2. Orbital Angular Momentum Operator / 39 \\
                 2.3. Spin Angular Momentum Operator / 42 \\
                 2.4. Polarization Operators / 44 \\
                 2.5. Spin Matrices for $S = 1/2$ / 47 \\
                 2.6. Spin Matrices and Polarization Operators for $S =
                 1$ / 51 \\
                 3: Irreducible Tensors / 61 \\
                 3.1. Definition and Properties of Irreducible Tensors /
                 61 \\
                 3.2. Relation Between the Irreducible Tensor Algebra
                 and Vector and Tensor Theory / 65 \\
                 3.3. Recoupling in Irreducible Tensor Products / 69 \\
                 4: Wigner $D$-Functions / 72 \\
                 4.1. Definition of $D^J_{M M'}(\alpha, \beta, \gamma)$
                 / 72 \\
                 4.2. Differential Equations for $D^J_{M M'}(\alpha,
                 \beta, \gamma)$ / 74 \\
                 4.3. Explicit Forms of the Wigner $D$-Functions / 76
                 \\
                 4.4. Symmetries of $d^J_{M M'}(\beta)$ and $D^J_{M
                 M'}(\alpha, \beta, \gamma)$ / 79 \\
                 4.5. Rotation Matrix $U^J_{M M'}$, in Terms of Angles
                 $\omega, \Theta, \Phi$ / 80 \\
                 4.6. Sums Involving $D$-Functions / 84 \\
                 4.7. Addition of Rotations / 87 \\
                 4.8. Recursion Relations for $D^J_{M M'}(\alpha, \beta,
                 \gamma)$ / 90 \\
                 4.9. Differential Relations for $D^J_{M M'}(\alpha,
                 \beta, \gamma)$ / 94 \\
                 4.10. Orthogonality and Completeness of the
                 $D$-Functions / 94 \\
                 4.11. Integrals Involving the $D$-Functions / 96 \\
                 4.12. Invariant Summation of Integrals Involving
                 $D^J_{M M'}(\alpha, \beta, \gamma)$ / 97 \\
                 4.13. Generating Functions for $d^J_{M M'}(\beta)$ / 98
                 \\
                 4.14. Characters $\chi^J(R)$ of Irreducible
                 Representations of Rotation Group / 99 \\
                 4.15. Generalized Characters, $\chi^J_\lambda(R)$ of
                 Irreducible Representations of the Rotation Group / 106
                 \\
                 4.16. $D^J_{M M'}(\alpha, \beta, \gamma)$ for
                 Particular Values of the Arguments / 112 \\
                 4.17. Special Cases of $D^J_{M M'}(\alpha, \beta,
                 \gamma)$ for Particular $M$ or $M'$ / 113 \\
                 4.18. Asymptotics of $D^J_{M M'}(\alpha, \beta,
                 \gamma)$ / 115 \\
                 4.19. Definitions of $D^J_{M M'}(\alpha, \beta,
                 \gamma)$ by Other Authors / 117 \\
                 4.20. Special Cases of $d^J_{M M'}(\beta)$ for
                 Particular $J$, $M$ and $M'$ / 117 \\
                 4.21. Tables of $d^J_{M M'}(\beta)$ for $\beta = \pi/2$
                 / 117 \\
                 4.22. Special Cases of $U^J_{M M'}(\omega; \Theta,
                 \Phi)$ / 117 \\
                 5: Spherical Harmonics / 130 \\
                 5.1. Definition / 130 \\
                 5.2. Explicit Forms of the Spherical Harmonics and
                 Their Relations to Other Functions / 133 \\
                 5.3. Integral Representations of the Spherical
                 Harmonics [4, 22, 27] / 139 \\
                 5.4. Symmetry Properties / 140 \\
                 5.5. Behaviour of $Y_{l m}(\theta, \phi)$ under
                 Transformations of Coordinate Systems / 141 \\
                 5.6. Expansions in Series of the Spherical Harmonics /
                 143 \\
                 5.7. Recursion Relations / 145 \\
                 5.8. Differential Relations / 146 \\
                 5.9. Some Integrals Involving Spherical Harmonics / 148
                 \\
                 5.10. Sums Involving Spherical Harmonics / 150 \\
                 5.11. Generating Functions for $Y_{l m}(\theta, \phi)$
                 / 151 \\
                 5.12. Asymptotic Expressions for $Y_{l m}(\theta,
                 \phi)$ / 152 \\
                 5.13. $Y_{l m}(\theta, \phi)$ for Special Values of $l$
                 and $m$ / 155 \\
                 5.14. $Y_{l m}(\theta, \phi)$ and $(\partial / \partial
                 \theta) Y_{l m}(\theta, \phi)$ for Special $\theta$ /
                 158 \\
                 5.15. Zeros of $Y_{l m}(\theta, \phi)$ and $(\partial /
                 \partial \theta) Y_{l m}(\theta, \phi)$ / 158 \\
                 5.16. Bipolar and Tripolar Spherical Harmonics / 160
                 \\
                 5.17. Expansions of Functions Which Depend on Two
                 Vectors / 163 \\
                 6: Spin Functions / 170 \\
                 6.1. Spin Functions of Particles with Arbitrary Spin /
                 170 \\
                 6.2. Spin Functions for $S = 1/2$ / 178 \\
                 6.3. Spin Functions for $S = 1$ / 185 \\
                 7: Tensor Spherical Harmonics / 196 \\
                 7.1. General Properties of Tensor Spherical Harmonics /
                 196 \\
                 7.2. Spinor Spherical Harmonics / 202 \\
                 7.3. Vector Spherical Harmonics / 208 \\
                 7.4. Other Notations for Tensor Spherical Harmonics /
                 234 \\
                 8: Clebsch--Gordan Coefficients and $3jm$ Symbols / 235
                 \\
                 8.1. Definition / 235 \\
                 8.2. Explicit Forms of the Clebsch--Gordan Coefficients
                 and Their Relations to Other Functions / 237 \\
                 8.3. Integral Representations / 243 \\
                 8.4. Symmetry Properties / 244 \\
                 8.5. Explicit Forms of the Clebsch--Gordan Coefficients
                 for Special Values of the Arguments / 248 \\
                 8.6. Recursion Relations for the Clebsch--Gordan
                 Coefficients / 252 \\
                 8.7. Sums of Products of the Clebsch--Gordan
                 Coefficients / 259 \\
                 8.8. Generating Functions / 263 \\
                 8.9. Classical Limit and Asymptotic Expressions for the
                 Clebsch--Gordan Coefficients / 264 \\
                 8.10. Zeros of the Vector-Addition Coefficients / 268
                 \\
                 8.11. Connection of the Clebsch--Gordan Coefficients
                 and the $3jm$ Symbols with Analogous Functions of Other
                 Authors / 268 \\
                 8.12. Algebraic Tables of the Clebsch--Gordan
                 Coefficients / 270 \\
                 8.13. Numerical Tables of the Clebsch--Gordan
                 Coefficients / 270 \\
                 9: $6j$ Symbols and the Racah Coefficients / 290 \\
                 9.1. Definition / 290 \\
                 9.2. General Expressions for the $6j$ Symbols.
                 Relations Between the $6j$ Symbols and Other Functions
                 / 293 \\
                 9.3. Integral Representations of the $6j$ Symbols / 297
                 \\
                 9.4. Symmetries of the $6j$ Symbols and the Racah
                 Coefficients / 298 \\
                 9.5. Explicit Forms of the &j Symbols for Certain
                 Arguments / 299 \\
                 9.6. Recursion Relations / 303 \\
                 9.7. Generating Function / 305 \\
                 9.8. Sums Involving the $6j$ Symbols / 305 \\
                 9.9. Asymptotics of the $6j$ Symbols for Large Angular
                 Momenta / 306 \\
                 9.10. Relations Between the Wigner $6j$ Symbols and
                 Analogous Functions of Other Authors / 310 \\
                 9.11. Tables of Algebraic Expressions for the $6j$
                 Symbols / 310 \\
                 9.12. Numerical Values of the $6j$ Symbols / 310 \\
                 10: $9j$ and $12j$ Symbols / 333 \\
                 10.1. Definition of the $9j$ Symbols / 333 \\
                 10.2. Explicit Forms of the $9j$ Symbols and Their
                 Relations to Other Functions / 336 \\
                 10.3. Integral Representations of the $9j$ Symbols /
                 340 \\
                 10.4. Symmetry Properties of the $9j$ Symbols / 342 \\
                 10.5. Recursion Relations for the $9j$ Symbols / 345
                 \\
                 10.6. Generating Function of the $9j$ Symbols / 351 \\
                 10.7. Asymptotic Expression for a $9j$ Symbol / 351 \\
                 10.8. Explicit Forms of the $9j$ Symbols at Some
                 Relations Between Arguments / 352 \\
                 10.9. Explicit Forms of the $9j$ Symbols for Special
                 Values of the Arguments / 357 \\
                 10.10. Relations Between the Wigner $9j$ Symbols and
                 Analogous Functions of Other Authors / 359 \\
                 10.11. Tables of Algebraic Formulas of the $9j$ Symbols
                 / 359 \\
                 10.12. Tables of Numerical Values of the $9j$ Symbols /
                 360 \\
                 10.13. $12j$ Symbols / 361 \\
                 11: The Graphical Method in Angular Momentum Theory /
                 412 \\
                 11.1. Graphical Representation of Functions / 412 \\
                 11.2. Graphical Representation of the Main Operations
                 of the Theory / 419 \\
                 11.3. Rules of the Graphical Technique / 424 \\
                 11.4. Summary of the Graphical Technique / 446 \\
                 12: Sums Involving Vector Addition and Recoupling
                 Coefficients / 452 \\
                 12.1. Summation of Products of $3jm$ Symbols / 452 \\
                 12.2. Summation of Products of $6j$ and $9j$ Symbols /
                 462 \\
                 13: Matrix Elements of Irreducible Tensor Operators /
                 475 \\
                 13.1. The Wigner--Eckart Theorem and the Evaluation of
                 Matrix Elements / 475 \\
                 13.2. Matrix Elements of Basic Tensor Operators / 485
                 \\
                 Glossary of Symbols and Notation / 505 \\
                 References / 509",
}


bibtype: article
filename: elefunt.bib
label: Zaritskaya:1986:ACE
author: Z. V. Zaritskaya and A. I. Shvaui and P. E. Antonyuk
title: Approximation of certain elementary functions in the metric $ L $. (Russian)
journal: Vestnik L'vov. Politekhn. Inst.
volume: 202
pages: 38--40
year: 1986
MRclass: 149.41A10 (33A10)
MRnumber: 87j:41030
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: Z. V. Zaritskaya and A. I. Shva{\u\i} and P. {\=E}. Antonyuk
rawtitle: Approximation of certain elementary functions in the metric $ {L} $. ({Russian})
entry:
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  author =       "Z. V. Zaritskaya and A. I. Shva{\u\i} and P. {\=E}.
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  title =        "Approximation of certain elementary functions in the
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  journal =      "Vestnik L'vov. Politekhn. Inst.",
  volume =       "202",
  pages =        "38--40",
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  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",
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bibtype: article
filename: elefunt.bib
label: Agarwal:1987:CNS
journal: j-IBM-JRD
volume: 31
number: 2
pages: 274--274
month: mar
monthnumber: 3
year: 1987
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.312.0274
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 76W05
MRnumber: MR894626
bibdate: Mon Feb 12 08:07:08 2001
bibtimestamp: 2001.02.12 08:07:08 ???
note: See cite Agarwal:1986:NSV.
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
ajournal: IBM J. Res. Develop.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawnote: See \cite{Agarwal:1986:NSV}.
author:
Ramesh C. Agarwal and James W. Cooley and Fred G. Gustavson and James B. Shearer and Gordon Slishman and Bryant Tuckerman

title:
Clarification: ``New scalar and vector elementary functions for the IBM System/370'' [IBM J. Res. Develop. bf 30 (1986), no. 2, 126--144]

bibsource:
http://www.research.ibm.com/journal/; 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/ibmjrd.bib

rawtitle:
Clarification: {``New scalar and vector elementary functions for the IBM System/370''} [{IBM J. Res. Develop. {\bf 30} (1986), no. 2, 126--144}]

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  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
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  title =        "Clarification: {``New scalar and vector elementary
                 functions for the IBM System/370''} [{IBM J. Res.
                 Develop. {\bf 30} (1986), no. 2, 126--144}]",
  journal =      j-IBM-JRD,
  volume =       "31",
  number =       "2",
  pages =        "274--274",
  month =        mar,
  year =         "1987",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.312.0274",
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  MRnumber =     "MR894626",
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  bibsource =    "http://www.research.ibm.com/journal/;
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                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  note =         "See \cite{Agarwal:1986:NSV}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
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bibtype: phdthesis
filename: elefunt.bib
label: Braune:1987:HSF
author: K. Braune
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1987
bibdate: Fri Sep 16 16:30:40 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 16:30:40 ???
acknowledgement: ack-nj
rawauthor: K. Braune
title:
Hochgenaue Standardfunktionen fur reelle und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern toenglish High-Accuracy Elementary Functions for Real and Complex Points and Intervals in Arbitrary Floating-Point Systems endtoenglish 

rawtitle:
{Hochgenaue Standardfunktionen f{\"u}r reelle und komplexe Punkte und Intervalle in beliebigen Gleitpunktrastern} \toenglish {High-Accuracy Elementary Functions for Real and Complex Points and Intervals in Arbitrary Floating-Point Systems} \endtoenglish

entry:
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  author =       "K. Braune",
  title =        "{Hochgenaue Standardfunktionen f{\"u}r reelle und
                 komplexe Punkte und Intervalle in beliebigen
                 Gleitpunktrastern} \toenglish {High-Accuracy Elementary
                 Functions for Real and Complex Points and Intervals in
                 Arbitrary Floating-Point Systems} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:40 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: Buhring:1987:BUA
author: Wolfgang Buhring
title: The behavior at unit argument of the hypergeometric function $_3 F_2$
journal: j-SIAM-J-MATH-ANA
volume: 18
number: 5
pages: 1227--1234
month: sep
monthnumber: 9
year: 1987
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33A30
MRnumber: 88j:33004
MRreviewer: K. M. Saksena
bibdate: Sun Nov 28 19:24:11 MST 2010
bibtimestamp: 2010.11.28 19:24:11 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: Wolfgang B{\"u}hring
rawtitle: The behavior at unit argument of the hypergeometric function {${}_3 F_2$}
bibsource:
http://epubs.siam.org/sam-bin/dbq/toc/SIMA/18/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib

entry:
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  author =       "Wolfgang B{\"u}hring",
  title =        "The behavior at unit argument of the hypergeometric
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  MRreviewer =   "K. M. Saksena",
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  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/18/5;
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  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
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bibtype: article
filename: elefunt.bib
label: Carlson:1987:TEI
author: B. C. Carlson
title: A Table of Elliptic Integrals of the Second Kind
journal: j-MATH-COMPUT
volume: 49
number: 180
pages: 595--606, S13--S17
month: oct
monthnumber: 10
year: 1987
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65A05 (33A25 65V05)
MRnumber: 89b:65013
MRreviewer: F. W. J. Olver
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: C4160 (Numerical integration and differentiation); C7310 (Mathematics)
corpsource: Dept. of Math., Iowa State Univ., Ames, IA, USA
journalURL: http://www.ams.org/mcom/
treatment: P Practical; T Theoretical or Mathematical; X Experimental
rawauthor: B. C. Carlson
rawtitle: A Table of Elliptic Integrals of the Second Kind
keywords:
elliptic integrals of the second kind; FORTRAN listings; integration; mathematics computing; standard R-functions

entry:
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  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals of the Second Kind",
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  number =       "180",
  pages =        "595--606, S13--S17",
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  year =         "1987",
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  MRnumber =     "89b:65013",
  MRreviewer =   "F. W. J. Olver",
  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,
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  keywords =     "elliptic integrals of the second kind; FORTRAN
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  treatment =    "P Practical; T Theoretical or Mathematical; X
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}


bibtype: article
filename: elefunt.bib
label: Crandall:1987:EFE
author: R. E. Crandall and J. P. Buhler
title: Elementary function expansions for Madelung constants
journal: j-J-PHYS-A
volume: 20
number: 16
pages: 5497--5510
year: 1987
CODEN: JPHAC5
ISSN: 0305-4470 (print), 1361-6447 (electronic) OR 03054470 (print), 13616447 (electronic)
ISSNL: 0305-4470 OR 03054470
MRclass: 82A60 (82-08)
MRnumber: MR924725 (88m:82034)
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Journal of Physics. A. Mathematical and General
acknowledgement: ack-nhfb
journalURL: http://iopscience.iop.org/0305-4470
rawauthor: R. E. Crandall and J. P. Buhler
rawtitle: Elementary function expansions for {Madelung} constants
entry:
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  author =       "R. E. Crandall and J. P. Buhler",
  title =        "Elementary function expansions for {Madelung}
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  journal =      j-J-PHYS-A,
  volume =       "20",
  number =       "16",
  pages =        "5497--5510",
  year =         "1987",
  CODEN =        "JPHAC5",
  ISSN =         "0305-4470 (print), 1361-6447 (electronic)",
  ISSN-L =       "0305-4470",
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  MRnumber =     "MR924725 (88m:82034)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Physics. A. Mathematical and General",
  journal-URL =  "http://iopscience.iop.org/0305-4470",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1987:AFS
author: Armido R. DiDonato and Alfred H. Morris Jr.
journal: j-TOMS
volume: 13
number: 3
pages: 318--319
month: sep
monthnumber: 9
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/29380.214348
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sun Sep 4 21:43:08 1994
bibtimestamp: 1994.09.04 21:43:08 ???
URL: https://dl.acm.org/doi/pdf/10.1145/29380.214348
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Armido R. {DiDonato} and Alfred H. {Morris Jr.}
title:
Algorithm 654: FORTRAN Subroutines for Computing the Incomplete Gamma Function Ratios and their Inverse

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

subject:
bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. bf G.m: Mathematics of Computing, MISCELLANEOUS.

rawtitle:
{Algorithm 654}: {FORTRAN} Subroutines for Computing the Incomplete Gamma Function Ratios and their Inverse

entry:
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  author =       "Armido R. {DiDonato} and Alfred H. {Morris Jr.}",
  title =        "{Algorithm 654}: {FORTRAN} Subroutines for Computing
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                 Inverse",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "318--319",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214348",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
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  bibdate =      "Sun Sep 4 21:43:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf G.m}: Mathematics of
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}


bibtype: article
filename: elefunt.bib
label: Dunham:1987:PMAa
author: Charles B. Dunham
title: Provably monotone approximations
journal: j-SIGNUM
volume: 22
number: 2
pages: 6--11
month: apr
monthnumber: 4
year: 1987
CODEN: SNEWD6
DOI: https://doi.org/10.1145/24936.24938
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:15 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 07:50:15 MDT
fjournal: ACM SIGNUM Newsletter
keywords: theory; verification
subject: G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Charles B. Dunham
rawtitle: Provably monotone approximations
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  title =        "Provably monotone approximations",
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  number =       "2",
  pages =        "6--11",
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bibtype: article
filename: elefunt.bib
label: Dunham:1987:PMAb
author: Charles B. Dunham
title: Provably monotone approximations, II
journal: j-SIGNUM
volume: 22
number: 3
pages: 30--31
month: jul
monthnumber: 7
year: 1987
CODEN: SNEWD6
DOI: https://doi.org/10.1145/36318.36323
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:15 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 07:50:15 MDT
fjournal: ACM SIGNUM Newsletter
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acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Charles B. Dunham
rawtitle: Provably monotone approximations, {II}
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bibtype: article
filename: elefunt.bib
label: Gervais:1987:RAF
author: R. Gervais and Q. I. Rahman and G. Schmeisser
title: Representation and approximation of functions via $ (0, 2) $-interpolation
journal: j-J-APPROX-THEORY
volume: 50
number: 2
pages: 89--110
month: jun
monthnumber: 6
year: 1987
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: R. Gervais and Q. I. Rahman and G. Schmeisser
rawtitle: Representation and approximation of functions via $ (0, 2) $-interpolation
entry:
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  title =        "Representation and approximation of functions via $
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  journal =      j-J-APPROX-THEORY,
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  acknowledgement = ack-nhfb,
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  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
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  jrldate =      "June 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
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bibtype: article
filename: elefunt.bib
label: Ifantis:1987:UBF
author: E. K. Ifantis and P. D. Siafarikas and C. B. Kouris
title: Upper bounds for the first zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 17
number: 3
pages: 355--358
month: mar
monthnumber: 3
year: 1987
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 11:59:57 MST 2017
bibtimestamp: 2017.02.25 11:59:57 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042787901117
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 and C. B. Kouris
rawtitle: Upper bounds for the first zeros of {Bessel} functions
entry:
@Article{Ifantis:1987:UBF,
  author =       "E. K. Ifantis and P. D. Siafarikas and C. B. Kouris",
  title =        "Upper bounds for the first zeros of {Bessel}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "17",
  number =       "3",
  pages =        "355--358",
  month =        mar,
  year =         "1987",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:57 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042787901117",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Johnson:1987:AES
author: Kenneth C. Johnson
title: Algorithm 650: Efficient Square Root Implementation on the 68000
journal: j-TOMS
volume: 13
number: 2
pages: 138--151
month: jun
monthnumber: 6
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/328512.328520
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 65D15
MRnumber: 898 489
bibdate: Sun Sep 4 21:36:32 1994
bibtimestamp: 1994.09.04 21:36:32 ???
note: See also cite Johnson:1987:CES.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/toms
rawauthor: Kenneth C. Johnson
rawnote: See also \cite{Johnson:1987:CES}.
rawtitle: {Algorithm 650}: Efficient Square Root Implementation on the 68000
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/toms.bib

entry:
@Article{Johnson:1987:AES,
  author =       "Kenneth C. Johnson",
  title =        "{Algorithm 650}: Efficient Square Root Implementation
                 on the 68000",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328520",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "898 489",
  bibdate =      "Sun Sep 4 21:36:32 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/toms.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Johnson:1987:CES
author: Kenneth C. Johnson
journal: j-TOMS
volume: 13
number: 3
pages: 320--320
month: sep
monthnumber: 9
year: 1987
CODEN: ACMSCU
DOI: https://doi.org/10.1145/29380.356210
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
MRclass: 320. 65D15
MRnumber: 918 582
bibdate: Thu Aug 08 15:52.08 2024
bibtimestamp: 2024.08.08 15:52.08 ???
note: See cite Johnson:1987:AES.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Kenneth C. Johnson
rawnote: See \cite{Johnson:1987:AES}.
title:
Corrigendum: ``Algorithm 650: efficient square root implementation on the 68000'' [ACM Trans. Math. Software bf 13 (1987), no. 2, 138--151]

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/toms.bib

rawtitle:
Corrigendum: {``Algorithm 650: efficient square root implementation on the 68000'' [ACM Trans. Math. Software {\bf 13} (1987), no. 2, 138--151]}

entry:
@Article{Johnson:1987:CES,
  author =       "Kenneth C. Johnson",
  title =        "Corrigendum: {``Algorithm 650: efficient square root
                 implementation on the 68000'' [ACM Trans. Math.
                 Software {\bf 13} (1987), no. 2, 138--151]}",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "320--320",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.356210",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "320. 65D15",
  MRnumber =     "918 582",
  bibdate =      "Thu Aug 08 15:52.08 2024",
  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/toms.bib",
  note =         "See \cite{Johnson:1987:AES}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kahan:1987:BCC
author: W. Kahan
title: Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit
crossref: Iserles:1987:SAN
volume: 9
pages: 165--211
year: 1987
MRclass: 65E05
MRnumber: 88k:65027
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: Inst. Math. Appl. Conf. Ser. New Ser.
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawtitle: Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit
entry:
@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  crossref =     "Iserles:1987:SAN",
  volume =       "9",
  pages =        "165--211",
  year =         "1987",
  MRclass =      "65E05",
  MRnumber =     "88k:65027",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Inst. Math. Appl. Conf. Ser. New Ser.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1987:BRC
author: K. S. Kolbig
journal: j-SIAM-REVIEW
volume: 29
number: 4
pages: 660--661
year: 1987
CODEN: SIREAD
DOI: https://doi.org/10.1137/1029138
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Sat Mar 29 09:54:19 MDT 2014
bibtimestamp: 2014.03.29 09:54:19 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: December 1987
rawauthor: K. S. K{\"o}lbig
title:
Book Review: booktitle Calculation of Special Functions, the Gamma Function, the Exponential Integrals and Error-Like Functions (C. G. van der Laan and N. M. Temme)

bibsource:
http://epubs.siam.org/toc/siread/29/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

rawtitle:
Book Review: {{\booktitle{Calculation of Special Functions, the Gamma Function, the Exponential Integrals and Error-Like Functions}} (C. G. van der Laan and N. M. Temme)}

entry:
@Article{Kolbig:1987:BRC,
  author =       "K. S. K{\"o}lbig",
  title =        "Book Review: {{\booktitle{Calculation of Special
                 Functions, the Gamma Function, the Exponential
                 Integrals and Error-Like Functions}} (C. G. van der
                 Laan and N. M. Temme)}",
  journal =      j-SIAM-REVIEW,
  volume =       "29",
  number =       "4",
  pages =        "660--661",
  month =        "????",
  year =         "1987",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1029138",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:54:19 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/29/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1987",
}


bibtype: phdthesis
filename: elefunt.bib
label: Kramer:1987:ISR
author: W. Kramer
type: Dissertation
school: Universitat Karlsruhe
address: Karlsruhe, Germany
year: 1987
bibdate: Fri Sep 16 16:30:41 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 16:30:41 ???
acknowledgement: ack-nj
authordates: 1952--2014 (WK)
rawauthor: W. Kr{\"a}mer
title:
Inverse Standardfunktionen fur reelle und komplexe Intervallargumente mit a priori Fehlerabschatzungen fur beliebige Datenformate toenglish Inverse Elementary Functions for Real and Complex Interval Arguments with A-Priori Error Estimates for Arbitrary Data Formats endtoenglish 

rawtitle:
Inverse Standardfunktionen f{\"u}r reelle und komplexe Intervallargumente mit a priori Fehlerabsch{\"a}tzungen f{\"u}r beliebige Datenformate \toenglish {Inverse Elementary Functions for Real and Complex Interval Arguments with A-Priori Error Estimates for Arbitrary Data Formats} \endtoenglish

entry:
@PhdThesis{Kramer:1987:ISR,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse Standardfunktionen f{\"u}r reelle und komplexe
                 Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
                 f{\"u}r beliebige Datenformate \toenglish {Inverse
                 Elementary Functions for Real and Complex Interval
                 Arguments with A-Priori Error Estimates for Arbitrary
                 Data Formats} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  author-dates = "1952--2014 (WK)",
}


bibtype: article
filename: elefunt.bib
label: Lewanowicz:1987:CRR
author: Stanislaw Lewanowicz
journal: j-MATH-COMPUT
volume: 48
number: 178
pages: 853--853
month: apr
monthnumber: 4
year: 1987
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A35 (65Q05)
MRnumber: 88a:33013
bibdate: Wed Jan 15 09:19:34 1997
bibtimestamp: 1997.01.15 09:19:34 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Stanis{\l}aw Lewanowicz
title:
Corrigendum: ``Recurrence relations for hypergeometric functions of unit argument'' [Math. Comp. bf 45 (1985), no. 172, 521--535, MR 86m:33004]

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib

rawtitle:
Corrigendum: {``Recurrence relations for hypergeometric functions of unit argument''} {[Math. Comp. {\bf 45} (1985), no. 172, 521--535, MR 86m:33004]}

entry:
@Article{Lewanowicz:1987:CRR,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "Corrigendum: {``Recurrence relations for
                 hypergeometric functions of unit argument''} {[Math.
                 Comp. {\bf 45} (1985), no. 172, 521--535, MR
                 86m:33004]}",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "178",
  pages =        "853--853",
  month =        apr,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A35 (65Q05)",
  MRnumber =     "88a:33013",
  bibdate =      "Wed Jan 15 09:19:34 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: mastersthesis
filename: elefunt.bib
label: Liu:1987:BEF
author: Z. A. Liu
title: Berkeley Elementary Function Test Suite
type: M.S. thesis
address: Berkeley, CA, USA
pages: 853--853
month: dec
monthnumber: 12
year: 1987
bibdate: Mon Sep 12 23:52:34 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.12 23:52:34 ???
acknowledgement: ack-nj
rawauthor: Z. A. Liu
rawtitle: {Berkeley} Elementary Function Test Suite
school:
Computer Science Division, Department of Electrical Engineering and Computer Science, Univerity of California at Berkeley

entry:
@MastersThesis{Liu:1987:BEF,
  author =       "Z. A. Liu",
  title =        "{Berkeley} Elementary Function Test Suite",
  type =         "{M.S.} thesis",
  school =       "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Lo:1987:HGA
author: Hao-Yung Lo and Jau-Ling Chen
title: A Hardwired Generalized Algorithm for Generating the Logarithm Base-$k$ by Iteration
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 11
pages: 1363--1367
month: nov
monthnumber: 11
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009477
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:57 MDT 2011
bibtimestamp: 2011.07.09 09:28:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009477
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nj
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Hao-Yung Lo and Jau-Ling Chen
rawtitle: A Hardwired Generalized Algorithm for Generating the Logarithm Base-$k$ by Iteration
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Lo:1987:HGA,
  author =       "Hao-Yung Lo and Jau-Ling Chen",
  title =        "A Hardwired Generalized Algorithm for Generating the
                 Logarithm Base-$k$ by Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1363--1367",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009477",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009477",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: elefunt.bib
label: Mathis:1987:EFP
author: Robert F. Mathis
title: Elementary Functions Package for Ada
crossref: ACM:1987:UAA
pages: 95--100
month: dec
monthnumber: 12
year: 1987
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
acknowledgement: ack-nhfb
rawauthor: Robert F. Mathis
rawtitle: Elementary Functions Package for {Ada}
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Mathis:1987:EFP,
  author =       "Robert F. Mathis",
  title =        "Elementary Functions Package for {Ada}",
  crossref =     "ACM:1987:UAA",
  pages =        "95--100",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Moricz:1987:ACF
author: Ferenc Moricz and Xianliang Shi
title: Approximation to continuous functions by Cesaro means of double Fourier series and conjugate series
journal: j-J-APPROX-THEORY
volume: 49
number: 4
pages: 346--377
month: apr
monthnumber: 4
year: 1987
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: Ferenc Moricz and Xianliang Shi
rawtitle:
Approximation to continuous functions by {Cesaro} means of double {Fourier} series and conjugate series

entry:
@Article{Moricz:1987:ACF,
  author =       "Ferenc Moricz and Xianliang Shi",
  title =        "Approximation to continuous functions by {Cesaro}
                 means of double {Fourier} series and conjugate series",
  journal =      j-J-APPROX-THEORY,
  volume =       "49",
  number =       "4",
  pages =        "346--377",
  month =        apr,
  year =         "1987",
  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 =        "30744",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Least squares
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09224",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Musielak:1987:AEG
author: J. Musielak
title: Approximation of elements of a generalized Orlicz sequence space by nonlinear, singular kernels
journal: j-J-APPROX-THEORY
volume: 50
number: 4
pages: 366--372
month: aug
monthnumber: 8
year: 1987
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. Musielak
rawtitle: Approximation of elements of a generalized {Orlicz} sequence space by nonlinear, singular kernels
subject:
G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Musielak:1987:AEG,
  author =       "J. Musielak",
  title =        "Approximation of elements of a generalized {Orlicz}
                 sequence space by nonlinear, singular kernels",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "4",
  pages =        "366--372",
  month =        aug,
  year =         "1987",
  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 =        "30716",
  catcode =      "G.2.1; G.1.5; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.5
                 Roots of Nonlinear Equations; G.1.5 Convergence; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Convergence; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09257",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Aug. 1987",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Pereira:1987:CEC
author: N. Costa Pereira
journal: j-MATH-COMPUT
volume: 48
number: 177
pages: 447--447
month: jan
monthnumber: 1
year: 1987
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11A25 (11N45 11Y35 33A70)
MRnumber: 87k:11006
bibdate: Thu Jun 15 07:27:03 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.06.15 07:27:03 ???
note: See cite Pereira:1985:ECF.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: N. Costa Pereira
rawnote: See \cite{Pereira:1985:ECF}.
title:
Corrigendum: ``Estimates for the Chebyshev function $ psi (x) - theta (x) $'' [Math. Comp. bf 44 (1985), no. 169, 211--221, MR 86k:11005]

rawtitle:
Corrigendum: {``Estimates for the Chebyshev function $ \psi (x) - \theta (x) $''} {[Math. Comp. {\bf 44} (1985), no. 169, 211--221, MR 86k:11005]}

entry:
@Article{Pereira:1987:CEC,
  author =       "N. Costa Pereira",
  title =        "Corrigendum: {``Estimates for the Chebyshev function $
                 \psi (x) - \theta (x) $''} {[Math. Comp. {\bf 44}
                 (1985), no. 169, 211--221, MR 86k:11005]}",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "177",
  pages =        "447--447",
  month =        jan,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11A25 (11N45 11Y35 33A70)",
  MRnumber =     "87k:11006",
  bibdate =      "Thu Jun 15 07:27:03 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Pereira:1985:ECF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Proinov:1987:NIA
author: Petko D. Proinov
title: Numerical integration and approximation of differentiable functions, II
journal: j-J-APPROX-THEORY
volume: 50
number: 4
pages: 373--393
month: aug
monthnumber: 8
year: 1987
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: Petko D. Proinov
rawtitle: Numerical integration and approximation of differentiable functions, {II}
entry:
@Article{Proinov:1987:NIA,
  author =       "Petko D. Proinov",
  title =        "Numerical integration and approximation of
                 differentiable functions, {II}",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "4",
  pages =        "373--393",
  month =        aug,
  year =         "1987",
  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 =        "30717",
  catcode =      "G.1.4; G.1.2",
  CRclass =      "G.1.4 Quadrature and Numerical Differentiation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09258",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Aug. 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Rolfe:1987:FIS
author: Timothy J. Rolfe
title: On a Fast Integer Square Root Algorithm
journal: j-SIGNUM
volume: 22
number: 4
pages: 6--11
month: oct
monthnumber: 10
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:16 MDT 2005
bibtimestamp: 2005.04.12 07:50:16 MDT
fjournal: ACM SIGNUM Newsletter
keywords: algorithms; performance; theory
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/signum
rawauthor: Timothy J. Rolfe
rawtitle: On a Fast Integer Square Root Algorithm
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/signum.bib

subject:
F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Number-theoretic computations

entry:
@Article{Rolfe:1987:FIS,
  author =       "Timothy J. Rolfe",
  title =        "On a Fast Integer Square Root Algorithm",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "4",
  pages =        "6--11",
  month =        oct,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  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/signum.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "algorithms; performance; theory",
  subject =      "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations",
}


bibtype: article
filename: elefunt.bib
label: Smith:1987:BAM
author: P. W. Smith and J. J. Swetits
title: Best approximation by monotone functions
journal: j-J-APPROX-THEORY
volume: 49
number: 4
pages: 398--403
month: apr
monthnumber: 4
year: 1987
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: P. W. Smith and J. J. Swetits
rawtitle: Best approximation by monotone functions
entry:
@Article{Smith:1987:BAM,
  author =       "P. W. Smith and J. J. Swetits",
  title =        "Best approximation by monotone functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "49",
  number =       "4",
  pages =        "398--403",
  month =        apr,
  year =         "1987",
  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 =        "30747",
  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 =      "theory; verification",
  guideno =      "1987-09227",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: book
filename: elefunt.bib
label: Spanier:1987:AF
author: Jerome Spanier and Keith B. Oldham
title: An Atlas of Functions
publisher: pub-HEMISPHERE
address: pub-HEMISPHERE:adr
pages: ix + 700
year: 1987
ISBN: 0-89116-573-8, 3-540-17395-1 OR 0891165738, 3540173951
ISBN13: 978-0-89116-573-6, 978-3-540-17395-3 OR 9780891165736, 9783540173953
LCCN: QA331 .S685 1987
bibdate: Fri Aug 31 16:20:13 MDT 2007
bibtimestamp: 2007.08.31 16:20:13 MDT
note: See also the second edition cite Oldham:2009:AF.
acknowledgement: ack-nhfb
rawauthor: Jerome Spanier and Keith B. Oldham
rawnote: See also the second edition \cite{Oldham:2009:AF}.
rawtitle: An Atlas of Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/canjstat.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

subject:
elementary functions; special functions; cognate functions; complementary incomplete gamma function; complementary modulus; complete beta function; complex argument when; cosecant functions; cotangent functions; digamma function; economized polynomial; error function complement; eta numbers; function and its reciprocal; hypergeometric algorithm; important definite integrals; incomplete elliptic integrals; inverse gudermannian function; inverse hyperbolic functions; negative integer order; other definite integrals; parabolic cylinder function; polygamma functions; purely imaginary argument; reciprocal linear function; reflection formula

TOC:
Preface / ix 0 General Considerations / 1 1 The Constant Function $c$ / 11 2 The Factorial Function $n!$ and Its Reciprocal / 19 3 The Zeta Numbers and Related Functions / 25 4 The Bernoulli Numbers, $B_n$ / 35 5 The Euler Numbers, $E_n$ / 39 6 The Binomial Coefficients $binom nu m$ / 43 7 The Linear Function $b x + c$ and Its Reciprocal / 53 8 The Unit-Step $u(x - a)$ and Related Functions / 63 9 The Integer-Value $tt Int(x)$ and Fractional-Value $tt frac(x)$ Functions / 71 10 The Dirac Delta Function $delta (x - a)$ / 79 11 The Integer Powers $(bx + c)^n$ and $x^n$ / 83 12 The Square-Root Function $sqrt b x + c$ and Its Reciprocal / 91 13 The Noninteger Powers $x^nu $ / 99 14 The $b sqrt a^2 - x^2$ Function and Its Reciprocal / 107 15 The $b sqrt x^2 + a$ Function and Its Reciprocal / 115 16 The Quadratic Function $a x^2 + b x + c$ and Its Reciprocal / 123 17 The Cubic Function $x^3 + a x^2 + b x + c$ and Higher Polynomials / 131 18 The Pochhammer Polynomials $(x)_n$ / 149 19 The Bernoulli Polynomials $B_n(x)$ / 167 20 The Euler Polynomials $E_n(x)$ / 175 21 The Legendre Polynomials $P_n(x)$ / 183 22 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 193 23 The Laguerre Polynomials $L_n(x)$ / 209 24 The Hermite Polynomials $H_n(x)$ / 217 25 The Logarithmic Function $ln (x)$ / 225 26 The Exponential Function $exp (b x + c)$ / 233 27 Exponentials of Powers $exp (-a x^nu )$ / 253 28 The Hyperbolic Sine $sinh (x)$ and Cosine $cosh (x)$ Functions / 263 29 The Hyperbolic Secant $sech (x)$ and Cosecant $csch (x)$ Functions / 273 30 The Hyperbolic Tangent $tanh (x)$ and Cotangent $coth (x)$ Functions / 279 31 The Inverse Hyperbolic Functions / 285 32 The Sine $sin (x)$ and Cosine $cos (x)$ Functions / 295 33 The Secant $sec (x)$ and Cosecant $csc (x)$ Functions / 311 34 The Tangent $tan (x)$ and Cotangent $cot (x)$ Functions / 319 35 The Inverse Trigonometric Functions / 331 36 Periodic Functions / 343 37 The Exponential Integral $Ei (x)$ and Related Functions / 351 38 Sine and Cosine Integrals / 361 39 The Fresnel Integrals $S(x)$ and $C(x)$ / 373 40 The Error Function $erf (x)$ and Its Complement $erfc (x)$ / 385 41 The $exp (x) erfc (sqrt x)$ and Related Functions / 395 42 Dawson's Integral / 405 43 The Gamma Function $Gamma (x)$ / 411 44 The Digamma Function $psi (x)$ / 423 45 The Incomplete Gamma $gamma (nu ,x)$ and Related Functions / 435 46 The Parabolic Cylinder Function $D_nu (x)$ / 445 47 The Kummer Function $M(a; c; x)$ / 459 48 The Tricomi Function $U(a; c; x)$ 471 49 The Hyperbolic Bessel Functions $I_0(x)$ and $I_1(x)$ / 479 50 The General Hyperbolic Bessel Function $I_nu (x)$ / 489 51 The Basset Function $K_nu (x)$ / 499 52 The Bessel Coefficients $J_0(x)$ and $J_1(x)$ / 509 53 The Bessel Function $J_nu (x)$ / 521 54 The Neumann Function $Y_nu (x)$ / 533 55 The Kelvin Functions / 543 56 The Airy Functions $Ai (x)$ and $Bi (x)$ / 555 57 The Struve Function / 563 58 The Incomplete Beta Function $B(nu ; mu ; x)$ / 573 59 The Legendre Functions $P_nu (x)$ and $Q_nu (x)$ / 581 60 The Gauss Function $F(a, b; c; x)$ / 599 61 The Complete Elliptic Integrals $K(p)$ and $E(p)$ / 609 62 The Incomplete Elliptic Integrals $F(p; phi )$ and $E(p; phi )$ / 621 63 The Jacobian Elliptic Functions / 635 64 The Hurwitz Function $zeta (nu ; u)$ / 653 Appendix A Utility Algorithms / 665 Appendix B Some Useful Data / 673 References and Bibliography / 679 Subject Index / 681 Symbol Index / 691

rawTOC:
Preface / ix \\ 0 General Considerations / 1 \\ 1 The Constant Function $c$ / 11 \\ 2 The Factorial Function $n!$ and Its Reciprocal / 19 \\ 3 The Zeta Numbers and Related Functions / 25 \\ 4 The Bernoulli Numbers, $B_n$ / 35 \\ 5 The Euler Numbers, $E_n$ / 39 \\ 6 The Binomial Coefficients $\binom{\nu}{m}$ / 43 \\ 7 The Linear Function $b x + c$ and Its Reciprocal / 53 \\ 8 The Unit-Step $u(x - a)$ and Related Functions / 63 \\ 9 The Integer-Value ${\tt Int}(x)$ and Fractional-Value ${\tt frac}(x)$ Functions / 71 \\ 10 The Dirac Delta Function $\delta(x - a)$ / 79 \\ 11 The Integer Powers $(bx + c)^n$ and $x^n$ / 83 \\ 12 The Square-Root Function $\sqrt{b x + c}$ and Its Reciprocal / 91 \\ 13 The Noninteger Powers $x^\nu$ / 99 \\ 14 The $b \sqrt{a^2 - x^2}$ Function and Its Reciprocal / 107 \\ 15 The $b \sqrt{x^2 + a}$ Function and Its Reciprocal / 115 \\ 16 The Quadratic Function $a x^2 + b x + c$ and Its Reciprocal / 123 \\ 17 The Cubic Function $x^3 + a x^2 + b x + c$ and Higher Polynomials / 131 \\ 18 The Pochhammer Polynomials $(x)_n$ / 149 \\ 19 The Bernoulli Polynomials $B_n(x)$ / 167 \\ 20 The Euler Polynomials $E_n(x)$ / 175 \\ 21 The Legendre Polynomials $P_n(x)$ / 183 \\ 22 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ / 193 \\ 23 The Laguerre Polynomials $L_n(x)$ / 209 \\ 24 The Hermite Polynomials $H_n(x)$ / 217 \\ 25 The Logarithmic Function $\ln(x)$ / 225 \\ 26 The Exponential Function $\exp(b x + c)$ / 233 \\ 27 Exponentials of Powers $\exp(-a x^\nu)$ / 253 \\ 28 The Hyperbolic Sine $\sinh(x)$ and Cosine $\cosh(x)$ Functions / 263 \\ 29 The Hyperbolic Secant $\sech(x)$ and Cosecant $\csch(x)$ Functions / 273 \\ 30 The Hyperbolic Tangent $\tanh(x)$ and Cotangent $\coth(x)$ Functions / 279 \\ 31 The Inverse Hyperbolic Functions / 285 \\ 32 The Sine $\sin(x)$ and Cosine $\cos(x)$ Functions / 295 \\ 33 The Secant $\sec(x)$ and Cosecant $\csc(x)$ Functions / 311 \\ 34 The Tangent $\tan(x)$ and Cotangent $\cot(x)$ Functions / 319 \\ 35 The Inverse Trigonometric Functions / 331 \\ 36 Periodic Functions / 343 \\ 37 The Exponential Integral $\Ei(x)$ and Related Functions / 351 \\ 38 Sine and Cosine Integrals / 361 \\ 39 The Fresnel Integrals $S(x)$ and $C(x)$ / 373 \\ 40 The Error Function $\erf(x)$ and Its Complement $\erfc(x)$ / 385 \\ 41 The $\exp(x) \erfc(\sqrt{x})$ and Related Functions / 395 \\ 42 Dawson's Integral / 405 \\ 43 The Gamma Function $\Gamma(x)$ / 411 \\ 44 The Digamma Function $\psi(x)$ / 423 \\ 45 The Incomplete Gamma $\gamma(\nu,x)$ and Related Functions / 435 \\ 46 The Parabolic Cylinder Function $D_\nu(x)$ / 445 \\ 47 The Kummer Function $M(a; c; x)$ / 459 \\ 48 The Tricomi Function $U(a; c; x)$ 471 \\ 49 The Hyperbolic Bessel Functions $I_0(x)$ and $I_1(x)$ / 479 \\ 50 The General Hyperbolic Bessel Function $I_\nu(x)$ / 489 \\ 51 The Basset Function $K_\nu(x)$ / 499 \\ 52 The Bessel Coefficients $J_0(x)$ and $J_1(x)$ / 509 \\ 53 The Bessel Function $J_\nu(x)$ / 521 \\ 54 The Neumann Function $Y_\nu(x)$ / 533 \\ 55 The Kelvin Functions / 543 \\ 56 The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 555 \\ 57 The Struve Function / 563 \\ 58 The Incomplete Beta Function $B(\nu; \mu; x)$ / 573 \\ 59 The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ / 581 \\ 60 The Gauss Function $F(a, b; c; x)$ / 599 \\ 61 The Complete Elliptic Integrals $K(p)$ and $E(p)$ / 609 \\ 62 The Incomplete Elliptic Integrals $F(p; \phi)$ and $E(p; \phi)$ / 621 \\ 63 The Jacobian Elliptic Functions / 635 \\ 64 The Hurwitz Function $\zeta(\nu; u)$ / 653 \\ Appendix A Utility Algorithms / 665 \\ Appendix B Some Useful Data / 673 \\ References and Bibliography / 679 \\ Subject Index / 681 \\ Symbol Index / 691

entry:
@Book{Spanier:1987:AF,
  author =       "Jerome Spanier and Keith B. Oldham",
  title =        "An Atlas of Functions",
  publisher =    pub-HEMISPHERE,
  address =      pub-HEMISPHERE:adr,
  pages =        "ix + 700",
  year =         "1987",
  ISBN =         "0-89116-573-8, 3-540-17395-1",
  ISBN-13 =      "978-0-89116-573-6, 978-3-540-17395-3",
  LCCN =         "QA331 .S685 1987",
  bibdate =      "Fri Aug 31 16:20:13 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/canjstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "See also the second edition \cite{Oldham:2009:AF}.",
  acknowledgement = ack-nhfb,
  subject =      "elementary functions; special functions; cognate
                 functions; complementary incomplete gamma function;
                 complementary modulus; complete beta function; complex
                 argument when; cosecant functions; cotangent functions;
                 digamma function; economized polynomial; error function
                 complement; eta numbers; function and its reciprocal;
                 hypergeometric algorithm; important definite integrals;
                 incomplete elliptic integrals; inverse gudermannian
                 function; inverse hyperbolic functions; negative
                 integer order; other definite integrals; parabolic
                 cylinder function; polygamma functions; purely
                 imaginary argument; reciprocal linear function;
                 reflection formula",
  tableofcontents = "Preface / ix \\
                 0 General Considerations / 1 \\
                 1 The Constant Function $c$ / 11 \\
                 2 The Factorial Function $n!$ and Its Reciprocal / 19
                 \\
                 3 The Zeta Numbers and Related Functions / 25 \\
                 4 The Bernoulli Numbers, $B_n$ / 35 \\
                 5 The Euler Numbers, $E_n$ / 39 \\
                 6 The Binomial Coefficients $\binom{\nu}{m}$ / 43 \\
                 7 The Linear Function $b x + c$ and Its Reciprocal / 53
                 \\
                 8 The Unit-Step $u(x - a)$ and Related Functions / 63
                 \\
                 9 The Integer-Value ${\tt Int}(x)$ and Fractional-Value
                 ${\tt frac}(x)$ Functions / 71 \\
                 10 The Dirac Delta Function $\delta(x - a)$ / 79 \\
                 11 The Integer Powers $(bx + c)^n$ and $x^n$ / 83 \\
                 12 The Square-Root Function $\sqrt{b x + c}$ and Its
                 Reciprocal / 91 \\
                 13 The Noninteger Powers $x^\nu$ / 99 \\
                 14 The $b \sqrt{a^2 - x^2}$ Function and Its Reciprocal
                 / 107 \\
                 15 The $b \sqrt{x^2 + a}$ Function and Its Reciprocal /
                 115 \\
                 16 The Quadratic Function $a x^2 + b x + c$ and Its
                 Reciprocal / 123 \\
                 17 The Cubic Function $x^3 + a x^2 + b x + c$ and
                 Higher Polynomials / 131 \\
                 18 The Pochhammer Polynomials $(x)_n$ / 149 \\
                 19 The Bernoulli Polynomials $B_n(x)$ / 167 \\
                 20 The Euler Polynomials $E_n(x)$ / 175 \\
                 21 The Legendre Polynomials $P_n(x)$ / 183 \\
                 22 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 193 \\
                 23 The Laguerre Polynomials $L_n(x)$ / 209 \\
                 24 The Hermite Polynomials $H_n(x)$ / 217 \\
                 25 The Logarithmic Function $\ln(x)$ / 225 \\
                 26 The Exponential Function $\exp(b x + c)$ / 233 \\
                 27 Exponentials of Powers $\exp(-a x^\nu)$ / 253 \\
                 28 The Hyperbolic Sine $\sinh(x)$ and Cosine $\cosh(x)$
                 Functions / 263 \\
                 29 The Hyperbolic Secant $\sech(x)$ and Cosecant
                 $\csch(x)$ Functions / 273 \\
                 30 The Hyperbolic Tangent $\tanh(x)$ and Cotangent
                 $\coth(x)$ Functions / 279 \\
                 31 The Inverse Hyperbolic Functions / 285 \\
                 32 The Sine $\sin(x)$ and Cosine $\cos(x)$ Functions /
                 295 \\
                 33 The Secant $\sec(x)$ and Cosecant $\csc(x)$
                 Functions / 311 \\
                 34 The Tangent $\tan(x)$ and Cotangent $\cot(x)$
                 Functions / 319 \\
                 35 The Inverse Trigonometric Functions / 331 \\
                 36 Periodic Functions / 343 \\
                 37 The Exponential Integral $\Ei(x)$ and Related
                 Functions / 351 \\
                 38 Sine and Cosine Integrals / 361 \\
                 39 The Fresnel Integrals $S(x)$ and $C(x)$ / 373 \\
                 40 The Error Function $\erf(x)$ and Its Complement
                 $\erfc(x)$ / 385 \\
                 41 The $\exp(x) \erfc(\sqrt{x})$ and Related Functions
                 / 395 \\
                 42 Dawson's Integral / 405 \\
                 43 The Gamma Function $\Gamma(x)$ / 411 \\
                 44 The Digamma Function $\psi(x)$ / 423 \\
                 45 The Incomplete Gamma $\gamma(\nu,x)$ and Related
                 Functions / 435 \\
                 46 The Parabolic Cylinder Function $D_\nu(x)$ / 445 \\
                 47 The Kummer Function $M(a; c; x)$ / 459 \\
                 48 The Tricomi Function $U(a; c; x)$ 471 \\
                 49 The Hyperbolic Bessel Functions $I_0(x)$ and
                 $I_1(x)$ / 479 \\
                 50 The General Hyperbolic Bessel Function $I_\nu(x)$ /
                 489 \\
                 51 The Basset Function $K_\nu(x)$ / 499 \\
                 52 The Bessel Coefficients $J_0(x)$ and $J_1(x)$ / 509
                 \\
                 53 The Bessel Function $J_\nu(x)$ / 521 \\
                 54 The Neumann Function $Y_\nu(x)$ / 533 \\
                 55 The Kelvin Functions / 543 \\
                 56 The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 555 \\
                 57 The Struve Function / 563 \\
                 58 The Incomplete Beta Function $B(\nu; \mu; x)$ / 573
                 \\
                 59 The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ /
                 581 \\
                 60 The Gauss Function $F(a, b; c; x)$ / 599 \\
                 61 The Complete Elliptic Integrals $K(p)$ and $E(p)$ /
                 609 \\
                 62 The Incomplete Elliptic Integrals $F(p; \phi)$ and
                 $E(p; \phi)$ / 621 \\
                 63 The Jacobian Elliptic Functions / 635 \\
                 64 The Hurwitz Function $\zeta(\nu; u)$ / 653 \\
                 Appendix A Utility Algorithms / 665 \\
                 Appendix B Some Useful Data / 673 \\
                 References and Bibliography / 679 \\
                 Subject Index / 681 \\
                 Symbol Index / 691",
}


bibtype: article
filename: elefunt.bib
label: Stoyanov:1987:AE
author: Basil J. Stoyanov and Richard A. Farrell
title: On the Asymptotic Evaluation of $ int ^pi / 2_0 J^2_0 (gamma sin x) d x $
journal: j-MATH-COMPUT
volume: 49
number: 179
pages: 275--279
month: jul
monthnumber: 7
year: 1987
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 41A60 (65D30)
MRnumber: 88e:41067
MRreviewer: Roderick Wong
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: C1120 (Analysis); C4180 (Integral equations)
corpsource: Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: Basil J. Stoyanov and Richard A. Farrell
rawtitle: On the Asymptotic Evaluation of $ \int^{\pi / 2}_0 {J}^2_0 (\gamma \sin x) d x $
keywords:
analytical expression; asymptotic behavior; asymptotic evaluation; Bessel functions; first kind; integral; integral equations; order Bessel function; positive parameter; zeroth-

entry:
@Article{Stoyanov:1987:AE,
  author =       "Basil J. Stoyanov and Richard A. Farrell",
  title =        "On the Asymptotic Evaluation of $ \int^{\pi / 2}_0
                 {J}^2_0 (\gamma \sin x) d x $",
  journal =      j-MATH-COMPUT,
  volume =       "49",
  number =       "179",
  pages =        "275--279",
  month =        jul,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A60 (65D30)",
  MRnumber =     "88e:41067",
  MRreviewer =   "Roderick Wong",
  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 =   "C1120 (Analysis); C4180 (Integral equations)",
  corpsource =   "Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analytical expression; asymptotic behavior; asymptotic
                 evaluation; Bessel functions; first kind; integral;
                 integral equations; order Bessel function; positive
                 parameter; zeroth-",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tanese:1987:PGA
author: Reiko Tanese
editor: John J. Grefenstette
title: Parallel genetic algorithms for a hypercube
publisher: pub-ERLBAUM
address: pub-ERLBAUM:adr
pages: 177--183
year: 1987
ISBN: 0-8058-0158-8, 0-8058-0159-6 (paperback) OR 0805801588, 0805801596 (paperback)
ISBN13: 978-0-8058-0158-3, 978-0-8058-0159-0 (paperback) OR 9780805801583, 9780805801590 (paperback)
LCCN: Q334 .I5561 1987
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: 260
rawauthor: Reiko Tanese
raweditor: John J. Grefenstette
rawtitle: Parallel genetic algorithms for a hypercube
booktitle:
Genetic algorithms and their applications: proceedings of the second International Conference on Genetic Algorithms: July 28--31, 1987 at the Massachusetts Institute of Technology, Cambridge, MA

subject:
I. Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C. Computer Systems Organization; C.1 PROCESSOR ARCHITECTURES

rawbooktitle:
Genetic algorithms and their applications: proceedings of the second International Conference on Genetic Algorithms: July 28--31, 1987 at the Massachusetts Institute of Technology, Cambridge, {MA}

entry:
@InProceedings{Tanese:1987:PGA,
  author =       "Reiko Tanese",
  editor =       "John J. Grefenstette",
  booktitle =    "Genetic algorithms and their applications: proceedings
                 of the second International Conference on Genetic
                 Algorithms: July 28--31, 1987 at the Massachusetts
                 Institute of Technology, Cambridge, {MA}",
  title =        "Parallel genetic algorithms for a hypercube",
  publisher =    pub-ERLBAUM,
  address =      pub-ERLBAUM:adr,
  bookpages =    "260",
  pages =        "177--183",
  year =         "1987",
  ISBN =         "0-8058-0158-8, 0-8058-0159-6 (paperback)",
  ISBN-13 =      "978-0-8058-0158-3, 978-0-8058-0159-0 (paperback)",
  LCCN =         "Q334 .I5561 1987",
  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\$39.95",
  acknowledgement = ack-nhfb,
  bibno =        "42536",
  catcode =      "I.2.6; G.1.0; G.1.2; C.1.2",
  CRclass =      "I.2.6 Learning; I.2.6 Analogies; G.1.0 General; G.1.0
                 Parallel algorithms; G.1.2 Approximation; G.1.2
                 Elementary function approximation; C.1.2 Multiple Data
                 Stream Architectures (Multiprocessors); C.1.2 Parallel
                 processors",
  descriptor =   "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Learning, Analogies; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Parallel processors",
  genterm =      "algorithms; performance; experimentation",
  guideno =      "1988-16888",
  procdate =     "Sponsored by Amer. Assoc. for AI, Naval Res. Lab. and
                 Bolt Beranek & Newman, July 28-31, 1987",
  procloc =      "Cambridge, MA",
  subject =      "I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; C. Computer Systems Organization;
                 C.1 PROCESSOR ARCHITECTURES",
}


bibtype: incollection
filename: elefunt.bib
label: Temme:1987:CIG
author: N. M. Temme
title: On the computation of the incomplete gamma functions for large values of the parameters
crossref: Mason:1987:AAB
pages: 479--489
year: 1987
bibdate: Fri Oct 18 16:42:44 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.10.18 16:42:44 ???
acknowledgement: ack-nhfb
rawauthor: N. M. Temme
rawtitle: On the computation of the incomplete gamma functions for large values of the parameters
entry:
@InCollection{Temme:1987:CIG,
  author =       "N. M. Temme",
  title =        "On the computation of the incomplete gamma functions
                 for large values of the parameters",
  crossref =     "Mason:1987:AAB",
  pages =        "479--489",
  year =         "1987",
  bibdate =      "Fri Oct 18 16:42:44 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Thompson:1987:IEF
author: Peter Thompson
title: Implementing an Elementary Function Library
journal: j-SIGNUM
volume: 22
number: 2
pages: 2--5
month: apr
monthnumber: 4
year: 1987
CODEN: SNEWD6
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Fri Nov 8 18:01:57 MST 2002
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: ACM SIGNUM Newsletter
subject: G. Mathematics of Computing; G.m MISCELLANEOUS; D. Software; D.3 PROGRAMMING LANGUAGES
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Peter Thompson
rawtitle: Implementing an Elementary Function Library
bibsource:
ACM Computing Archive CD-ROM database (1991); garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Thompson:1987:IEF,
  author =       "Peter Thompson",
  title =        "Implementing an Elementary Function Library",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "2--5",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  bibno =        "24937",
  catcode =      "G.m; D.3.2",
  CRclass =      "D.3.2 Language Classifications; D.3.2 OCCAM",
  descriptor =   "Mathematics of Computing, MISCELLANEOUS; Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 OCCAM",
  fjournal =     "ACM SIGNUM Newsletter",
  genterm =      "theory; languages",
  guideno =      "1987-03363",
  journal-URL =  "https://dl.acm.org/loi/signum",
  journalabbrev = "SIGNUM Newsl.",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.m MISCELLANEOUS; D.
                 Software; D.3 PROGRAMMING LANGUAGES",
}


bibtype: article
filename: elefunt.bib
label: Thompson:1987:MBF
author: I. J. Thompson and A. R. Barnett
journal: j-COMP-PHYS-COMM
volume: 47
number: 2--3
pages: 245--257
month: nov
monthnumber: 11
year: 1987
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(87)90111-1
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 10:28:21 MST 2012
bibtimestamp: 2012.02.13 10:28:21 MST
note: See erratum cite Thompson:2004:EBB.
URL: http://www.sciencedirect.com/science/article/pii/0010465587901111
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: I. J. Thompson and A. R. Barnett
rawnote: See erratum \cite{Thompson:2004:EBB}.
title:
Modified Bessel functions $ I_nu (z) $ and $ K_nu (z) $ of real order and complex argument, to selected accuracy

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Modified {Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $} of real order and complex argument, to selected accuracy

entry:
@Article{Thompson:1987:MBF,
  author =       "I. J. Thompson and A. R. Barnett",
  title =        "Modified {Bessel} functions {$ I_\nu (z) $} and {$
                 K_\nu (z) $} of real order and complex argument, to
                 selected accuracy",
  journal =      j-COMP-PHYS-COMM,
  volume =       "47",
  number =       "2--3",
  pages =        "245--257",
  month =        nov # "\slash " # dec,
  year =         "1987",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(87)90111-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Thompson:2004:EBB}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465587901111",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Timan:1987:DFP
author: A. F. Timan
journal: j-J-APPROX-THEORY
volume: 50
number: 2
pages: 167--174
month: jun
monthnumber: 6
year: 1987
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. F. Timan
title:
Distribution of fractional parts and approximation of functions with singularities by Bernstein polynomials

rawtitle:
Distribution of fractional parts and approximation of functions with singularities by {Bernstein} polynomials

entry:
@Article{Timan:1987:DFP,
  author =       "A. F. Timan",
  title =        "Distribution of fractional parts and approximation of
                 functions with singularities by {Bernstein}
                 polynomials",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "2",
  pages =        "167--174",
  month =        jun,
  year =         "1987",
  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 =        "30725",
  catcode =      "G.1.5; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.5 Polynomials,
                 methods for; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Polynomials, methods for;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09244",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Visentin:1987:FAE
author: Kley Visentin and Pablo Martin
title: Fractional approximation to elliptic functions
journal: j-J-MATH-PHYS
volume: 28
number: 2
pages: 330--333
month: feb
monthnumber: 2
year: 1987
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.527661
ISSNL: 0022-2488 OR 00222488
MRclass: 41A10 (33A65)
MRnumber: 87m:41009
bibdate: Mon Oct 31 11:57:55 MDT 2011
bibtimestamp: 2011.10.31 11:57:55 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v28/i2/p330_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Kley Visentin and Pablo Mart{\'\i}n
rawtitle: Fractional approximation to elliptic functions
entry:
@Article{Visentin:1987:FAE,
  author =       "Kley Visentin and Pablo Mart{\'\i}n",
  title =        "Fractional approximation to elliptic functions",
  journal =      j-J-MATH-PHYS,
  volume =       "28",
  number =       "2",
  pages =        "330--333",
  month =        feb,
  year =         "1987",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.527661",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A10 (33A65)",
  MRnumber =     "87m:41009",
  bibdate =      "Mon Oct 31 11:57:55 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/v28/i2/p330_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "4",
}


bibtype: book
filename: elefunt.bib
label: Zare:1987:AMU
author: Richard N. Zare
title: Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics
publisher: pub-WILEY
address: pub-WILEY:adr
pages: viii + 349
year: 1987
ISBN: 0-471-85892-7 OR 0471858927
ISBN13: 978-0-471-85892-8 OR 9780471858928
LCCN: QC793.3.A5 Z37 1987
bibdate: Tue Aug 5 06:06:20 MDT 2025
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.08.05 06:06:20 MDT
URL: http://catalog.hathitrust.org/api/volumes/oclc/214728550.html
acknowledgement: ack-nhfb
rawauthor: Richard N. Zare
rawtitle: Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics
remark:
Based on lectures given to the Chemistry Department, Cornell University, in the autumn of 1980 as part of their Baker lecture series.

subject:
Angular momentum (Nuclear physics); Moment angulaire (Physique nucleaire); Angular momentum (Nuclear physics); Drehimpuls; Quantenmechanik

TOC:
Angular Momentum Operators and Wave Functions Coupling of Two Angular Momentum Vectors Transformation under Rotation The Coupling of More than Two Angular Momentum Vectors Spherical Tensor Operators Energy-level Structure and Wave Functions of a Rigid Rotor Appendix: Computer Programs for 3J, 6J, and 9J Symbols Index

rawTOC:
Angular Momentum Operators and Wave Functions \\ Coupling of Two Angular Momentum Vectors \\ Transformation under Rotation \\ The Coupling of More than Two Angular Momentum Vectors \\ Spherical Tensor Operators \\ Energy-level Structure and Wave Functions of a Rigid Rotor \\ Appendix: Computer Programs for 3J, 6J, and 9J Symbols \\ Index

entry:
@Book{Zare:1987:AMU,
  author =       "Richard N. Zare",
  title =        "Angular Momentum: Understanding Spatial Aspects in
                 Chemistry and Physics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "viii + 349",
  year =         "1987",
  ISBN =         "0-471-85892-7",
  ISBN-13 =      "978-0-471-85892-8",
  LCCN =         "QC793.3.A5 Z37 1987",
  bibdate =      "Tue Aug 5 06:06:20 MDT 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/214728550.html",
  acknowledgement = ack-nhfb,
  remark =       "Based on lectures given to the Chemistry Department,
                 Cornell University, in the autumn of 1980 as part of
                 their Baker lecture series.",
  subject =      "Angular momentum (Nuclear physics); Moment angulaire
                 (Physique nucl{\'e}aire); Angular momentum (Nuclear
                 physics); Drehimpuls; Quantenmechanik",
  tableofcontents = "Angular Momentum Operators and Wave Functions \\
                 Coupling of Two Angular Momentum Vectors \\
                 Transformation under Rotation \\
                 The Coupling of More than Two Angular Momentum Vectors
                 \\
                 Spherical Tensor Operators \\
                 Energy-level Structure and Wave Functions of a Rigid
                 Rotor \\
                 Appendix: Computer Programs for 3J, 6J, and 9J Symbols
                 \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: Zurawski:1987:DHS
author: J. H. P. Zurawski and J. B. Gosling
title: Design of a High-Speed Square Root Multiply and Divide Unit
journal: j-IEEE-TRANS-COMPUT
volume: C-36
number: 1
pages: 13--23
month: jan
monthnumber: 1
year: 1987
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1987.5009445
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 9 09:28:49 MDT 2011
bibtimestamp: 2011.07.09 09:28:49 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. H. P. Zurawski and J. B. Gosling
rawtitle: Design of a High-Speed Square Root Multiply and Divide Unit
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/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib

entry:
@Article{Zurawski:1987:DHS,
  author =       "J. H. P. Zurawski and J. B. Gosling",
  title =        "Design of a High-Speed Square Root Multiply and Divide
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "1",
  pages =        "13--23",
  month =        jan,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009445",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:49 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/ieeetranscomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
  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: Zwick:1987:BAC
author: D. Zwick
title: Best approximation by convex functions
journal: j-AMER-MATH-MONTHLY
volume: 94
number: 6
pages: 528--534
month: jul
monthnumber: 7
year: 1987
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
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
affiliation: University of Vermont, Vermont, NY
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: D. Zwick
rawtitle: Best approximation by convex functions
entry:
@Article{Zwick:1987:BAC,
  author =       "D. Zwick",
  title =        "Best approximation by convex functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "6",
  pages =        "528--534",
  month =        jul,
  year =         "1987",
  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 =  "University of Vermont, Vermont, NY",
  bibno =        "43727",
  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 =     "American Mathematical Monthly",
  genterm =      "theory; verification",
  guideno =      "1988-04405",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "June/July 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: book
filename: elefunt.bib
label: Aberth:1988:PNA
author: Oliver Aberth
title: Precise Numerical Analysis
publisher: pub-WCB
address: pub-WCB:adr
pages: x + 225
year: 1988
ISBN: 0-697-06760-2 OR 0697067602
ISBN13: 978-0-697-06760-9 OR 9780697067609
LCCN: QA297 .A28 1988
bibdate: Mon Oct 24 11:37:20 2011
bibsource: file://sunrise/u/sy/beebe/tex/bib/all_brec.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
acknowledgement: ack-nj
rawauthor: Oliver Aberth
rawtitle: Precise Numerical Analysis
abstract:
Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number $ pm $ a range. Rational arithmetic is also considered. Chapters are devoted to begin enumerate item rootfinding, item polynomial rootfinding, item numerical linear algebra, item differentiation and integration, and item ordinary differential equations.end enumerate Differentiation is handled by a codelist approach like [Rall81a], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an it a priori bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.

keywords:
differentiation; differentiation arithmetic; general numerical analysis; integration; interval techniques; linear algebra; ordinary differential equations.; variable precision arithmetic

rawabstract:
Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number $ \pm $ a range. Rational arithmetic is also considered. Chapters are devoted to \begin{enumerate} \item rootfinding, \item polynomial rootfinding, \item numerical linear algebra, \item differentiation and integration, and \item ordinary differential equations.\end{enumerate} Differentiation is handled by a codelist approach like [Rall81a], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an {\it a priori\/} bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.

entry:
@Book{Aberth:1988:PNA,
  author =       "Oliver Aberth",
  title =        "Precise Numerical Analysis",
  publisher =    pub-WCB,
  address =      pub-WCB:adr,
  pages =        "x + 225",
  year =         "1988",
  ISBN =         "0-697-06760-2",
  ISBN-13 =      "978-0-697-06760-9",
  LCCN =         "QA297 .A28 1988",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "file://sunrise/u/sy/beebe/tex/bib/all_brec.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Aberth addresses elementary issues of precise floating
                 point computations using variable precision range
                 arithmetic. Numbers are represented as a variable
                 precision number $ \pm $ a range. Rational arithmetic
                 is also considered. Chapters are devoted to
                 \begin{enumerate} \item rootfinding, \item polynomial
                 rootfinding, \item numerical linear algebra, \item
                 differentiation and integration, and \item ordinary
                 differential equations.\end{enumerate} Differentiation
                 is handled by a codelist approach like [Rall81a], and
                 applications to Taylor series are given. Interval
                 techniques for ordinary differential equations are
                 based on using an {\it a priori\/} bound to capture
                 remainder terms. Several methods are illustrated,
                 including Taylor series methods.",
  acknowledgement = ack-nj,
  comment =      "Text for a one semester, junior level course in
                 numerical analysis. Includes PC disk with software
                 written in PBASIC. Sound introductory level discussion
                 of code lists and error capture techniques.",
  keywords =     "differentiation; differentiation arithmetic; general
                 numerical analysis; integration; interval techniques;
                 linear algebra; ordinary differential equations.;
                 variable precision arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Alonso:1988:SCN
author: Javier Alonso and Carlos Benitez
title: Some characteristic and non-characteristic properties of inner product spaces
journal: j-J-APPROX-THEORY
volume: 55
number: 3
pages: 318--325
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: Javier Alonso and Carlos Benitez
rawtitle: Some characteristic and non-characteristic properties of inner product spaces
entry:
@Article{Alonso:1988:SCN,
  author =       "Javier Alonso and Carlos Benitez",
  title =        "Some characteristic and non-characteristic properties
                 of inner product spaces",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "318--325",
  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 =        "56052",
  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 =      "theory; verification",
  guideno =      "1988-10198",
  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: article
filename: elefunt.bib
label: Anderson:1988:MRE
author: Ned Anderson
title: Minimum relative error approximations for $ 1 / t $
journal: j-NUM-MATH
volume: 54
number: 2
pages: 117--124
month: nov
monthnumber: 11
year: 1988
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01396969
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65D15
MRnumber: 90a:65037
MRreviewer: Mariano Gasca
bibdate: Mon May 26 11:49:34 MDT 1997
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Corp. Res., Digital Equipment Corp., Hudson, MA, USA
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Ned Anderson
rawtitle: Minimum relative error approximations for $ 1 / t $
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/nummath.bib

keywords:
approximation theory; functional equation; geometric convergence rates; iterative methods; minimum relative error approximations; polynomial approximations; polynomials

entry:
@Article{Anderson:1988:MRE,
  author =       "Ned Anderson",
  title =        "Minimum relative error approximations for $ 1 / t $",
  journal =      j-NUM-MATH,
  volume =       "54",
  number =       "2",
  pages =        "117--124",
  month =        nov,
  year =         "1988",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01396969",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D15",
  MRnumber =     "90a:65037",
  MRreviewer =   "Mariano Gasca",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  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/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Corp. Res., Digital Equipment Corp., Hudson, MA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "approximation theory; functional equation; geometric
                 convergence rates; iterative methods; minimum relative
                 error approximations; polynomial approximations;
                 polynomials",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Bailey:1988:CDD
author: David H. Bailey
journal: j-MATH-COMPUT
volume: 50
number: 181
pages: 283--296
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: 11Y60 (11-04 11K16 65-04)
MRnumber: 88m:11114
MRreviewer: A. J. van der Poorten
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: NASA Ames Res. Centre, Moffet Field, CA, USA
journalURL: http://www.ams.org/mcom/
treatment: X Experimental
rawauthor: David H. Bailey
title:
The computation of $ pi $ to $ 29, 360, 000 $ decimal digits using Borweins' quartically convergent algorithm

keywords:
Borwein quartically convergent algorithm; computation of pi; computer testing; Cray 2 computer test; decimal expansion; elliptic integrals; iterative methods; mathematics computing; multiprecision arithmetic; number theory; prime modulus; series (mathematics); statistical analyses; statistical analysis; transform

classcodes:
C1140Z (Other and miscellaneous); C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C5470 (Performance evaluation and testing); C7310 (Mathematics)

rawtitle:
The computation of $ \pi $ to $ 29, 360, 000 $ decimal digits using {Borweins}' quartically convergent algorithm

entry:
@Article{Bailey:1988:CDD,
  author =       "David H. Bailey",
  title =        "The computation of $ \pi $ to $ 29, 360, 000 $ decimal
                 digits using {Borweins}' quartically convergent
                 algorithm",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "283--296",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y60 (11-04 11K16 65-04)",
  MRnumber =     "88m:11114",
  MRreviewer =   "A. J. van der Poorten",
  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 =   "C1140Z (Other and miscellaneous); C1160 (Combinatorial
                 mathematics); C4130 (Interpolation and function
                 approximation); C5470 (Performance evaluation and
                 testing); C7310 (Mathematics)",
  corpsource =   "NASA Ames Res. Centre, Moffet Field, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Borwein quartically convergent algorithm; computation
                 of pi; computer testing; Cray 2 computer test; decimal
                 expansion; elliptic integrals; iterative methods;
                 mathematics computing; multiprecision arithmetic;
                 number theory; prime modulus; series (mathematics);
                 statistical analyses; statistical analysis; transform",
  treatment =    "X Experimental",
}


bibtype: article
filename: elefunt.bib
label: Bloom:1988:LCL
author: Thomas Bloom
title: The Lebesgue constant for Lagrange interpolation in the simplex
journal: j-J-APPROX-THEORY
volume: 54
number: 3
pages: 338--353
month: sep
monthnumber: 9
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: Thomas Bloom
rawtitle: The {Lebesgue} constant for {Lagrange} interpolation in the simplex
entry:
@Article{Bloom:1988:LCL,
  author =       "Thomas Bloom",
  title =        "The {Lebesgue} constant for {Lagrange} interpolation
                 in the simplex",
  journal =      j-J-APPROX-THEORY,
  volume =       "54",
  number =       "3",
  pages =        "338--353",
  month =        sep,
  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 =        "56887",
  catcode =      "G.1.1; G.1.2; G.1.2; G.1.7; G.1.7",
  CRclass =      "G.1.1 Interpolation; G.1.1 Interpolation formulas;
                 G.1.2 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; G.1.7 Ordinary Differential
                 Equations; G.1.7 Convergence and stability; G.1.7
                 Ordinary Differential Equations; G.1.7 Boundary value
                 problems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Interpolation formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Convergence
                 and stability; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems",
  fjournal =     "Journal of Approximation Theory",
  guideno =      "1988-10170",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Borwein:1988:CFF
author: J. M. Borwein and P. B. Borwein
title: On the Complexity of Familiar Functions and Numbers
journal: j-SIAM-REVIEW
volume: 30
number: 4
pages: 589--601
month: dec
monthnumber: 12
year: 1988
CODEN: SIREAD
DOI: https://doi.org/10.1137/1030134
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 68Q25 (03D15 11Y16)
MRnumber: 967961; 89k:68061
MRreviewer: Klaus W. Wagner
bibdate: Sat Mar 29 09:54:29 MDT 2014
bibtimestamp: 2014.03.29 09:54:29 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
affiliationaddress: Halifax, NS, Can
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: December 1988
rawauthor: J. M. Borwein and P. B. Borwein
rawtitle: On the Complexity of Familiar Functions and Numbers
bibsource:
ACM Computing Archive CD-ROM database (1991); Compendex database; http://epubs.siam.org/toc/siread/30/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

abstract:
This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that it is possible to base a taxonomy of such functions and numbers on their computational complexity. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious. For most functions, provably optimal methods are not known; however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.

keywords:
Algebraic Approximation; Approximation Theory; Computation of Digits; Familiar Functions; Low Complexity Approximation; Mathematical Techniques; Rational Approximation; Reduced Complexity 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.1 COMPUTATION BY ABSTRACT DEVICES

rawabstract:
This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that it is possible to base a taxonomy of such functions and numbers on their computational complexity. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious. For most functions, provably optimal methods are not known; however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.

entry:
@Article{Borwein:1988:CFF,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Complexity of Familiar Functions and Numbers",
  journal =      j-SIAM-REVIEW,
  volume =       "30",
  number =       "4",
  pages =        "589--601",
  month =        dec,
  year =         "1988",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1030134",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "68Q25 (03D15 11Y16)",
  MRnumber =     "967961; 89k:68061",
  MRreviewer =   "Klaus W. Wagner",
  bibdate =      "Sat Mar 29 09:54:29 MDT 2014",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 Compendex database;
                 http://epubs.siam.org/toc/siread/30/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "This paper examines low-complexity approximations to
                 familiar functions and numbers. The intent is to
                 suggest that it is possible to base a taxonomy of such
                 functions and numbers on their computational
                 complexity. A central theme is that traditional methods
                 of approximation are often very far from optimal, while
                 good or optimal methods are often very far from
                 obvious. For most functions, provably optimal methods
                 are not known; however the gap between what is known
                 and what is possible is often small. A considerable
                 number of open problems are posed and a number of
                 related examples are presented.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Halifax, NS, Can",
  bibno =        "58008",
  catcode =      "G.1.2; F.2.1; F.1.3",
  classification = "921",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; F.2.1 Numerical Algorithms and Problems;
                 F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  fjournal =     "SIAM Review",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13907",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabbrev = "SIAM Rev.",
  journalabr =   "SIAM Rev",
  jrldate =      "Dec. 1988",
  keywords =     "Algebraic Approximation; Approximation Theory;
                 Computation of Digits; Familiar Functions; Low
                 Complexity Approximation; Mathematical Techniques;
                 Rational Approximation; Reduced Complexity
                 Approximation",
  onlinedate =   "December 1988",
  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.1
                 COMPUTATION BY ABSTRACT DEVICES",
}


bibtype: article
filename: elefunt.bib
label: Borwein:1988:PAE
author: Peter B. Borwein
title: Pade approximants for the $q$-elementary functions
journal: j-CONST-APPROX
volume: 4
number: 4
pages: 391--402
year: 1988
ISSN: 0176-4276 (print), 1432-0940 (electronic) OR 01764276 (print), 14320940 (electronic)
ISSNL: 0176-4276 OR 01764276
MRclass: 41A21 (33A10 41A20)
MRnumber: 89f:41022
MRreviewer: Annie A. M. Cuyt
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: Constructive Approximation
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/365
rawauthor: Peter B. Borwein
rawtitle: {Pad{\'e}} approximants for the $q$-elementary functions
entry:
@Article{Borwein:1988:PAE,
  author =       "Peter B. Borwein",
  title =        "{Pad{\'e}} approximants for the $q$-elementary
                 functions",
  journal =      j-CONST-APPROX,
  volume =       "4",
  number =       "4",
  pages =        "391--402",
  year =         "1988",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "41A21 (33A10 41A20)",
  MRnumber =     "89f:41022",
  MRreviewer =   "Annie A. M. Cuyt",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Constructive Approximation",
  journal-URL =  "http://link.springer.com/journal/365",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:1988:BRS
author: C. Brezinski
journal: j-MATH-COMPUT-SIMUL
volume: 30
number: 4
pages: 376--376
month: sep
monthnumber: 9
year: 1988
CODEN: MCSIDR
DOI: https://doi.org/10.1016/S0378-4754(98)90019-2
ISSN: 0378-4754 (print), 1872-7166 (electronic) OR 03784754 (print), 18727166 (electronic)
ISSNL: 0378-4754 OR 03784754
bibdate: Mon Aug 18 16:03:56 MDT 2025
bibtimestamp: 2025.08.18 16:03:56 MDT
URL: https://www.sciencedirect.com/science/article/pii/S0378475498900192
fjournal: Mathematics and Computers in Simulation
acknowledgement: ack-nhfb
ajournal: Math. Comput. Simul.
journalURL: https://www.sciencedirect.com/science/journal/03784754
rawauthor: C. Brezinski
title:
Book Review: booktitle Special functions of mathematical physics: A. F. Nikiforov and V. B. Uvarov, Birkhauser, Basel, 1988, xviii + 427 pages, Sfr 168.00, ISBN 3-7643-3183-6

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib

rawtitle:
Book Review: {{\booktitle{Special functions of mathematical physics}}: A. F. Nikiforov and V. B. Uvarov, Birkh{\"a}user, Basel, 1988, xviii + 427 pages, Sfr 168.00, ISBN 3-7643-3183-6}

entry:
@Article{Brezinski:1988:BRS,
  author =       "C. Brezinski",
  title =        "Book Review: {{\booktitle{Special functions of
                 mathematical physics}}: A. F. Nikiforov and V. B.
                 Uvarov, Birkh{\"a}user, Basel, 1988, xviii + 427 pages,
                 Sfr 168.00, ISBN 3-7643-3183-6}",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "4",
  pages =        "376--376",
  month =        sep,
  year =         "1988",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/S0378-4754(98)90019-2",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:56 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0378475498900192",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}


bibtype: incollection
filename: elefunt.bib
label: Brezinski:1988:NAC
author: Claude Brezinski
booktitle: Nonlinear numerical methods and rational approximation (Wilrijk, 1987)
title: A new approach to convergence acceleration methods
volume: 43
publisher: Reidel
address: Dordrecht
pages: 373--405
year: 1988
MRclass: 65Bxx (40A25)
MRnumber: 1005369 (90m:65010)
MRreviewer: John P. Coleman
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 ???
series: Math. Appl.
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Claude Brezinski
rawbooktitle: {Nonlinear numerical methods and rational approximation (Wilrijk, 1987)}
rawtitle: A new approach to convergence acceleration methods
entry:
@InCollection{Brezinski:1988:NAC,
  author =       "Claude Brezinski",
  booktitle =    "{Nonlinear numerical methods and rational
                 approximation (Wilrijk, 1987)}",
  title =        "A new approach to convergence acceleration methods",
  volume =       "43",
  publisher =    "Reidel",
  address =      "Dordrecht",
  pages =        "373--405",
  year =         "1988",
  MRclass =      "65Bxx (40A25)",
  MRnumber =     "1005369 (90m:65010)",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Math. Appl.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1988:TEI
author: B. C. Carlson
title: A Table of Elliptic Integrals of the Third Kind
journal: j-MATH-COMPUT
volume: 51
number: 183
pages: 267--280, S1--S5
month: jul
monthnumber: 7
year: 1988
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33A25 (65A05)
MRnumber: 89k:33003
MRreviewer: F. W. J. Olver
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: Iowa State Univ., Ames, IA, USA
journalURL: http://www.ams.org/mcom/
treatment: P Practical; T Theoretical or Mathematical
rawauthor: B. C. Carlson
rawtitle: A Table of Elliptic Integrals of the Third Kind
keywords:
Cauchy principal values; elliptic integrals; FORTRAN listings; function evaluation; integral equations; integration; points; real singular; recurrence relations; standard R-functions

classcodes:
B0290R (Integral equations); B0220 (Analysis); B0290D (Functional analysis); B0290M (Numerical integration and differentiation); C4180 (Integral equations); C1120 (Analysis); C4120 (Functional analysis); C4160 (Numerical integration and differentiation)

entry:
@Article{Carlson:1988:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals of the Third Kind",
  journal =      j-MATH-COMPUT,
  volume =       "51",
  number =       "183",
  pages =        "267--280, S1--S5",
  month =        jul,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A25 (65A05)",
  MRnumber =     "89k:33003",
  MRreviewer =   "F. W. J. Olver",
  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 =   "B0290R (Integral equations); B0220 (Analysis); B0290D
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                 and differentiation); C4180 (Integral equations); C1120
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                 (Numerical integration and differentiation)",
  corpsource =   "Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Cauchy principal values; elliptic integrals; FORTRAN
                 listings; function evaluation; integral equations;
                 integration; points; real singular; recurrence
                 relations; standard R-functions",
  treatment =    "P Practical; T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Cartwright:1988:JTC
author: Donald I. Cartwright and Krzysztof Kucharski
title: Jackson's Theorem for compact connect Lie groups
journal: j-J-APPROX-THEORY
volume: 55
number: 3
pages: 352--359
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
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Donald I. Cartwright and Krzysztof Kucharski
rawtitle: {Jackson's Theorem} for compact connect {Lie} groups
subject:
G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

entry:
@Article{Cartwright:1988:JTC,
  author =       "Donald I. Cartwright and Krzysztof Kucharski",
  title =        "{Jackson's Theorem} for compact connect {Lie} groups",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "352--359",
  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 =        "56056",
  catcode =      "G.2.m; G.1.2",
  CRclass =      "G.2.m Miscellaneous; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
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                 ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10202",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Chellali:1988:ACN
author: Mustapha Chellali
journal: j-J-NUMBER-THEORY
volume: 28
number: 3
pages: 347--362
month: mar
monthnumber: 3
year: 1988
CODEN: JNUTA9
DOI: https://doi.org/10.1016/0022-314X(88)90047-9
ISSN: 0022-314X (print), 1096-1658 (electronic) OR 0022314X (print), 10961658 (electronic)
ISSNL: 0022-314X OR 0022314X
bibdate: Wed Jul 15 08:46:57 MDT 2020
bibtimestamp: 2020.07.15 08:46:57 MDT
URL: http://www.sciencedirect.com/science/article/pii/0022314X88900479
fjournal: Journal of Number Theory
language: French
acknowledgement: ack-nhfb
ajournal: J. Number Theory
journalURL: http://www.sciencedirect.com/science/journal/0022314X
rawauthor: Mustapha Chellali
title:
Acceleration de calcul de nombres de Bernoulli. (French) [Bernoulli number calculation acceleration]

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jnumbertheory1980.bib

rawtitle:
Acc{\'e}l{\'e}ration de calcul de nombres de {Bernoulli}. ({French}) [{Bernoulli} number calculation acceleration]

entry:
@Article{Chellali:1988:ACN,
  author =       "Mustapha Chellali",
  title =        "Acc{\'e}l{\'e}ration de calcul de nombres de
                 {Bernoulli}. ({French}) [{Bernoulli} number calculation
                 acceleration]",
  journal =      j-J-NUMBER-THEORY,
  volume =       "28",
  number =       "3",
  pages =        "347--362",
  month =        mar,
  year =         "1988",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/0022-314X(88)90047-9",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:46:57 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0022314X88900479",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
  language =     "French",
}


bibtype: article
filename: elefunt.bib
label: Chiccoli:1988:EGE
author: C. Chiccoli and S. Lorenzutta and G. Maino
title: On the evaluation of generalized exponential integrals $ E_nu (x) $
journal: j-J-COMPUT-PHYS
volume: 78
number: 2
pages: 278--287
month: oct
monthnumber: 10
year: 1988
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(88)90050-2
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:42 MST 2012
bibtimestamp: 2012.01.01 15:59:42 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999188900502
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: C. Chiccoli and S. Lorenzutta and G. Maino
rawtitle: On the evaluation of generalized exponential integrals {$ E_\nu (x) $}
entry:
@Article{Chiccoli:1988:EGE,
  author =       "C. Chiccoli and S. Lorenzutta and G. Maino",
  title =        "On the evaluation of generalized exponential integrals
                 {$ E_\nu (x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "78",
  number =       "2",
  pages =        "278--287",
  month =        oct,
  year =         "1988",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(88)90050-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:42 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/0021999188900502",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Cover:1988:DII
author: Thomas M. Cover and Joy A. Thomas
title: Determinant inequalities via information theory
journal: j-SIAM-J-MAT-ANA-APPL
volume: 9
number: 3
pages: 384--392
month: jul
monthnumber: 7
year: 1988
CODEN: SJMAEL
ISSN: 0895-4798 (print), 1095-7162 (electronic) OR 08954798 (print), 10957162 (electronic)
ISSNL: 0895-4798 OR 08954798
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 Matrix Analysis and Applications
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/simax
rawauthor: Thomas M. Cover and Joy A. Thomas
rawtitle: Determinant inequalities via information theory
subject:
H. Information Systems; H.1 MODELS AND PRINCIPLES; 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:
@Article{Cover:1988:DII,
  author =       "Thomas M. Cover and Joy A. Thomas",
  title =        "Determinant inequalities via information theory",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "9",
  number =       "3",
  pages =        "384--392",
  month =        jul,
  year =         "1988",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  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 =        "58040",
  catcode =      "H.1.1; G.1.3; F.2.1; G.1.2",
  CRclass =      "H.1.1 Systems and Information Theory; H.1.1
                 Information theory; G.1.3 Numerical Linear Algebra;
                 G.1.3 Determinants; F.2.1 Numerical Algorithms and
                 Problems; F.2.1 Computations on matrices; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Information Systems, MODELS AND PRINCIPLES, Systems
                 and Information Theory, Information theory; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Determinants; Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13777",
  journal-URL =  "http://epubs.siam.org/simax",
  journalabbrev = "SIAM J. Matrix Anal. Appl.",
  jrldate =      "July 1988",
  subject =      "H. Information Systems; H.1 MODELS AND PRINCIPLES; 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",
}


bibtype: inproceedings
filename: elefunt.bib
label: Davenport:1988:ICF
author: J. H. Davenport
editor: N. M. Stephens and M. P. Thorne
title: Integration in closed form
volume: 14
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
pages: 384--392
year: 1988
ISBN: 0-19-853620-8 OR 0198536208
ISBN13: 978-0-19-853620-8 OR 9780198536208
LCCN: QA11.A1 C618 1986
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: Institute of Mathematics and its applications conference series, new series
acknowledgement: ack-nhfb
affiliation: Univ. of Bath
bookpages: 235
rawauthor: J. H. Davenport
raweditor: N. M. Stephens and M. P. Thorne
rawtitle: Integration in closed form
booktitle:
Computers in mathematical research: based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on computers in mathematical research, held at University College, Cardiff in September 1986

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

rawbooktitle:
Computers in mathematical research: based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on computers in mathematical research, held at University College, Cardiff in September 1986

entry:
@InProceedings{Davenport:1988:ICF,
  author =       "J. H. Davenport",
  editor =       "N. M. Stephens and M. P. Thorne",
  booktitle =    "Computers in mathematical research: based on the
                 proceedings of a conference organized by the Institute
                 of Mathematics and its Applications on computers in
                 mathematical research, held at University College,
                 Cardiff in September 1986",
  title =        "Integration in closed form",
  volume =       "14",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  bookpages =    "235",
  year =         "1988",
  ISBN =         "0-19-853620-8",
  ISBN-13 =      "978-0-19-853620-8",
  LCCN =         "QA11.A1 C618 1986",
  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\$57.50",
  series =       "Institute of Mathematics and its applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Bath",
  bibno =        "52474",
  catcode =      "J.2; F.2.1; G.1.2; G.1.2; I.2.9; F.2.1",
  CRclass =      "J.2 Mathematics and statistics; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Number-theoretic
                 computations; G.1.2 Approximation; G.1.2 Rational
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                 function approximation; I.2.9 Robotics; F.2.1 Numerical
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  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
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                 Number-theoretic computations; Mathematics of
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                 ANALYSIS, Approximation, Elementary function
                 approximation; Computing Methodologies, ARTIFICIAL
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  genterm =      "algorithms; theory",
  guideno =      "1988-16247",
  page =         "119--134",
  procdate =     "Sept. 1986",
  procloc =      "Cardiff, Wales",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
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                 ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of
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                 of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY",
  waffil =       "Univ. College, Cardiff, Wales; Univ. College, Cardiff,
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}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1988:SDC
author: Armido I. DiDonato and Alfred H. Morris, Jr.
title: Significant Digit Computation of the Incomplete Beta Function Ratios
type: Technical Report
number: NSWC TR 88-365
institution: Naval Surface Warfare Center (K33)
address: Dahlgren, VA 22448-5000, USA
pages: 384--392
month: nov
monthnumber: 11
year: 1988
bibdate: Sat Nov 15 10:30:20 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2014.11.15 10:30:20 ???
URL: http://www.dtic.mil/dtic/tr/fulltext/u2/a210118.pdf
keywords: bratio; continued fraction; expm1; gamma; incomplete gamma function; ln; log1p; r1mach; spmpar
acknowledgement: ack-nhfb
rawauthor: Armido I. DiDonato and Alfred H. {Morris, Jr.}
rawtitle: Significant Digit Computation of the Incomplete Beta Function Ratios
abstract:
An algorithm is given for evaluating the incomplete beta function ratio $ I_x(a, b) $ and its complement $ 1 - I_x(a, b) $. Two new procedures are used with classical results. A listing of a transportable Fortran subroutine using this algorithm is given. The subroutine is accurate to 14 significant digits when the precision is not restricted by inherent error.

rawabstract:
An algorithm is given for evaluating the incomplete beta function ratio $ I_x(a, b) $ and its complement $ 1 - I_x(a, b) $. Two new procedures are used with classical results. A listing of a transportable Fortran subroutine using this algorithm is given. The subroutine is accurate to 14 significant digits when the precision is not restricted by inherent error.

entry:
@TechReport{DiDonato:1988:SDC,
  author =       "Armido I. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "Significant Digit Computation of the Incomplete Beta
                 Function Ratios",
  type =         "Technical Report",
  number =       "NSWC TR 88-365",
  institution =  "Naval Surface Warfare Center (K33)",
  address =      "Dahlgren, VA 22448-5000, USA",
  month =        nov,
  year =         "1988",
  bibdate =      "Sat Nov 15 10:30:20 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a210118.pdf",
  abstract =     "An algorithm is given for evaluating the incomplete
                 beta function ratio $ I_x(a, b) $ and its complement $
                 1 - I_x(a, b) $. Two new procedures are used with
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                 subroutine using this algorithm is given. The
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                 the precision is not restricted by inherent error.",
  acknowledgement = ack-nhfb,
  keywords =     "bratio; continued fraction; expm1; gamma; incomplete
                 gamma function; ln; log1p; r1mach; spmpar",
}


bibtype: article
filename: elefunt.bib
label: Dunham:1988:PMA
author: Charles B. Dunham
title: Provably monotone approximations, III
journal: j-SIGNUM
volume: 23
number: 1
pages: 10--10
month: jan
monthnumber: 1
year: 1988
CODEN: SNEWD6
DOI: https://doi.org/10.1145/43931.43934
ISSN: 0163-5778 (print), 1558-0237 (electronic) OR 01635778 (print), 15580237 (electronic)
ISSNL: 0163-5778 OR 01635778
bibdate: Tue Apr 12 07:50:16 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.12 07:50:16 MDT
fjournal: ACM SIGNUM Newsletter
keywords: theory
subject: G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/signum
rawauthor: Charles B. Dunham
rawtitle: Provably monotone approximations, {III}
entry:
@Article{Dunham:1988:PMA,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations, {III}",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "10--10",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/43931.43934",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}


bibtype: techreport
filename: elefunt.bib
label: Duprat:1988:EPE
author: J. Duprat and J. M. Muller
title: Evaluation of Polynomials and elementary Functions by integrated Circuits
number: RR698-I
institution: IMAG
address: Grenoble, France
pages: 10--10
month: jan
monthnumber: 1
year: 1988
bibdate: Mon Oct 24 11:37:20 2011
bibtimestamp: 2011.10.24 11:37:20 ???
acknowledgement: ack-nhfb
rawauthor: J. Duprat and J. M. Muller
rawtitle: Evaluation of Polynomials and elementary Functions by integrated Circuits
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Duprat:1988:EPE,
  author =       "J. Duprat and J. M. Muller",
  title =        "Evaluation of Polynomials and elementary Functions by
                 integrated Circuits",
  number =       "RR698-I",
  institution =  "IMAG",
  address =      "Grenoble, France",
  month =        jan,
  year =         "1988",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Duprat:1988:HPE
author: Jean Duprat and Jean-Michel Muller
title: Hardwired polynomial evaluation
journal: j-J-PAR-DIST-COMP
volume: 5
number: 3
pages: 291--309
month: jun
monthnumber: 6
year: 1988
CODEN: JPDCER
ISSN: 0743-7315 (print), 1096-0848 (electronic) OR 07437315 (print), 10960848 (electronic)
ISSNL: 0743-7315 OR 07437315
bibdate: Sat Apr 12 19:06:31 MDT 1997
bibsource: Compendex database; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.04.12 19:06:31 MDT
fjournal: Journal of Parallel and Distributed Computing
acknowledgement: ack-nhfb
affiliationaddress: CNRS, Grenoble, Fr
corpsource: Inst. Nat. Polytech. de Grenoble, France
journalURL: http://www.sciencedirect.com/science/journal/07437315
journalabr: J Parallel Distrib Comput
treatment: P Practical
rawauthor: Jean Duprat and Jean-Michel Muller
rawtitle: Hardwired polynomial evaluation
keywords:
computer architecture; computers, digital --- Circuits; digital arithmetic; elementary functions; hardwired polynomial evaluation; mathematical functions; mathematical techniques; Polynomials; polynomials; special-purpose circuits; VLSI implementation

entry:
@Article{Duprat:1988:HPE,
  author =       "Jean Duprat and Jean-Michel Muller",
  title =        "Hardwired polynomial evaluation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "291--309",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "CNRS, Grenoble, Fr",
  classification = "721; 722; 723; 921; C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Inst. Nat. Polytech. de Grenoble, France",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "computer architecture; computers, digital ---
                 Circuits; digital arithmetic; elementary functions;
                 hardwired polynomial evaluation; mathematical
                 functions; mathematical techniques; Polynomials;
                 polynomials; special-purpose circuits; VLSI
                 implementation",
  treatment =    "P Practical",
}


bibtype: article
filename: elefunt.bib
label: Feng:1988:AIN
author: Y. Y. Feng and J. Kozak
title: An approach to the interpolation of nonuniformly spaced data
journal: j-J-COMPUT-APPL-MATH
volume: 23
number: 2
pages: 169--178
month: aug
monthnumber: 8
year: 1988
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
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 Computational and Applied Mathematics
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Y. Y. Feng and J. Kozak
rawtitle: An approach to the interpolation of nonuniformly spaced data
entry:
@Article{Feng:1988:AIN,
  author =       "Y. Y. Feng and J. Kozak",
  title =        "An approach to the interpolation of nonuniformly
                 spaced data",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "23",
  number =       "2",
  pages =        "169--178",
  month =        aug,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  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 =        "56475",
  catcode =      "G.1.1; G.1.2; G.1.7; G.1.1; G.1.4",
  CRclass =      "G.1.1 Interpolation; G.1.1 Spline and piecewise
                 polynomial interpolation; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.7 Ordinary
                 Differential Equations; G.1.7 Boundary value problems;
                 G.1.1 Interpolation; G.1.1 Smoothing; G.1.4 Quadrature
                 and Numerical Differentiation; G.1.4 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Smoothing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Error analysis",
  fjournal =     "Journal of Computational and Applied Mathematics",
  genterm =      "algorithms; theory",
  guideno =      "1988-10490",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  journalabbrev = "J. Comput. Appl. Math.",
  jrldate =      "August 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Gawronski:1988:ZLT
author: Wolfgang Gawronski and Ulrich Stadtmuller
title: On the zeros of Lerch's transcendental function of real parameters
journal: j-J-APPROX-THEORY
volume: 53
number: 3
pages: 354--364
month: jun
monthnumber: 6
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 Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Wolfgang Gawronski and Ulrich Stadtm{\"u}ller
rawtitle: On the zeros of {Lerch}'s transcendental function of real parameters
entry:
@Article{Gawronski:1988:ZLT,
  author =       "Wolfgang Gawronski and Ulrich Stadtm{\"u}ller",
  title =        "On the zeros of {Lerch}'s transcendental function of
                 real parameters",
  journal =      j-J-APPROX-THEORY,
  volume =       "53",
  number =       "3",
  pages =        "354--364",
  month =        jun,
  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 Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG",
  bibno =        "49727",
  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 =      "1988-10146",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Gillman:1988:ARG
author: E. Gillman and H. R. Fiebig
journal: j-COMPUT-PHYS
volume: 2
number: 1
pages: 62--??
month: jan
monthnumber: 1
year: 1988
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168296
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:45:10 MDT 2019
bibtimestamp: 2019.04.10 08:45:10 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168296
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: E. Gillman and H. R. Fiebig
title:
Accurate recursive generation of spherical Bessel and Neumann functions for a large range of indices

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

rawtitle:
Accurate recursive generation of spherical {Bessel} and {Neumann} functions for a large range of indices

entry:
@Article{Gillman:1988:ARG,
  author =       "E. Gillman and H. R. Fiebig",
  title =        "Accurate recursive generation of spherical {Bessel}
                 and {Neumann} functions for a large range of indices",
  journal =      j-COMPUT-PHYS,
  volume =       "2",
  number =       "1",
  pages =        "62--??",
  month =        jan,
  year =         "1988",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168296",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:10 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/10.1063/1.168296",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Guerrero:1988:HOT
author: Antonio L. Guerrero and Pablo Martin
journal: j-J-COMPUT-PHYS
volume: 77
number: 1
pages: 276--281
month: jul
monthnumber: 7
year: 1988
CODEN: JCTPAH
DOI: https://doi.org/10.1016/0021-9991(88)90168-4
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Sun Jan 1 15:59:41 MST 2012
bibtimestamp: 2012.01.01 15:59:41 MST
URL: http://www.sciencedirect.com/science/article/pii/0021999188901684
fjournal: Journal of Computational Physics
remark: This work produces only 3D approximations.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Antonio L. Guerrero and Pablo Martin
title:
Higher order two-point quasi-fractional approximations to the Bessel functions $ J_0 (x) $ and $ J_1 (x) $

rawtitle:
Higher order two-point quasi-fractional approximations to the {Bessel} functions {$ J_0 (x) $} and {$ J_1 (x) $}

entry:
@Article{Guerrero:1988:HOT,
  author =       "Antonio L. Guerrero and Pablo Martin",
  title =        "Higher order two-point quasi-fractional approximations
                 to the {Bessel} functions {$ J_0 (x) $} and {$ J_1 (x)
                 $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "77",
  number =       "1",
  pages =        "276--281",
  month =        jul,
  year =         "1988",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(88)90168-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:41 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/0021999188901684",
  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: article
filename: elefunt.bib
label: Hautot:1988:CAC
author: A. Hautot
title: Convergence acceleration of continued fractions of Poincare type
journal: j-APPL-NUM-MATH
volume: 4
number: 2--4
pages: 309--322
month: jun
monthnumber: 6
year: 1988
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B05 (40A15)
MRnumber: 90b:65005
MRreviewer: Gh. Adam
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: A. Hautot
rawtitle: Convergence acceleration of continued fractions of {Poincar{\'e}} type
bibsource:
https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Hautot:1988:CAC,
  author =       "A. Hautot",
  title =        "Convergence acceleration of continued fractions of
                 {Poincar{\'e}} type",
  journal =      j-APPL-NUM-MATH,
  volume =       "4",
  number =       "2--4",
  pages =        "309--322",
  month =        jun,
  year =         "1988",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "90b:65005",
  MRreviewer =   "Gh. Adam",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Heilmann:1988:SSM
author: Margareta Heilmann
title: $ L_p $-saturation of some modified Bernstein operators
journal: j-J-APPROX-THEORY
volume: 54
number: 3
pages: 260--273
month: sep
monthnumber: 9
year: 1988
CODEN: JAXTAZ
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Margareta Heilmann
rawtitle: {$ L_p $}-saturation of some modified {Bernstein} operators
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

entry:
@Article{Heilmann:1988:SSM,
  author =       "Margareta Heilmann",
  title =        "{$ L_p $}-saturation of some modified {Bernstein}
                 operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "54",
  number =       "3",
  pages =        "260--273",
  month =        sep,
  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 =        "56880",
  catcode =      "G.1.2; G.1.9; G.1.7; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.9 Integral Equations; G.1.9
                 Integro-differential equations; G.1.7 Ordinary
                 Differential Equations; G.1.7 Boundary value problems;
                 G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Boundary value problems; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Convergence and stability",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1988-10163",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1988",
  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",
}


bibtype: article
filename: elefunt.bib
label: Horwitz:1988:TPF
author: Alan L. Horwitz and Lee A. Rubel
title: Totally positive functions and totally bounded functions on $ [ - 1, 1] $
journal: j-J-APPROX-THEORY
volume: 52
number: 2
pages: 204--216
month: feb
monthnumber: 2
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: Pennsylvania State Univ., University Park; Univ. of Illinois, Urbana
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Alan L. Horwitz and Lee A. Rubel
rawtitle: Totally positive functions and totally bounded functions on $ [ - 1, 1] $
entry:
@Article{Horwitz:1988:TPF,
  author =       "Alan L. Horwitz and Lee A. Rubel",
  title =        "Totally positive functions and totally bounded
                 functions on $ [ - 1, 1] $",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "2",
  pages =        "204--216",
  month =        feb,
  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 =  "Pennsylvania State Univ., University Park; Univ. of
                 Illinois, Urbana",
  bibno =        "49653",
  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 =      "1988-10106",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "February 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Ifantis:1988:BFP
author: E. K. Ifantis and P. D. Siafarikas
title: Bounds for the first positive zero of a mixed Bessel function
journal: j-J-COMPUT-APPL-MATH
volume: 21
number: 2
pages: 245--249
month: feb
monthnumber: 2
year: 1988
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:38 MST 2017
bibtimestamp: 2017.02.25 12:20:38 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042788902737
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: Bounds for the first positive zero of a mixed {Bessel} function
entry:
@Article{Ifantis:1988:BFP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "Bounds for the first positive zero of a mixed {Bessel}
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "21",
  number =       "2",
  pages =        "245--249",
  month =        feb,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:38 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042788902737",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Jacobsen:1988:CAL
author: Lisa Jacobsen and Haakon Waadeland
title: Convergence acceleration of limit periodic continued fractions under asymptotic side conditions
journal: j-NUM-MATH
volume: 53
number: 3
pages: 285--298
month: jul
monthnumber: 7
year: 1988
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65B99 (30B70 40A15)
MRnumber: 89h:65010
MRreviewer: Claude Brezinski
bibdate: Mon May 26 11:49:34 MDT 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.26 11:49:34 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
corpsource: Dept. of Math. and Stat., Trondheim Univ., Dragvoll, Norway
journalURL: http://link.springer.com/journal/211
treatment: T Theoretical or Mathematical
rawauthor: Lisa Jacobsen and Haakon Waadeland
rawtitle: Convergence acceleration of limit periodic continued fractions under asymptotic side conditions
keywords:
asymptotic side conditions; convergence acceleration; convergence of numerical methods; hypergeometric functions; limit periodic continued fractions; regular C-fraction expansions

entry:
@Article{Jacobsen:1988:CAL,
  author =       "Lisa Jacobsen and Haakon Waadeland",
  title =        "Convergence acceleration of limit periodic continued
                 fractions under asymptotic side conditions",
  journal =      j-NUM-MATH,
  volume =       "53",
  number =       "3",
  pages =        "285--298",
  month =        jul,
  year =         "1988",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B99 (30B70 40A15)",
  MRnumber =     "89h:65010",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Dept. of Math. and Stat., Trondheim Univ., Dragvoll,
                 Norway",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "asymptotic side conditions; convergence acceleration;
                 convergence of numerical methods; hypergeometric
                 functions; limit periodic continued fractions; regular
                 C-fraction expansions",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: inproceedings
filename: elefunt.bib
label: Johnsson:1988:DPP
author: S. L. Johnsson
editor: J. R. Rice
booktitle: Mathematical aspects of scientific software
title: Data parallel programming and basic linear algebra subroutines
volume: 14
publisher: pub-SV
address: pub-SV:adr
pages: 183--196
year: 1988
ISBN: 0-387-96706-0 OR 0387967060
ISBN13: 978-0-387-96706-6 OR 9780387967066
LCCN: QA76.76.D47 M366 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 IMS volumes in mathematics and its applications
acknowledgement: ack-nhfb
bookpages: vi + 208
rawauthor: S. L. Johnsson
rawbooktitle: Mathematical aspects of scientific software
raweditor: J. R. Rice
rawtitle: Data parallel programming and basic linear algebra subroutines
subject:
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE

entry:
@InProceedings{Johnsson:1988:DPP,
  author =       "S. L. Johnsson",
  editor =       "J. R. Rice",
  booktitle =    "Mathematical aspects of scientific software",
  title =        "Data parallel programming and basic linear algebra
                 subroutines",
  volume =       "14",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "vi + 208",
  pages =        "183--196",
  year =         "1988",
  ISBN =         "0-387-96706-0",
  ISBN-13 =      "978-0-387-96706-6",
  LCCN =         "QA76.76.D47 M366 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 =       "The IMS volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  bibno =        "42725",
  catcode =      "G.1.2; D.1.m; G.4",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; D.1.m Miscellaneous",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Software, PROGRAMMING TECHNIQUES, Miscellaneous;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE",
  genterm =      "theory; algorithms; design; languages",
  guideno =      "1988-02324",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics
                 of Computing; G.4 MATHEMATICAL SOFTWARE",
  waffil =       "Purdue Univ., West Lafayette, IN",
}


bibtype: article
filename: elefunt.bib
label: Kirby:1988:ELA
author: James C. Kirby
title: An Efficient Logarithm Algorithm for Calculators
journal: j-COLLEGE-MATH-J
volume: 19
number: 3
pages: 257--260
month: may
monthnumber: 5
year: 1988
DOI: https://doi.org/10.1080/07468342.1988.11973125
ISSN: 0746-8342 (print), 1931-1346 (electronic) OR 07468342 (print), 19311346 (electronic)
ISSNL: 0746-8342 OR 07468342
bibdate: Thu Feb 14 09:50:43 MST 2019
bibtimestamp: 2019.02.14 09:50:43 MST
URL: http://www.tandfonline.com/doi/abs/10.1080/07468342.1988.11973125
fjournal: College Mathematics Journal
acknowledgement: ack-nhfb
journalURL: https://maa.tandfonline.com/loi/ucmj20; https://www.jstor.org/journal/collmathj
onlinedate: 30 Jan 2018
rawauthor: James C. Kirby
rawtitle: An Efficient Logarithm Algorithm for Calculators
entry:
@Article{Kirby:1988:ELA,
  author =       "James C. Kirby",
  title =        "An Efficient Logarithm Algorithm for Calculators",
  journal =      j-COLLEGE-MATH-J,
  volume =       "19",
  number =       "3",
  pages =        "257--260",
  month =        may,
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1988.11973125",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:43 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1988.11973125",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}


bibtype: article
filename: elefunt.bib
label: Kowalski:1988:ASP
author: Marek Kowalski and Waldemar Sielski
title: Approximation of smooth periodic functions in several variables
journal: j-J-COMPLEXITY
volume: 4
number: 4
pages: 356--372
month: dec
monthnumber: 12
year: 1988
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
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/0885064X
rawauthor: Marek Kowalski and Waldemar Sielski
rawtitle: Approximation of smooth periodic functions in several variables
entry:
@Article{Kowalski:1988:ASP,
  author =       "Marek Kowalski and Waldemar Sielski",
  title =        "Approximation of smooth periodic functions in several
                 variables",
  journal =      j-J-COMPLEXITY,
  volume =       "4",
  number =       "4",
  pages =        "356--372",
  month =        dec,
  year =         "1988",
  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,
  bibno =        "56811",
  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 complexity",
  genterm =      "algorithms; verification; theory",
  guideno =      "1988-10411",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0885064X",
  journalabbrev = "J. Complexity",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}


bibtype: article
filename: elefunt.bib
label: Kramer:1988:ISF
author: W. Kramer
title: Inverse standard functions for real and complex point and interval arguments with dynamic accuracy
journal: j-COMPUTING-SUPPLEMENTUM
pages: 185--212
year: 1988
CODEN: COSPDM
ISSN: 0344-8029 OR 03448029
bibdate: Thu Dec 14 17:19:38 MST 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.14 17:19:38 MST
note: Computer Arithmetic and Scientific Computation.
fjournal: Computing. Supplementum
acknowledgement: ack-nhfb
affiliation: Karlsruhe Univ., West Germany
authordates: 1952--2014 (WK)
thesaurus: Error analysis; Function approximation
issue: no.6 p. 185-212
rawauthor: W. Kr{\"a}mer
rawnote: Computer Arithmetic and Scientific Computation.
rawtitle: Inverse standard functions for real and complex point and interval arguments with dynamic accuracy
abstract:
Algorithms to compute inverse standard functions to arbitrary accuracy with safe error bounds are given. Not only approximation errors but also all possible rounding errors are considered. The desired accuracy of the function as well as the base of the number system used are parameters of the error formula. For implementation it is only assumed that the four elementary arithmetic operations are performed with a certain number of correct digits of the function value. The interval routines are constructed out of the point routines considering the monotonicity behaviour of the functions. The ambiguity of the complex functions is briefly discussed.

keywords:
Approximation errors; Dynamic accuracy; Error formula; Interval arguments; Inverse standard functions; Monotonicity behaviour; Rounding errors

rawabstract:
Algorithms to compute inverse standard functions to arbitrary accuracy with safe error bounds are given. Not only approximation errors but also all possible rounding errors are considered. The desired accuracy of the function as well as the base of the number system used are parameters of the error formula. For implementation it is only assumed that the four elementary arithmetic operations are performed with a certain number of correct digits of the function value. The interval routines are constructed out of the point routines considering the monotonicity behaviour of the functions. The ambiguity of the complex functions is briefly discussed.

entry:
@Article{Kramer:1988:ISF,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse standard functions for real and complex point
                 and interval arguments with dynamic accuracy",
  journal =      j-COMPUTING-SUPPLEMENTUM,
  pages =        "185--212",
  year =         "1988",
  CODEN =        "COSPDM",
  ISSN =         "0344-8029",
  bibdate =      "Thu Dec 14 17:19:38 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Computer Arithmetic and Scientific Computation.",
  abstract =     "Algorithms to compute inverse standard functions to
                 arbitrary accuracy with safe error bounds are given.
                 Not only approximation errors but also all possible
                 rounding errors are considered. The desired accuracy of
                 the function as well as the base of the number system
                 used are parameters of the error formula. For
                 implementation it is only assumed that the four
                 elementary arithmetic operations are performed with a
                 certain number of correct digits of the function value.
                 The interval routines are constructed out of the point
                 routines considering the monotonicity behaviour of the
                 functions. The ambiguity of the complex functions is
                 briefly discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Karlsruhe Univ., West Germany",
  author-dates = "1952--2014 (WK)",
  classification = "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  confdate =     "30 Sept.-2 Oct. 1987",
  conflocation = "Karlsruhe, West Germany",
  confsponsor =  "Karlsruhe Univ.; GAMM Committee",
  fjournal =     "Computing. Supplementum",
  issue =        "no.6 p. 185-212",
  keywords =     "Approximation errors; Dynamic accuracy; Error formula;
                 Interval arguments; Inverse standard functions;
                 Monotonicity behaviour; Rounding errors",
  pubcountry =   "Austria",
  thesaurus =    "Error analysis; Function approximation",
}


bibtype: article
filename: elefunt.bib
label: Laforgia:1988:MRI
author: Andrea Laforgia and Silvana Sismondi
title: Monotonicity results and inequalities for the gamma and error functions
journal: j-J-COMPUT-APPL-MATH
volume: 23
number: 1
pages: 25--33
month: jul
monthnumber: 7
year: 1988
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:20:39 MST 2017
bibtimestamp: 2017.02.25 12:20:39 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042788903287
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Andrea Laforgia and Silvana Sismondi
rawtitle: Monotonicity results and inequalities for the gamma and error functions
entry:
@Article{Laforgia:1988:MRI,
  author =       "Andrea Laforgia and Silvana Sismondi",
  title =        "Monotonicity results and inequalities for the gamma
                 and error functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "23",
  number =       "1",
  pages =        "25--33",
  month =        jul,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:39 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042788903287",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lembarki:1988:CAL
author: Alami Lembarki
title: Convergence acceleration of limit $k$-periodic continued fractions
journal: j-APPL-NUM-MATH
volume: 4
number: 2--4
pages: 337--349
month: jun
monthnumber: 6
year: 1988
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B05 (40A15)
MRnumber: 89j:65012
MRreviewer: Thomas A. Atchison
bibdate: Sat Feb 8 10:09:54 MST 1997
bibtimestamp: 1997.02.08 10:09:54 MST
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Alami Lembarki
rawtitle: Convergence acceleration of limit $k$-periodic continued fractions
bibsource:
https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Lembarki:1988:CAL,
  author =       "Alami Lembarki",
  title =        "Convergence acceleration of limit $k$-periodic
                 continued fractions",
  journal =      j-APPL-NUM-MATH,
  volume =       "4",
  number =       "2--4",
  pages =        "337--349",
  month =        jun,
  year =         "1988",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "89j:65012",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: incollection
filename: elefunt.bib
label: Levrie:1988:CAM
author: Paul Levrie and Robert Piessens
booktitle: Nonlinear numerical methods and rational approximation (Wilrijk, 1987)
title: Convergence acceleration for Miller's algorithm
volume: 43
publisher: Reidel
address: Dordrecht, The Netherlands
pages: 349--370
year: 1988
MRclass: 65B10 (26C15 39A10)
MRnumber: 1005368 (90m:65012)
MRreviewer: Pierre Hillion
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 ???
series: Math. Appl.
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: Paul Levrie and Robert Piessens
rawbooktitle: {Nonlinear numerical methods and rational approximation (Wilrijk, 1987)}
rawtitle: Convergence acceleration for {Miller}'s algorithm
entry:
@InCollection{Levrie:1988:CAM,
  author =       "Paul Levrie and Robert Piessens",
  booktitle =    "{Nonlinear numerical methods and rational
                 approximation (Wilrijk, 1987)}",
  title =        "Convergence acceleration for {Miller}'s algorithm",
  volume =       "43",
  publisher =    "Reidel",
  address =      "Dordrecht, The Netherlands",
  pages =        "349--370",
  year =         "1988",
  MRclass =      "65B10 (26C15 39A10)",
  MRnumber =     "1005368 (90m:65012)",
  MRreviewer =   "Pierre Hillion",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Math. Appl.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Lou:1988:ETR
author: Lou van den Dries
title: On the elementary theory of restricted elementary functions
journal: j-J-SYMBOLIC-LOGIC
volume: 53
number: 3
pages: 796--808
year: 1988
CODEN: JSYLA6
ISSN: 0022-4812 (print), 1943-5886 (electronic) OR 00224812 (print), 19435886 (electronic)
ISSNL: 0022-4812 OR 00224812
MRclass: 03C65 (03C40 03C68 12L12)
MRnumber: 89i:03074
MRreviewer: M. Yasuhara
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: Journal of Symbolic Logic
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/euclid.jsl; http://www.jstor.org/journal/jsymboliclogic
rawauthor: Lou van den Dries
rawtitle: On the elementary theory of restricted elementary functions
entry:
@Article{Lou:1988:ETR,
  author =       "Lou van den Dries",
  title =        "On the elementary theory of restricted elementary
                 functions",
  journal =      j-J-SYMBOLIC-LOGIC,
  volume =       "53",
  number =       "3",
  pages =        "796--808",
  year =         "1988",
  CODEN =        "JSYLA6",
  ISSN =         "0022-4812 (print), 1943-5886 (electronic)",
  ISSN-L =       "0022-4812",
  MRclass =      "03C65 (03C40 03C68 12L12)",
  MRnumber =     "89i:03074",
  MRreviewer =   "M. Yasuhara",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Logic",
  journal-URL =  "http://projecteuclid.org/euclid.jsl;
                 http://www.jstor.org/journal/jsymboliclogic",
}


bibtype: phdthesis
filename: elefunt.bib
label: Marsaglia:1988:CES
author: John Christopher Winston Marsaglia
title: Computer Evaluation of the special functions of probability and statistics
type: Ph.D. Dissertation
school: Department of Computer Science, Washington State University
address: Pullman, WA, USA
pages: vii + 79
month: aug
monthnumber: 8
year: 1988
bibdate: Wed Jun 22 07:17:49 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.06.22 07:17:49 ???
acknowledgement: ack-nhfb
rawauthor: John Christopher Winston Marsaglia
rawtitle: Computer Evaluation of the special functions of probability and statistics
keywords:
$exp (x)$; $Phi (x)$; Bernoulli numbers; chi-square distribution; continued fraction; continuous Poisson distribution; Erlang distribution; exponential distribution; Gamma function; incomplete Gamma function; normal distribution; normal probability distribution; Poisson distribution; Stirling's approximation

entry:
@PhdThesis{Marsaglia:1988:CES,
  author =       "John Christopher Winston Marsaglia",
  title =        "Computer Evaluation of the special functions of
                 probability and statistics",
  type =         "{Ph.D.} Dissertation",
  school =       "Department of Computer Science, Washington State
                 University",
  address =      "Pullman, WA, USA",
  pages =        "vii + 79",
  month =        aug,
  year =         "1988",
  bibdate =      "Wed Jun 22 07:17:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "$\exp(x)$; $\Phi(x)$; Bernoulli numbers; chi-square
                 distribution; continued fraction; continuous Poisson
                 distribution; Erlang distribution; exponential
                 distribution; Gamma function; incomplete Gamma
                 function; normal distribution; normal probability
                 distribution; Poisson distribution; Stirling's
                 approximation",
}


bibtype: article
filename: elefunt.bib
label: Milone:1988:EDF
author: L. A. Milone and A. A. E. Milone
title: Evaluation of Dawson's function
journal: j-ASTROPHYS-SPACE-SCI
volume: 147
number: 1
pages: 189--191
year: 1988
CODEN: APSSBE
DOI: https://doi.org/10.1007/bf00656618
ISSN: 0004-640X (print), 1572-946X (electronic) OR 0004640X (print), 1572946X (electronic)
ISSNL: 0004-640X OR 0004640X
bibdate: Sat Feb 17 11:54:06 2024
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.17 11:54:06 ???
fjournal: Astrophysics and Space Science
acknowledgement: ack-nhfb
ajournal: Astrophys. Space Sci.
journalURL: http://link.springer.com/journal/10509
rawauthor: L. A. Milone and A. A. E. Milone
rawtitle: Evaluation of {Dawson}'s function
entry:
@Article{Milone:1988:EDF,
  author =       "L. A. Milone and A. A. E. Milone",
  title =        "Evaluation of {Dawson}'s function",
  journal =      j-ASTROPHYS-SPACE-SCI,
  volume =       "147",
  number =       "1",
  pages =        "189--191",
  year =         "1988",
  CODEN =        "APSSBE",
  DOI =          "https://doi.org/10.1007/bf00656618",
  ISSN =         "0004-640X (print), 1572-946X (electronic)",
  ISSN-L =       "0004-640X",
  bibdate =      "Sat Feb 17 11:54:06 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Astrophys. Space Sci.",
  fjournal =     "Astrophysics and Space Science",
  journal-URL =  "http://link.springer.com/journal/10509",
}


bibtype: article
filename: elefunt.bib
label: Mimachi:1988:PRI
author: Katsuhisa Mimachi
title: A proof of Ramanujan's identity by use of loop integrals
journal: j-SIAM-J-MATH-ANA
volume: 19
number: 6
pages: 1490--1493
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: Katsuhisa Mimachi
rawtitle: A proof of {Ramanujan}'s identity by use of loop integrals
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

entry:
@Article{Mimachi:1988:PRI,
  author =       "Katsuhisa Mimachi",
  title =        "A proof of {Ramanujan}'s identity by use of loop
                 integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "19",
  number =       "6",
  pages =        "1490--1493",
  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 =        "58904",
  catcode =      "G.1.9; G.1.2; F.2.2",
  CRclass =      "G.1.9 Integral Equations; G.1.9 Integro-differential
                 equations; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; 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",
  fjournal =     "SIAM Journal on Mathematical Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1988-13744",
  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",
}


bibtype: article
filename: elefunt.bib
label: Muroi:1988:ECR
author: Kazuo Muroi
title: Extraction of Cube Roots in Babylonian Mathematics
journal: j-CENTAURUS
volume: 31
number: 3
pages: 181--188
month: oct
monthnumber: 10
year: 1988
CODEN: CENTA4
DOI: https://doi.org/10.1111/j.1600-0498.1988.tb00736.x
ISSN: 0008-8994 (print), 1600-0498 (electronic) OR 00088994 (print), 16000498 (electronic)
ISSNL: 0008-8994 OR 00088994
bibdate: Sat Jul 27 18:43:36 MDT 2013
bibtimestamp: 2013.07.27 18:43:36 MDT
fjournal: Centaurus: An International Journal of the History of Science and its Cultural Aspects
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1600-0498/
onlinedate: 26 Jul 2007
rawauthor: Kazuo Muroi
rawtitle: Extraction of Cube Roots in {Babylonian} Mathematics
bibsource:
https://www.math.utah.edu/pub/tex/bib/centaurus.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Muroi:1988:ECR,
  author =       "Kazuo Muroi",
  title =        "Extraction of Cube Roots in {Babylonian} Mathematics",
  journal =      j-CENTAURUS,
  volume =       "31",
  number =       "3",
  pages =        "181--188",
  month =        oct,
  year =         "1988",
  CODEN =        "CENTA4",
  DOI =          "https://doi.org/10.1111/j.1600-0498.1988.tb00736.x",
  ISSN =         "0008-8994 (print), 1600-0498 (electronic)",
  ISSN-L =       "0008-8994",
  bibdate =      "Sat Jul 27 18:43:36 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/centaurus.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centaurus: An International Journal of the History of
                 Science and its Cultural Aspects",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1600-0498/",
  onlinedate =   "26 Jul 2007",
}


bibtype: book
filename: elefunt.bib
label: Nikiforov:1988:SFM
author: Arnol'd F. Nikiforov and Vasilij B. Uvarov
title: Special functions of mathematical physics: a unified introduction with applications
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: xviii + 427
year: 1988
ISBN: 3-7643-3183-6, 0-8176-3183-6 OR 3764331836, 0817631836
ISBN13: 978-3-7643-3183-2, 978-0-8176-3183-3 OR 9783764331832, 9780817631833
LCCN: QC20.7.F87 N692e
bibdate: Sat Oct 30 18:34:41 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.gbv.de:20011/gvk
bibtimestamp: 2010.10.30 18:34:41 MDT
note: Translated from the Russian by Ralph P. Boas.
URL: http://www.gbv.de/dms/hbz/toc/ht002696178
acknowledgement: ack-nhfb
rawauthor: Arnol'd F. Nikiforov and Vasilij B. Uvarov
rawnote: Translated from the Russian by Ralph P. Boas.
rawtitle: Special functions of mathematical physics: a unified introduction with applications
entry:
@Book{Nikiforov:1988:SFM,
  author =       "Arnol'd F. Nikiforov and Vasilij B. Uvarov",
  title =        "Special functions of mathematical physics: a unified
                 introduction with applications",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xviii + 427",
  year =         "1988",
  ISBN =         "3-7643-3183-6, 0-8176-3183-6",
  ISBN-13 =      "978-3-7643-3183-2, 978-0-8176-3183-3",
  LCCN =         "QC20.7.F87 N692e",
  bibdate =      "Sat Oct 30 18:34:41 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.gbv.de:20011/gvk",
  note =         "Translated from the Russian by Ralph P. Boas.",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002696178",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Olver:1988:EBL
author: F. W. J. Olver
title: Error Bounds for Linear Recurrence Relations
journal: j-MATH-COMPUT
volume: 50
number: 182
pages: 481--499
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: 65Q05 (39A10 65G05)
MRnumber: 89e:65146
MRreviewer: B. Choczewski
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: B0290B (Error analysis in numerical methods); C4110 (Error analysis in numerical methods)
corpsource: Maryland Univ., College Park, MD, USA
journalURL: http://www.ams.org/mcom/
treatment: T Theoretical or Mathematical
rawauthor: F. W. J. Olver
rawtitle: Error Bounds for Linear Recurrence Relations
keywords:
a posteriori methods; analysis; Bessel function; bounds; computational complexity; difference equations; error; homogeneous second order; Legendre function; linear recurrence relations; monotonic systems; numerical examples; O(r) arithmetic operations; oscillatory systems; realistic error; relations; rounded interval arithmetic

entry:
@Article{Olver:1988:EBL,
  author =       "F. W. J. Olver",
  title =        "Error Bounds for Linear Recurrence Relations",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "182",
  pages =        "481--499",
  month =        apr,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65Q05 (39A10 65G05)",
  MRnumber =     "89e:65146",
  MRreviewer =   "B. Choczewski",
  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 =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Maryland Univ., College Park, MD, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "a posteriori methods; analysis; Bessel function;
                 bounds; computational complexity; difference equations;
                 error; homogeneous second order; Legendre function;
                 linear recurrence relations; monotonic systems;
                 numerical examples; O(r) arithmetic operations;
                 oscillatory systems; realistic error; relations;
                 rounded interval arithmetic",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Polyak:1988:SOM
author: R. A. Polyak
title: Smooth optimization methods for minimax problems
journal: j-SIAM-J-CONTROL-OPTIM
volume: 26
number: 6
pages: 1274--1286
month: nov
monthnumber: 11
year: 1988
CODEN: SJCODC
ISSN: 0363-0129 (print), 1095-7138 (electronic) OR 03630129 (print), 10957138 (electronic)
ISSNL: 0363-0129 OR 03630129
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 Control and Optimization
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sicon
rawauthor: R. A. Polyak
rawtitle: Smooth optimization methods for minimax problems
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

entry:
@Article{Polyak:1988:SOM,
  author =       "R. A. Polyak",
  title =        "Smooth optimization methods for minimax problems",
  journal =      j-SIAM-J-CONTROL-OPTIM,
  volume =       "26",
  number =       "6",
  pages =        "1274--1286",
  month =        nov,
  year =         "1988",
  CODEN =        "SJCODC",
  ISSN =         "0363-0129 (print), 1095-7138 (electronic)",
  ISSN-L =       "0363-0129",
  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 =        "57989",
  catcode =      "G.1.6; G.1.2; F.2.1; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2
                 Approximation; G.1.2 Minimax approximation and
                 algorithms; F.2.1 Numerical Algorithms and Problems;
                 F.2.1 Computation of transforms; G.1.2 Approximation;
                 G.1.2 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "SIAM Journal on Control and Optimization",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13621",
  journal-URL =  "http://epubs.siam.org/sicon",
  journalabbrev = "SIAM J. Control Optim.",
  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; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}


bibtype: incollection
filename: elefunt.bib
label: Powell:1988:RBF
author: J. D. Powell
editor: D. F. (David Francis) Griffiths and G. A. Watson
booktitle: Numerical analysis 1987
title: Radial basis function approximations to polynomials
volume: 170
publisher: Longman, Inc.
address: New York, NY, USA
pages: 223--241
year: 1988
ISBN: 0-582-02157-X OR 058202157X
ISBN13: 978-0-582-02157-0 OR 9780582021570
LCCN: QA297.N828 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: Pitman research notes in mathematics series
subject: G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.3 PROBABILITY AND STATISTICS
acknowledgement: ack-nhfb
bookpages: 300
rawauthor: J. D. Powell
rawbooktitle: Numerical analysis 1987
raweditor: D. F. (David Francis) Griffiths and G. A. Watson
rawtitle: Radial basis function approximations to polynomials
entry:
@InCollection{Powell:1988:RBF,
  author =       "J. D. Powell",
  editor =       "D. F. (David Francis) Griffiths and G. A. Watson",
  booktitle =    "Numerical analysis 1987",
  title =        "Radial basis function approximations to polynomials",
  volume =       "170",
  publisher =    "Longman, Inc.",
  address =      "New York, NY, USA",
  bookpages =    "300",
  pages =        "223--241",
  year =         "1988",
  ISBN =         "0-582-02157-X",
  ISBN-13 =      "978-0-582-02157-0",
  LCCN =         "QA297.N828 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\$54.95",
  series =       "Pitman research notes in mathematics series",
  acknowledgement = ack-nhfb,
  bibno =        "54996",
  catcode =      "G.1.2; G.1.2; G.1.9; G.1.1; G.3; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation; G.1.9 Integral
                 Equations; G.1.9 Integro-differential equations; G.1.1
                 Interpolation; G.1.1 Spline and piecewise polynomial
                 interpolation; G.3 Statistical computing; G.1.7
                 Ordinary Differential Equations; G.1.7 Convergence and
                 stability",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations, Integro-differential
                 equations; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation; Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Statistical computing;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability",
  genterm =      "algorithms; performance",
  guideno =      "1988-01246",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.3 PROBABILITY AND STATISTICS",
  waffil =       "Univ. of Dundee; Univ. of Dundee",
}


