# bibtab

bibtype: misc
filename: elefunt.bib
label: Kahan:1999:SRD
author: W. Kahan
title: Square Root Without Division
pages: 3
day: 23
month: feb
monthnumber: 2
year: 1999
bibdate: Mon Apr 25 18:01:49 2005
bibtimestamp: 2005.04.25 18:01:49 ???
URL: http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: W. Kahan
rawtitle: Square Root Without Division
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

entry:
@Misc{Kahan:1999:SRD,
  author =       "W. Kahan",
  title =        "Square Root Without Division",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "23",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:01:49 2005",
  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 =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Krukier:1999:CAT
author: L. A. Krukier
journal: j-APPL-NUM-MATH
volume: 30
number: 2--3
pages: 281--290
day: 10
month: jun
monthnumber: 6
year: 1999
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Wed Jul 28 14:37:31 MDT 1999
bibtimestamp: 1999.07.28 14:37:31 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: L. A. Krukier
title:
Convergence acceleration of triangular iterative methods based on the skew-symmetric part of the matrix

bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981

rawtitle:
Convergence acceleration of triangular iterative methods based on the skew-symmetric part of the matrix

entry:
@Article{Krukier:1999:CAT,
  author =       "L. A. Krukier",
  title =        "Convergence acceleration of triangular iterative
                 methods based on the skew-symmetric part of the
                 matrix",
  journal =      j-APPL-NUM-MATH,
  volume =       "30",
  number =       "2--3",
  pages =        "281--290",
  day =          "10",
  month =        jun,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Wed Jul 28 14:37:31 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981",
  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: Kzaz:1999:CAG
author: M. Kzaz
title: Convergence acceleration of the Gauss--Laguerre quadrature formula
journal: j-APPL-NUM-MATH
volume: 29
number: 2
pages: 201--220
day: 1
month: feb
monthnumber: 2
year: 1999
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
bibdate: Wed Jul 28 14:37:22 MDT 1999
bibtimestamp: 1999.07.28 14:37:22 MDT
URL: http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: M. Kzaz
rawtitle: Convergence acceleration of the {Gauss--Laguerre} quadrature formula
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Kzaz:1999:CAG,
  author =       "M. Kzaz",
  title =        "Convergence acceleration of the {Gauss--Laguerre}
                 quadrature formula",
  journal =      j-APPL-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "201--220",
  day =          "1",
  month =        feb,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Wed Jul 28 14:37:22 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf",
  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: Lang:1999:VHR
author: T. Lang and P. Montuschi
title: Very high radix square root with prescaling and rounding and a combined division / square root unit
journal: j-IEEE-TRANS-COMPUT
volume: 48
number: 8
pages: 827--841
month: aug
monthnumber: 8
year: 1999
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.795124
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. Lang and P. Montuschi
rawtitle:
Very high radix square root with prescaling and rounding and a combined division\slash square root unit

entry:
@Article{Lang:1999:VHR,
  author =       "T. Lang and P. Montuschi",
  title =        "Very high radix square root with prescaling and
                 rounding and a combined division\slash square root
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "827--841",
  month =        aug,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795124",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An algorithm for square root with prescaling and
                 selection by rounding is developed and combined with a
                 similar scheme for division. Since division is usually
                 more frequent than square root, the main concern of the
                 combined implementation is to \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lee:1999:STS
author: Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and Seung-Ho Hwang
booktitle: 6th International Conference on VLSI and CAD: ICVC '99
title: Self-timed shared division and square-root implementation using full redundant signed digit numbers
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 541--544
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and Seung-Ho Hwang
rawbooktitle: 6th International Conference on {VLSI} and {CAD}: {ICVC '99}
rawtitle: Self-timed shared division and square-root implementation using full redundant signed digit numbers
entry:
@InProceedings{Lee:1999:STS,
  author =       "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
                 Seung-Ho Hwang",
  booktitle =    "6th International Conference on {VLSI} and {CAD}:
                 {ICVC '99}",
  title =        "Self-timed shared division and square-root
                 implementation using full redundant signed digit
                 numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "541--544",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A radix-$2$ square root implementation for self-timed
                 dividers using redundant signed-digit (RSD) adders is
                 presented. In this method, two self-timed RSD adder
                 stages are used for each result bit selection. A very
                 efficient and simple result bit \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:1999:DDM
author: Daniel W. Lozier and B. R. Miller and B. V. Saunders
title: Design of a Digital Mathematical Library for Science, Technology and Education
crossref: IEEE:1999:PIF
pages: 118--128
year: 1999
bibdate: Fri Jul 09 06:33:35 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:33:35 ???
URL: http://dlmf.nist.gov/about/publications/nistir6297.ps.gz
remark: Preprint: NISTIR 6297, Feb. 1999, 13 pages
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier and B. R. Miller and B. V. Saunders
rawtitle: Design of a Digital Mathematical Library for Science, Technology and Education
entry:
@InProceedings{Lozier:1999:DDM,
  author =       "Daniel W. Lozier and B. R. Miller and B. V. Saunders",
  title =        "Design of a Digital Mathematical Library for Science,
                 Technology and Education",
  crossref =     "IEEE:1999:PIF",
  pages =        "118--128",
  year =         "1999",
  bibdate =      "Fri Jul 09 06:33:35 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz",
  acknowledgement = ack-nhfb,
  remark =       "Preprint: NISTIR 6297, Feb. 1999, 13 pages",
}


bibtype: article
filename: elefunt.bib
label: Morita:1999:CEI
author: T. Morita
title: Calculation of the elliptic integrals of the first and second kinds with complex modulus
journal: j-NUM-MATH
volume: 82
number: 4
pages: 677--688
month: jun
monthnumber: 6
year: 1999
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 10:45:11 MDT 1999
bibtimestamp: 1999.10.18 10:45:11 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: T. Morita
rawtitle: Calculation of the elliptic integrals of the first and second kinds with complex modulus
bibsource:
http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm; http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf

entry:
@Article{Morita:1999:CEI,
  author =       "T. Morita",
  title =        "Calculation of the elliptic integrals of the first and
                 second kinds with complex modulus",
  journal =      j-NUM-MATH,
  volume =       "82",
  number =       "4",
  pages =        "677--688",
  month =        jun,
  year =         "1999",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 10:45:11 MDT 1999",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm;
                 http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Muller:1999:CAT
author: J. Muller
title: Convergence acceleration of Taylor sections by convolution
journal: j-CONST-APPROX
volume: 15
number: 4
pages: 523--536
year: 1999
DOI: https://doi.org/10.1007/s003659900120
ISSN: 0176-4276 (print), 1432-0940 (electronic) OR 01764276 (print), 14320940 (electronic)
ISSNL: 0176-4276 OR 01764276
MRclass: 41A58 (30E10)
MRnumber: 1702803 (2000i:41040)
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: Constructive Approximation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/365
rawauthor: J. M{\"u}ller
rawtitle: Convergence acceleration of {Taylor} sections by convolution
entry:
@Article{Muller:1999:CAT,
  author =       "J. M{\"u}ller",
  title =        "Convergence acceleration of {Taylor} sections by
                 convolution",
  journal =      j-CONST-APPROX,
  volume =       "15",
  number =       "4",
  pages =        "523--536",
  year =         "1999",
  DOI =          "https://doi.org/10.1007/s003659900120",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "41A58 (30E10)",
  MRnumber =     "1702803 (2000i:41040)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  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",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Muroi:1999:ESR
author: Kazuo Muroi
title: Extraction of square roots in Babylonian mathematics
journal: j-HIST-SCI-2
volume: 9
number: 2
pages: 127--133
month: nov
monthnumber: 11
year: 1999
CODEN: HISCDU
ISSN: 0285-4821 OR 02854821
ISSNL: 0285-4821 OR 02854821
MRclass: 01A17
MRnumber: 1762167
MRreviewer: Bruno Poizat
bibdate: Sat Oct 6 17:22:25 2018
bibtimestamp: 2018.10.06 17:22:25 ???
acknowledgement: ack-nhfb
journalURL: http://hssj.info/
rawauthor: Kazuo Muroi
rawtitle: Extraction of square roots in {Babylonian} mathematics
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/histscijpn.bib

fjournal:
Historia Scientiarum. Second Series. International Journal of the History of Science Society of Japan

entry:
@Article{Muroi:1999:ESR,
  author =       "Kazuo Muroi",
  title =        "Extraction of square roots in {Babylonian}
                 mathematics",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "127--133",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A17",
  MRnumber =     "1762167",
  MRreviewer =   "Bruno Poizat",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  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/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Nannarelli:1999:LPR
author: A. Nannarelli and T. Lang
booktitle: (ICCD '99) International Conference on Computer Design
title: Low-power radix-$4$ combined division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 236--242
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Nannarelli and T. Lang
rawbooktitle: {(ICCD '99)} International Conference on Computer Design
rawtitle: Low-power radix-$4$ combined division and square root
entry:
@InProceedings{Nannarelli:1999:LPR,
  author =       "A. Nannarelli and T. Lang",
  booktitle =    "{(ICCD '99)} International Conference on Computer
                 Design",
  title =        "Low-power radix-$4$ combined division and square
                 root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "236--242",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Because of the similarities in the algorithm it is
                 quite common to implement division and square root in
                 the same unit. The purpose of this work is to implement
                 a low-power combined radix-$4$ division and square root
                 floating-point double precision \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Oberman:1999:FPD
author: S. F. Oberman
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 106--115
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: S. F. Oberman
title:
Floating point division and square root algorithms and implementation in the AMD-K7TM microprocessor

URL:
http://euler.ecs.umass.edu/paper/final/paper-139.pdf; http://euler.ecs.umass.edu/paper/final/paper-139.ps

rawtitle:
Floating point division and square root algorithms and implementation in the {AMD-K7{\TM}} microprocessor

entry:
@InProceedings{Oberman:1999:FPD,
  author =       "S. F. Oberman",
  title =        "Floating point division and square root algorithms and
                 implementation in the {AMD-K7{\TM}} microprocessor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "106--115",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-139.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "This paper presents the AMD-K7 IEEE 754 and $\times$87
                 compliant floating point division and square root
                 algorithms and implementation. The AMD-K7 processor
                 employs an iterative implementation of a series
                 expansion to converge quadratically to the \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Parhami:1999:ALT
author: B. Parhami
booktitle: Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers, 1999
title: Analysis of the lookup table size for square-rooting
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1327--1330
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: B. Parhami
rawbooktitle: Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers, 1999
rawtitle: Analysis of the lookup table size for square-rooting
entry:
@InProceedings{Parhami:1999:ALT,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Analysis of the lookup table size for square-rooting",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1327--1330",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Convergence methods are widely used for division,
                 reciprocation, and square-rooting. With such methods,
                 it is common to use an initial table lookup step for
                 obtaining an approximate result that leads to faster
                 convergence. In the case of division \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Russinoff:1999:MCP
author: David M. Russinoff
title: A mechanically checked proof of correctness of the AMD K5 floating point square root microcode
journal: j-FORM-METHODS-SYST-DES
volume: 14
number: 1
pages: 75--125
month: jan
monthnumber: 1
year: 1999
CODEN: FMSDE6
ISSN: 0925-9856 (print), 1572-8102 (electronic) OR 09259856 (print), 15728102 (electronic)
ISSNL: 0925-9856 OR 09259856
bibdate: Sat Jun 02 07:51:51 2001
bibtimestamp: 2001.06.02 07:51:51 ???
note: Special issue on arithmetic circuits.
URL: http://www.wkap.nl/jrnltoc.htm/0925-9856; http://www.wkap.nl/oasis.htm/194808
fjournal: Formal Methods in System Design
acknowledgement: ack-nhfb
rawauthor: David M. Russinoff
rawnote: Special issue on arithmetic circuits.
rawtitle: A mechanically checked proof of correctness of the {AMD K5} floating point square root microcode
entry:
@Article{Russinoff:1999:MCP,
  author =       "David M. Russinoff",
  title =        "A mechanically checked proof of correctness of the
                 {AMD K5} floating point square root microcode",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "75--125",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 07:51:51 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special issue on arithmetic circuits.",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194808",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
}


bibtype: article
filename: elefunt.bib
label: Schraudolph:1999:FCA
author: N. N. Schraudolph
title: A Fast, Compact Approximation of the Exponential Function
journal: j-NEURAL-COMP
volume: 11
number: 4
pages: 853--862
day: 1
month: may
monthnumber: 5
year: 1999
CODEN: NEUCEB
DOI: https://doi.org/10.1162/089976699300016467
ISSN: 0899-7667 (print), 1530-888x (electronic) OR 08997667 (print), 1530888x (electronic)
ISSNL: 0899-7667 OR 08997667
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
URL: https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016467
fjournal: Neural Computation
acknowledgement: ack-nhfb
journalURL: http://www.mitpressjournals.org/loi/neco
rawauthor: N. N. Schraudolph
rawtitle: A Fast, Compact Approximation of the Exponential Function
entry:
@Article{Schraudolph:1999:FCA,
  author =       "N. N. Schraudolph",
  title =        "A Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "11",
  number =       "4",
  pages =        "853--862",
  day =          "1",
  month =        may,
  year =         "1999",
  CODEN =        "NEUCEB",
  DOI =          "https://doi.org/10.1162/089976699300016467",
  ISSN =         "0899-7667 (print), 1530-888x (electronic)",
  ISSN-L =       "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  URL =          "https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016467",
  acknowledgement = ack-nhfb,
  fjournal =     "Neural Computation",
  journal-URL =  "http://www.mitpressjournals.org/loi/neco",
  pagecount =    "10",
}


bibtype: article
filename: elefunt.bib
label: Schulte:1999:AEF
author: M. Schulte and J. Stine
title: Approximating Elementary Functions with Symmetric Bipartite Tables
journal: j-IEEE-TRANS-COMPUT
volume: 48
number: 8
pages: 842--847
year: 1999
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.795125
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Jun 24 20:20:58 2005
bibtimestamp: 2005.06.24 20:20:58 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Schulte and J. Stine
rawtitle: Approximating Elementary Functions with Symmetric Bipartite Tables
entry:
@Article{Schulte:1999:AEF,
  author =       "M. Schulte and J. Stine",
  title =        "Approximating Elementary Functions with Symmetric
                 Bipartite Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "842--847",
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795125",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 20:20:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
  acknowledgement = 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: Schulte:1999:ESO
author: M. J. Schulte and K. E. Wires
title: Efficient Second Order Approximations for Reciprocals and Square Roots
crossref: Luk:1999:PSA
volume: 3807
pages: 10--18
year: 1999
bibdate: Sun Mar 04 11:10:48 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:10:48 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and K. E. Wires
rawtitle: Efficient Second Order Approximations for Reciprocals and Square Roots
entry:
@InProceedings{Schulte:1999:ESO,
  author =       "M. J. Schulte and K. E. Wires",
  title =        "Efficient Second Order Approximations for Reciprocals
                 and Square Roots",
  crossref =     "Luk:1999:PSA",
  volume =       "3807",
  pages =        "10--18",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:10:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1999:HSI
author: Michael J. Schulte and Kent E. Wires
title: High-Speed Inverse Square Roots
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 124--131
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: Michael J. Schulte and Kent E. Wires
rawtitle: High-Speed Inverse Square Roots
URL:
http://euler.ecs.umass.edu/paper/final/paper-109.pdf; http://euler.ecs.umass.edu/paper/final/paper-109.ps

entry:
@InProceedings{Schulte:1999:HSI,
  author =       "Michael J. Schulte and Kent E. Wires",
  title =        "High-Speed Inverse Square Roots",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-109.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "Inverse square roots are used in several digital
                 signal processing, multimedia, and scientific computing
                 applications. This paper presents a high-speed method
                 for computing inverse square roots. This method uses a
                 table lookup, operand modification, \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Segura:1999:EGT
author: J. Segura and A. Gil
journal: j-COMP-PHYS-COMM
volume: 117
number: 3
pages: 250--262
day: 11
month: mar
monthnumber: 3
year: 1999
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00193-3
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:36 MST 2012
bibtimestamp: 2012.02.13 21:30:36 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465598001933
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Segura and A. Gil
title:
ELF and GNOME: Two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders

rawtitle:
{ELF} and {GNOME}: Two tiny codes to evaluate the real zeros of the {Bessel} functions of the first kind for real orders

entry:
@Article{Segura:1999:EGT,
  author =       "J. Segura and A. Gil",
  title =        "{ELF} and {GNOME}: Two tiny codes to evaluate the real
                 zeros of the {Bessel} functions of the first kind for
                 real orders",
  journal =      j-COMP-PHYS-COMM,
  volume =       "117",
  number =       "3",
  pages =        "250--262",
  day =          "11",
  month =        mar,
  year =         "1999",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00193-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598001933",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Seidel:1999:HSR
author: P.-M. Seidel
title: High-speed redundant reciprocal approximation
journal: j-INTEGRATION-VLSI-J
volume: 28
number: 1
pages: 1--12
month: sep
monthnumber: 9
year: 1999
CODEN: IVJODL
ISSN: 0167-9260 (print), 1872-7522 (electronic) OR 01679260 (print), 18727522 (electronic)
ISSNL: 0167-9260 OR 01679260
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Integration, the VLSI journal
acknowledgement: ack-nhfb
rawauthor: P.-M. Seidel
rawtitle: High-speed redundant reciprocal approximation
entry:
@Article{Seidel:1999:HSR,
  author =       "P.-M. Seidel",
  title =        "High-speed redundant reciprocal approximation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "28",
  number =       "1",
  pages =        "1--12",
  month =        sep,
  year =         "1999",
  CODEN =        "IVJODL",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  pagecount =    "12",
}


bibtype: article
filename: elefunt.bib
label: Stine:1999:STA
author: E. Stine and M. J. Schulte
title: The Symmetric Table Addition Method for Accurate Function Approximation
journal: j-J-VLSI-SIGNAL-PROC
volume: 21
number: 2
pages: 167--177
month: jun
monthnumber: 6
year: 1999
CODEN: JVSPED
ISSN: 0922-5773 (print), 1573-109x (electronic) OR 09225773 (print), 1573109x (electronic)
ISSNL: 0922-5773 OR 09225773
bibdate: Sun Mar 04 11:02:59 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:02:59 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf
fjournal: Journal of VLSI Signal Processing
acknowledgement: ack-nhfb
rawauthor: E. Stine and M. J. Schulte
rawtitle: The Symmetric Table Addition Method for Accurate Function Approximation
entry:
@Article{Stine:1999:STA,
  author =       "E. Stine and M. J. Schulte",
  title =        "The Symmetric Table Addition Method for Accurate
                 Function Approximation",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "21",
  number =       "2",
  pages =        "167--177",
  month =        jun,
  year =         "1999",
  CODEN =        "JVSPED",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sun Mar 04 11:02:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}


bibtype: inproceedings
filename: elefunt.bib
label: Story:1999:NAI
author: S. Story and P. T. P. Tang
title: New Algorithms for Improved Transcendental Functions on IA-64
crossref: Koren:1999:ISC
pages: 4--11
year: 1999
bibdate: Mon Feb 7 07:28:26 MST 2000
bibtimestamp: 2000.02.07 07:28:26 MST
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: S. Story and P. T. P. Tang
rawtitle: New Algorithms for Improved Transcendental Functions on {IA-64}
URL:
http://euler.ecs.umass.edu/paper/final/paper-118.pdf; http://euler.ecs.umass.edu/paper/final/paper-118.ps

entry:
@InProceedings{Story:1999:NAI,
  author =       "S. Story and P. T. P. Tang",
  title =        "New Algorithms for Improved Transcendental Functions
                 on {IA-64}",
  crossref =     "Koren:1999:ISC",
  pages =        "4--11",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-118.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
}


bibtype: book
filename: elefunt.bib
label: Suetin:1999:OPT
author: P. K. (Pavel Kondratevich) Suetin
title: Orthogonal Polynomials in Two Variables
volume: 3
publisher: Gordon and Breach Science Publishers
address: Amsterdam, The Netherlands
pages: xx + 348
year: 1999
ISBN: 90-5699-167-1 OR 9056991671
ISBN13: 978-90-5699-167-8 OR 9789056991678
LCCN: QA404.5 .S8813 1999
bibdate: Sat Oct 30 17:21:54 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:21:54 MDT
note: Translated from the Russian by E. V. Pankratiev.
series: Analytical methods and special functions
remark: Originally published in Russian in 1988 by Nauka, Moscow.
subject: Orthogonal polynomials
acknowledgement: ack-nhfb
rawauthor: P. K. (Pavel Kondratevich) Suetin
rawnote: Translated from the Russian by E. V. Pankratiev.
rawtitle: Orthogonal Polynomials in Two Variables
TOC:
Preface / ix Preface to the English Edition / xv Notation / xix I. General properties of polynomials orthogonal over a domain / 1 1. Polynomials in two variables orthogonal over a domain / 1 2. The existence theorem and criteria of orthogonality / 6 3. Algebraic properties / 10 4. Monic orthogonal polynomials / 18 5. Normal biorthogonal Systems / 24 6. Fourier series of orthogonal polynomials in two variables / 28 7. Fourier series for differentiable functions / 31 II. Some typical examples and special cases of orthogonality over a domain / 37 1. Different products of classical orthogonal polynomials / 37 2. Various cases of connection between orthogonality over a domain and orthogonality on an interval / 42 3. Some theorems in the case of a weight function with separating variables / 48 4. Conditions of interconnection between the weight function and the domain of orthogonality / 52 5. Examples of computations of weight function moments / 57 III. Classical Appell's orthogonal polynomials / 63 1. Rodrigues formula for Appell's polynomials / 63 2. Representation of the Appell polynomials via the hypergeometric function of two variables / 69 3. Differential equation for the Appell polynomials / 72 4. Orthogonality of eigenfunctions of the Appell equation / 75 5. Normal biorthogonal Appell System / 79 6. Series in the Appell polynomials / 83 IV. Admissible differential equation for polynomials orthogonal over a domain / 87 1. The main differential Operator and a theorem on orthogonality / 87 2. Admissibility conditions for the main differential equation / 92 3. Some examples and properties of admissible differential equations / 97 4. Affine transformations of the arguments of the main differential equation / 101 5. Transformation of the coefficients of the characteristic polynomial / 105 6. Normal forms of the admissible differential equation / 115 7. Normal forms when reducing the degree of the characteristic polynomial / 123 V. Potentially self-adjoint equation and Rodrigues formula / 131 1. Potentially self-adjoint Operators / 131 2. Admissible and potentially self-adjoint equations / 135 3. Rodrigues formula for polynomials orthogonal over a domain / 146 4. Weight functions and the Rodrigues formula in the most typical cases / 153 VI. Harmonic polynomials orthogonal over a domain / 163 1. Homogeneous harmonic polynomials / 163 2. An analogue of the Christoffel--Darboux formula / 169 3. Harmonic polynomials orthogonal in the unit disk / 173 4. Harmonic polynomials orthogonal over a domain in the general case / 176 5. Harmonic polynomials superorthogonal over a domain / 179 VII. Polynomials in two variables orthogonal on a contour / 187 1. Main definitions and the simplest properties / 187 2. Polynomials in two variables orthogonal on an algebraic curve / 191 3. Harmonic polynomials orthogonal on a contour / 196 4. Fourier series in harmonic polynomials orthogonal on a contour / 200 5. Harmonic polynomials superorthogonal on a contour / 206 6. Examples of superorthogonal Systems of harmonic polynomials / 213 VIII. Generalized orthogonal polynomials in two variables / 223 1. Main definitions and the simplest properties / 223 2. The existence theorem in the most general form / 228 3. Fourier series in generalized orthogonal polynomials in two variables / 233 4. Monic orthogonal polynomials under minimal conditions / 241 5. Generalized generating functions for monic orthogonal polynomials / 247 IX. Other results concerning the connection between orthogonal polynomials and differential equations / 253 1. Canonical admissible differential equation and monic orthogonal polynomials / 253 2. Necessary consistency conditions of the canonical Operator and the functional / 258 3. Sufficient conditions of consistency of the canonical Operator and the functional / 262 4. The deduction of the differential equation from the Pearson equation System / 268 5. An admissible partial differential equation of an arbitrary order / 276 X. Original results of T. Koornwinder / 285 1. Examples of the representation of polynomials orthogonal over a domain via the Jacobi polynomials / 285 2. Orthogonal polynomials in two conjugate complex variables / 291 3. The Chebyshev polynomials in two conjugate complex variables for the Steiner domain / 296 4. Another generalization of the Jacobi polynomials onto the case of two variables / 308 XI. Some recent results / 313 1. A new generalization of the Appell polynomials / 313 2. Some properties of the Koornwinder--Steiner polynomials / 318 3. A two-dimensional analogue of the Chebyshev--Laguerre polynomials / 319 Comments and Supplements / 323 References / 329 Author Index / 343 Subject Index / 345

rawTOC:
Preface / ix \\ Preface to the English Edition / xv \\ Notation / xix \\ I. General properties of polynomials orthogonal over a domain / 1 \\ 1. Polynomials in two variables orthogonal over a domain / 1 \\ 2. The existence theorem and criteria of orthogonality / 6 \\ 3. Algebraic properties / 10 \\ 4. Monic orthogonal polynomials / 18 \\ 5. Normal biorthogonal Systems / 24 \\ 6. Fourier series of orthogonal polynomials in two variables / 28 \\ 7. Fourier series for differentiable functions / 31 \\ II. Some typical examples and special cases of orthogonality over a domain / 37 \\ 1. Different products of classical orthogonal polynomials / 37 \\ 2. Various cases of connection between orthogonality over a domain and orthogonality on an interval / 42 \\ 3. Some theorems in the case of a weight function with separating variables / 48 \\ 4. Conditions of interconnection between the weight function and the domain of orthogonality / 52 \\ 5. Examples of computations of weight function moments / 57 \\ III. Classical Appell's orthogonal polynomials / 63 \\ 1. Rodrigues formula for Appell's polynomials / 63 \\ 2. Representation of the Appell polynomials via the hypergeometric function of two variables / 69 \\ 3. Differential equation for the Appell polynomials / 72 \\ 4. Orthogonality of eigenfunctions of the Appell equation / 75 \\ 5. Normal biorthogonal Appell System / 79 \\ 6. Series in the Appell polynomials / 83 \\ IV. Admissible differential equation for polynomials orthogonal over a domain / 87 \\ 1. The main differential Operator and a theorem on orthogonality / 87 \\ 2. Admissibility conditions for the main differential equation / 92 \\ 3. Some examples and properties of admissible differential equations / 97 \\ 4. Affine transformations of the arguments of the main differential equation / 101 \\ 5. Transformation of the coefficients of the characteristic polynomial / 105 \\ 6. Normal forms of the admissible differential equation / 115 \\ 7. Normal forms when reducing the degree of the characteristic polynomial / 123 \\ V. Potentially self-adjoint equation and Rodrigues formula / 131 \\ 1. Potentially self-adjoint Operators / 131 \\ 2. Admissible and potentially self-adjoint equations / 135 \\ 3. Rodrigues formula for polynomials orthogonal over a domain / 146 \\ 4. Weight functions and the Rodrigues formula in the most typical cases / 153 \\ VI. Harmonic polynomials orthogonal over a domain / 163 \\ 1. Homogeneous harmonic polynomials / 163 \\ 2. An analogue of the Christoffel--Darboux formula / 169 \\ 3. Harmonic polynomials orthogonal in the unit disk / 173 \\ 4. Harmonic polynomials orthogonal over a domain in the general case / 176 \\ 5. Harmonic polynomials superorthogonal over a domain / 179 \\ VII. Polynomials in two variables orthogonal on a contour / 187 \\ 1. Main definitions and the simplest properties / 187 \\ 2. Polynomials in two variables orthogonal on an algebraic curve / 191 \\ 3. Harmonic polynomials orthogonal on a contour / 196 \\ 4. Fourier series in harmonic polynomials orthogonal on a contour / 200 \\ 5. Harmonic polynomials superorthogonal on a contour / 206 \\ 6. Examples of superorthogonal Systems of harmonic polynomials / 213 \\ VIII. Generalized orthogonal polynomials in two variables / 223 \\ 1. Main definitions and the simplest properties / 223 \\ 2. The existence theorem in the most general form / 228 \\ 3. Fourier series in generalized orthogonal polynomials in two variables / 233 \\ 4. Monic orthogonal polynomials under minimal conditions / 241 \\ 5. Generalized generating functions for monic orthogonal polynomials / 247 \\ IX. Other results concerning the connection between orthogonal polynomials and differential equations / 253 \\ 1. Canonical admissible differential equation and monic orthogonal polynomials / 253 \\ 2. Necessary consistency conditions of the canonical Operator and the functional / 258 \\ 3. Sufficient conditions of consistency of the canonical Operator and the functional / 262 \\ 4. The deduction of the differential equation from the Pearson equation System / 268 \\ 5. An admissible partial differential equation of an arbitrary order / 276 \\ X. Original results of T. Koornwinder / 285 \\ 1. Examples of the representation of polynomials orthogonal over a domain via the Jacobi polynomials / 285 \\ 2. Orthogonal polynomials in two conjugate complex variables / 291 \\ 3. The Chebyshev polynomials in two conjugate complex variables for the Steiner domain / 296 \\ 4. Another generalization of the Jacobi polynomials onto the case of two variables / 308 \\ XI. Some recent results / 313 \\ 1. A new generalization of the Appell polynomials / 313 \\ 2. Some properties of the Koornwinder--Steiner polynomials / 318 \\ 3. A two-dimensional analogue of the Chebyshev--Laguerre polynomials / 319 \\ Comments and Supplements / 323 \\ References / 329 \\ Author Index / 343 \\ Subject Index / 345

entry:
@Book{Suetin:1999:OPT,
  author =       "P. K. (Pavel Kondratevich) Suetin",
  title =        "Orthogonal Polynomials in Two Variables",
  volume =       "3",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "xx + 348",
  year =         "1999",
  ISBN =         "90-5699-167-1",
  ISBN-13 =      "978-90-5699-167-8",
  LCCN =         "QA404.5 .S8813 1999",
  bibdate =      "Sat Oct 30 17:21:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Translated from the Russian by E. V. Pankratiev.",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in Russian in 1988 by Nauka,
                 Moscow.",
  subject =      "Orthogonal polynomials",
  tableofcontents = "Preface / ix \\
                 Preface to the English Edition / xv \\
                 Notation / xix \\
                 I. General properties of polynomials orthogonal over a
                 domain / 1 \\
                 1. Polynomials in two variables orthogonal over a
                 domain / 1 \\
                 2. The existence theorem and criteria of orthogonality
                 / 6 \\
                 3. Algebraic properties / 10 \\
                 4. Monic orthogonal polynomials / 18 \\
                 5. Normal biorthogonal Systems / 24 \\
                 6. Fourier series of orthogonal polynomials in two
                 variables / 28 \\
                 7. Fourier series for differentiable functions / 31 \\
                 II. Some typical examples and special cases of
                 orthogonality over a domain / 37 \\
                 1. Different products of classical orthogonal
                 polynomials / 37 \\
                 2. Various cases of connection between orthogonality
                 over a domain and orthogonality on an interval / 42 \\
                 3. Some theorems in the case of a weight function with
                 separating variables / 48 \\
                 4. Conditions of interconnection between the weight
                 function and the domain of orthogonality / 52 \\
                 5. Examples of computations of weight function moments
                 / 57 \\
                 III. Classical Appell's orthogonal polynomials / 63 \\
                 1. Rodrigues formula for Appell's polynomials / 63 \\
                 2. Representation of the Appell polynomials via the
                 hypergeometric function of two variables / 69 \\
                 3. Differential equation for the Appell polynomials /
                 72 \\
                 4. Orthogonality of eigenfunctions of the Appell
                 equation / 75 \\
                 5. Normal biorthogonal Appell System / 79 \\
                 6. Series in the Appell polynomials / 83 \\
                 IV. Admissible differential equation for polynomials
                 orthogonal over a domain / 87 \\
                 1. The main differential Operator and a theorem on
                 orthogonality / 87 \\
                 2. Admissibility conditions for the main differential
                 equation / 92 \\
                 3. Some examples and properties of admissible
                 differential equations / 97 \\
                 4. Affine transformations of the arguments of the main
                 differential equation / 101 \\
                 5. Transformation of the coefficients of the
                 characteristic polynomial / 105 \\
                 6. Normal forms of the admissible differential equation
                 / 115 \\
                 7. Normal forms when reducing the degree of the
                 characteristic polynomial / 123 \\
                 V. Potentially self-adjoint equation and Rodrigues
                 formula / 131 \\
                 1. Potentially self-adjoint Operators / 131 \\
                 2. Admissible and potentially self-adjoint equations /
                 135 \\
                 3. Rodrigues formula for polynomials orthogonal over a
                 domain / 146 \\
                 4. Weight functions and the Rodrigues formula in the
                 most typical cases / 153 \\
                 VI. Harmonic polynomials orthogonal over a domain / 163
                 \\
                 1. Homogeneous harmonic polynomials / 163 \\
                 2. An analogue of the Christoffel--Darboux formula /
                 169 \\
                 3. Harmonic polynomials orthogonal in the unit disk /
                 173 \\
                 4. Harmonic polynomials orthogonal over a domain in the
                 general case / 176 \\
                 5. Harmonic polynomials superorthogonal over a domain /
                 179 \\
                 VII. Polynomials in two variables orthogonal on a
                 contour / 187 \\
                 1. Main definitions and the simplest properties / 187
                 \\
                 2. Polynomials in two variables orthogonal on an
                 algebraic curve / 191 \\
                 3. Harmonic polynomials orthogonal on a contour / 196
                 \\
                 4. Fourier series in harmonic polynomials orthogonal on
                 a contour / 200 \\
                 5. Harmonic polynomials superorthogonal on a contour /
                 206 \\
                 6. Examples of superorthogonal Systems of harmonic
                 polynomials / 213 \\
                 VIII. Generalized orthogonal polynomials in two
                 variables / 223 \\
                 1. Main definitions and the simplest properties / 223
                 \\
                 2. The existence theorem in the most general form / 228
                 \\
                 3. Fourier series in generalized orthogonal polynomials
                 in two variables / 233 \\
                 4. Monic orthogonal polynomials under minimal
                 conditions / 241 \\
                 5. Generalized generating functions for monic
                 orthogonal polynomials / 247 \\
                 IX. Other results concerning the connection between
                 orthogonal polynomials and differential equations / 253
                 \\
                 1. Canonical admissible differential equation and monic
                 orthogonal polynomials / 253 \\
                 2. Necessary consistency conditions of the canonical
                 Operator and the functional / 258 \\
                 3. Sufficient conditions of consistency of the
                 canonical Operator and the functional / 262 \\
                 4. The deduction of the differential equation from the
                 Pearson equation System / 268 \\
                 5. An admissible partial differential equation of an
                 arbitrary order / 276 \\
                 X. Original results of T. Koornwinder / 285 \\
                 1. Examples of the representation of polynomials
                 orthogonal over a domain via the Jacobi polynomials /
                 285 \\
                 2. Orthogonal polynomials in two conjugate complex
                 variables / 291 \\
                 3. The Chebyshev polynomials in two conjugate complex
                 variables for the Steiner domain / 296 \\
                 4. Another generalization of the Jacobi polynomials
                 onto the case of two variables / 308 \\
                 XI. Some recent results / 313 \\
                 1. A new generalization of the Appell polynomials / 313
                 \\
                 2. Some properties of the Koornwinder--Steiner
                 polynomials / 318 \\
                 3. A two-dimensional analogue of the
                 Chebyshev--Laguerre polynomials / 319 \\
                 Comments and Supplements / 323 \\
                 References / 329 \\
                 Author Index / 343 \\
                 Subject Index / 345",
}


bibtype: article
filename: elefunt.bib
label: Vrahatis:1999:ESP
author: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
journal: j-COMP-PHYS-COMM
volume: 117
number: 3
pages: 290--290
day: 11
month: mar
monthnumber: 3
year: 1999
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00109-X
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:36 MST 2012
bibtimestamp: 2012.02.13 21:30:36 MST
note: See cite Vrahatis:1995:RPP.
URL: http://www.sciencedirect.com/science/article/pii/S001046559800109X
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A. Zafiropoulos and T. N. Grapsa
rawnote: See \cite{Vrahatis:1995:RPP}.
title:
Erratum to: booktitle RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions [Comput. Phys. Commun. bf 92 (1995) 252--266]

rawtitle:
Erratum to: {{\booktitle{RFSFNS: a portable package for the numerical determination of the number and the calculation of roots of Bessel functions}} [Comput. Phys. Commun. {\bf 92} (1995) 252--266]}

entry:
@Article{Vrahatis:1999:ESP,
  author =       "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
                 Zafiropoulos and T. N. Grapsa",
  title =        "Erratum to: {{\booktitle{RFSFNS: a portable package
                 for the numerical determination of the number and the
                 calculation of roots of Bessel functions}} [Comput.
                 Phys. Commun. {\bf 92} (1995) 252--266]}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "117",
  number =       "3",
  pages =        "290--290",
  day =          "11",
  month =        mar,
  year =         "1999",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00109-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Vrahatis:1995:RPP}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046559800109X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Vyridis:1999:ICA
author: D. G. Vyridis and S. D. Panteliou and I. N. Katz
title: An inverse convergence approach for arguments of Jacobian elliptic functions
journal: j-COMPUT-MATH-APPL
volume: 37
number: 2
pages: 21--26
month: jan
monthnumber: 1
year: 1999
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:56 MST 2017
bibtimestamp: 2017.03.01 21:48:56 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122198002508
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: D. G. Vyridis and S. D. Panteliou and I. N. Katz
rawtitle: An inverse convergence approach for arguments of {Jacobian} elliptic functions
entry:
@Article{Vyridis:1999:ICA,
  author =       "D. G. Vyridis and S. D. Panteliou and I. N. Katz",
  title =        "An inverse convergence approach for arguments of
                 {Jacobian} elliptic functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "37",
  number =       "2",
  pages =        "21--26",
  month =        jan,
  year =         "1999",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198002508",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Wieder:1999:ANH
author: Thomas Wieder
title: Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL
journal: j-TOMS
volume: 25
number: 2
pages: 240--250
month: jun
monthnumber: 6
year: 1999
CODEN: ACMSCU
DOI: https://doi.org/10.1145/317275.317284
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Oct 20 18:21:35 MDT 1999
bibsource: http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.20 18:21:35 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: Hankel transform; numerical analysis
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Thomas Wieder
rawtitle: {Algorithm 794}: Numerical {Hankel} transform by the {Fortran} program {HANKEL}
URL:
ftp://netlib.bell-labs.com/netlib/toms/794.gz; http://phase.etl.go.jp/netlib/toms/794; http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/; http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH; http://www.hensa.ac.uk/netlib/toms/794.gz; http://www.netlib.no/netlib/toms/794; http://www.netlib.org/toms/794

abstract:
The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.

subject:
Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computation of transforms

rawabstract:
The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.

entry:
@Article{Wieder:1999:ANH,
  author =       "Thomas Wieder",
  title =        "{Algorithm 794}: Numerical {Hankel} transform by the
                 {Fortran} program {HANKEL}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "240--250",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317284",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/794.gz;
                 http://phase.etl.go.jp/netlib/toms/794;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH;
                 http://www.hensa.ac.uk/netlib/toms/794.gz;
                 http://www.netlib.no/netlib/toms/794;
                 http://www.netlib.org/toms/794",
  abstract =     "The numerical evaluation of the Hankel transform poses
                 the problems of both infinite integration and Bessel
                 function calculation. Using the corresponding numerical
                 program routines from the literature, a Fortran program
                 has been written to perform the Hankel transform for
                 real functions, given either in analytical form as
                 subroutines or in discrete form as tabulated data.",
  accepted =     "February 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Hankel transform; numerical analysis",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Theory of
                 Computation --- Analysis of Algorithms and Problem
                 Complexity --- Numerical Algorithms and Problems
                 (F.2.1): Computation of transforms",
}


bibtype: techreport
filename: elefunt.bib
label: Zimmermann:1999:KSR
author: Paul Zimmermann
title: Karatsuba Square Root
type: Research Report
number: 3805
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 8
year: 1999
bibdate: Sun Sep 10 08:56:48 2006
bibtimestamp: 2006.09.10 08:56:48 ???
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
rawtitle: {Karatsuba} Square Root
URL:
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf; ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz; http://www.inria.fr/rrrt/rr-3805.html

abstract:
We exhibit an algorithm to compute the square-root with remainder of a $n$-word number in $ 3 / 2 $ word operations, where $ K(n) $ is the number of words operations to multiply two $n$-word numbers using Karatsuba's algorithm. If the remainder is not needed, the cost can be reduced to $ K(n) $ on average. This algorithm can be used for floating-point or polynomial computations too; although not optimal asymptotically, its simplicity gives a wide range of use, from about 50 to 1,000,000 digits, as shown by computer experiments.

rawabstract:
We exhibit an algorithm to compute the square-root with remainder of a $n$-word number in $ 3 / 2 $ word operations, where $ K(n) $ is the number of words operations to multiply two $n$-word numbers using Karatsuba's algorithm. If the remainder is not needed, the cost can be reduced to $ K(n) $ on average. This algorithm can be used for floating-point or polynomial computations too; although not optimal asymptotically, its simplicity gives a wide range of use, from about 50 to 1,000,000 digits, as shown by computer experiments.

entry:
@TechReport{Zimmermann:1999:KSR,
  author =       "Paul Zimmermann",
  title =        "{Karatsuba} Square Root",
  type =         "Research Report",
  number =       "3805",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "8",
  year =         "1999",
  bibdate =      "Sun Sep 10 08:56:48 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
                 http://www.inria.fr/rrrt/rr-3805.html",
  abstract =     "We exhibit an algorithm to compute the square-root
                 with remainder of a $n$-word number in $ 3 / 2 $ word
                 operations, where $ K(n) $ is the number of words
                 operations to multiply two $n$-word numbers using
                 Karatsuba's algorithm. If the remainder is not needed,
                 the cost can be reduced to $ K(n) $ on average. This
                 algorithm can be used for floating-point or polynomial
                 computations too; although not optimal asymptotically,
                 its simplicity gives a wide range of use, from about 50
                 to 1,000,000 digits, as shown by computer
                 experiments.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Alhargan:2000:ACA
author: Fayez A. Alhargan
title: Algorithms for the Computation of all Mathieu Functions of Integer Orders
journal: j-TOMS
volume: 26
number: 3
pages: 390--407
month: sep
monthnumber: 9
year: 2000
CODEN: ACMSCU
DOI: https://doi.org/10.1145/358407.358420
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Fayez A. Alhargan
rawtitle: Algorithms for the Computation of all {Mathieu} Functions of Integer Orders
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$ ).

rawabstract:
The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$ ).

entry:
@Article{Alhargan:2000:ACA,
  author =       "Fayez A. Alhargan",
  title =        "Algorithms for the Computation of all {Mathieu}
                 Functions of Integer Orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "390--407",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358420",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The paper presents methods for the computation of all
                 Mathieu functions of integer order, which cover a large
                 range of $n$ and $h$; previous algorithms were limited
                 to small values of $n$. The algorithms are given in
                 sufficient details to enable straightforward
                 implementation. The algorithms can handle a large range
                 of the order $n$ (0-200) and the parameter $h$ (0-4$n$
                 ).",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Alhargan:2000:ASC
author: Fayez A. Alhargan
title: Algorithm 804: subroutines for the computation of Mathieu functions of integer orders
journal: j-TOMS
volume: 26
number: 3
pages: 408--414
month: sep
monthnumber: 9
year: 2000
CODEN: ACMSCU
DOI: https://doi.org/10.1145/358407.358422
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Fayez A. Alhargan
rawtitle: {Algorithm 804}: subroutines for the computation of {Mathieu} functions of integer orders
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.

rawabstract:
Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.

entry:
@Article{Alhargan:2000:ASC,
  author =       "Fayez A. Alhargan",
  title =        "{Algorithm 804}: subroutines for the computation of
                 {Mathieu} functions of integer orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "408--414",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358422",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computer subroutines in C++ for computing Mathieu
                 functions of integer orders are described. The core
                 routines for computing Mathieu characteristic numbers
                 and Mathieu coefficients are described in details, the
                 rest of the subroutines are standard implementation of
                 the series summations for each function. The routines
                 can handle a large range of the order $n$ and the
                 parameter $h$.",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Anderson:2000:RAF
author: Stuart Anderson
title: Remark on Algorithm 723: Fresnel integrals
journal: j-TOMS
volume: 26
number: 4
pages: 617--617
month: dec
monthnumber: 12
year: 2000
CODEN: ACMSCU
DOI: https://doi.org/10.1145/365723.365737
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Stuart Anderson
rawtitle: Remark on {Algorithm 723}: {Fresnel} integrals
entry:
@Article{Anderson:2000:RAF,
  author =       "Stuart Anderson",
  title =        "Remark on {Algorithm 723}: {Fresnel} integrals",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "617--617",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365737",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  accepted =     "16 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Ball:2000:ACZ
author: James S. Ball
title: Automatic Computation of Zeros of Bessel Functions and Other Special Functions
journal: j-SIAM-J-SCI-COMP
volume: 21
number: 4
pages: 1458--1464
month: jul
monthnumber: 7
year: 2000
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827598339074
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Oct 27 13:32:22 MDT 2000
bibtimestamp: 2000.10.27 13:32:22 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/33907
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: James S. Ball
rawtitle: Automatic Computation of Zeros of {Bessel} Functions and Other Special Functions
bibsource:
http://epubs.siam.org/toc/sjoce3/21/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

entry:
@Article{Ball:2000:ACZ,
  author =       "James S. Ball",
  title =        "Automatic Computation of Zeros of {Bessel} Functions
                 and Other Special Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "21",
  number =       "4",
  pages =        "1458--1464",
  month =        jul,
  year =         "2000",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827598339074",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Oct 27 13:32:22 MDT 2000",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/21/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/33907",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}


bibtype: inproceedings
filename: elefunt.bib
label: Batten:2000:NAD
author: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and P. D'arcy
title: A New Approach to DSP Intrinsic Functions
crossref: Sprague:2000:PAH
pages: 2892--2901
year: 2000
bibdate: Sun Mar 04 11:18:38 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:18:38 ???
URL: http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf
acknowledgement: ack-nhfb
rawauthor: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and P. D'arcy
rawtitle: A New Approach to {DSP} Intrinsic Functions
entry:
@InProceedings{Batten:2000:NAD,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and P. D'arcy",
  title =        "A New Approach to {DSP} Intrinsic Functions",
  crossref =     "Sprague:2000:PAH",
  pages =        "2892--2901",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:18:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Becken:2000:ACG
author: W. Becken and P. Schmelcher
journal: j-J-COMPUT-APPL-MATH
volume: 126
number: 1--2
pages: 449--478
day: 30
month: dec
monthnumber: 12
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00267-3
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 33C05 (33F05)
MRnumber: MR1806771 (2002e:33003)
bibdate: Sat Feb 25 12:43:38 MST 2017
bibtimestamp: 2017.02.25 12:43:38 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700002673
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: W. Becken and P. Schmelcher
title:
The analytic continuation of the Gaussian hypergeometric function $_2 F_1 (a, b; c; z)$ for arbitrary parameters

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

rawtitle:
The analytic continuation of the {Gaussian} hypergeometric function {$_2 F_1 (a, b; c; z)$} for arbitrary parameters

entry:
@Article{Becken:2000:ACG,
  author =       "W. Becken and P. Schmelcher",
  title =        "The analytic continuation of the {Gaussian}
                 hypergeometric function {$_2 F_1 (a, b; c; z)$} for
                 arbitrary parameters",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "126",
  number =       "1--2",
  pages =        "449--478",
  day =          "30",
  month =        dec,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00267-3",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33C05 (33F05)",
  MRnumber =     "MR1806771 (2002e:33003)",
  bibdate =      "Sat Feb 25 12:43:38 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002673",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: incollection
filename: elefunt.bib
label: Borwein:2000:AGM
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:2000:PSB
pages: 537--552
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-3240-5_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Borwein:2000:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2000:PSB",
  pages =        "537--552",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: elefunt.bib
label: Borwein:2000:CSR
author: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
title: Computational Strategies for the Riemann Zeta Function
journal: j-J-COMPUT-APPL-MATH
volume: 121
number: 1--2
pages: 247--296
month: sep
monthnumber: 9
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00336-8
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 11M06 (11Y35 33F05)
MRnumber: 1780051
MRreviewer: Cem Y. Y{\i}ld{\i}r{\i}m
bibdate: Mon Oct 24 11:41:28 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:41:28 ???
URL: http://people.reed.edu/~crandall/papers/attach01.pdf
fjournal: Journal of Computational and Applied Mathematics
remark: CECM Preprint 98:118.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
rawtitle: Computational Strategies for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.

rawabstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.

entry:
@Article{Borwein:2000:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "247--296",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00336-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "11M06 (11Y35 33F05)",
  MRnumber =     "1780051",
  MRreviewer =   "Cem Y. Y{\i}ld{\i}r{\i}m",
  bibdate =      "Mon Oct 24 11:41:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling''.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:118.",
}


bibtype: book
filename: elefunt.bib
label: Bressoud:2000:CCN
author: David M. Bressoud and S. Wagon
title: A Course in Computational Number Theory
publisher: Key College Publishers in cooperation with Springer
address: New York, NY, USA
pages: xii + 367
year: 2000
ISBN: 1-930190-10-7 OR 1930190107
ISBN13: 978-1-930190-10-8 OR 9781930190108
LCCN: QA241 .B788 2000
bibdate: Fri Sep 26 14:29:31 MDT 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2008.09.26 14:29:31 MDT
subject: Number theory; Algorithms
acknowledgement: ack-nhfb
rawauthor: David M. Bressoud and S. Wagon
rawtitle: A Course in Computational Number Theory
URL:
http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html; http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html

TOC:
Preface Vv Notation Xi Chapter 1. Fundamentals / 1 1.0 Introduction / 1 1.1 A Famous Sequence of Numbers / 2 1.2 The Euclidean Algorithm / 6 The Oldest Algorithm Reversing the Euclidean Algorithm The Extended GCD Algorithm The Fundamental Theorem of Arithmetic Two Applications 1.3 Modular Arithmetic / 25 1.4 Fast Powers / 30 A Fast Algorithm for Exponentiation Powers of Matrices, Big-O Notation Chapter 2. Congruences, Equations, and Powers / 41 2.0 Introduction / / 41 2.1 Solving Linear Congruences / 41 Linear Diophantine Equations in Two Variables Linear Equations in Several Variables Linear Congruences The Conductor An Important Quadratic Congruence 2.2 The Chinese Remainder Theorem / 49 2.3 PowerMod Patterns / 55 Fermat's Little Theorem More Patterns in Powers 2.4 Pseudoprimes / 59 Using the Pseudoprime Test Chapter 3. Euler's $phi $ Function / 65 3.0 Introduction / 65 3.1 Euler's $phi $ Function / 656 3.2 Perfect Numbers and Their Relatives / 12 The Sum of Divisors Function Perfect Numbers Amicable, Abundant, and Deficient Numbers 3.3 Euler's Theorem / 81 3.4 Primitive Roots for Primes / 84 The Order of an Integer Primes Have Primitive Roots Repeating Decimals 3.5 Primitive Roots for Composites / 70 3.6 The Universal Exponent / 73 Universal Exponents Power Towers The Form of Carmichael Numbers Chapter 4. Prime Numbers / 99 4.0 Introduction / 99 4.1 The number of Primes / 100 We'll Never Run Out of Primes The Sieve of Eratosthenes Chebyshev's Theorem and Bertrand's Postulate 4.2 Prime Testing and Certification / 114 Strong Pseudoprimes Industrial-Grade Primes Prime Certification Via Primitive Roots An Improvement Pratt Certificates 4.3 Refinements and Other Directions / 131 Other Primality Tests Strong Liars Are Scarce Finding the $n$th Prime 4.4 A Dozen Prime Mysteries / 141 5.0 Introduction / 145 5.1 Coding Secrets / 145 Tossing a Coin into a Well The RSA Cryptosystem Digital Signatures 5.2 The Yao Millionaire Problem / 155 5.3 Check Digits .158 Basic Check Digit Schemes A Perfect Check Digit Method Beyond Perfection: Correcting Errors 5.4 Factoring Algorithms / 167 Trial Division Fermat's Algorithm Pollard Rho Pollard $p - 1$ The Current Scene Chapter 6. Quadratic Residues / 179 6.0 Introduction / 179 6.1 Pepin's Test / 119 Quadratic Residues Pepin's Test Primes Congruent to 1 (Mod 4) 6.2 Proof of Quadratic Reciprocity / 185 Gauss's Lemma Proof of Quadratic Reciprocity Jacobi's Extension An Application to Factoring 6.3 Quadratic Equations / 194 Chapter 7. Continued Fractions / 201 7.0 Introduction / 201 7.1 Finite Continued Fractions / 202 7.2 Infinite Continued Fractions / 207 7.3 Periodic Continued Fractions / 213 7.4 Pell's Equation / 227 7.5 Archimedes and the Sun God's Cattle / 232 Wurm's Version: Using Rectangular Bulls The Real Cattle Problem 7.6 Factoring via Continued Fractions / 238 Chapter 8. Prime Testing with Lucas Sequences / 247 8.0 Introduction / 247 8.1 Divisibility Properties of Lucas Sequences / 248 8.2 Prime Tests Using Lucas Sequences / 259 Lucas Certification The Lucas--Lehmer Algorithm Explained Lucas Pseudoprimes Strong Quadratic Pseudoprimes Primality Testing's Holy Grail Chapter 9. Prime Imaginaries and Imaginary Primes / 279 9.0 Introduction / 279 9.1 Sums of Two Squares / 279 Primes The General Problem How Many Ways Number Theory and Salt 9.2 The Gaussian Integers / 302 Complex Number Theory Gaussian Primes The Moat Problem The Gaussian Zoo 9.3 Higher Reciprocity / 325 Appendix A. Mathematica Basics / 333 A.0 Introduction / 333 A.1 Plotting / 336 A.2 Typesetting / 338 Sending Files By E-Mail A.3 Types of Functions / 341 A.4 Programs / 345 A.6 Solving Equations / 347 A.7 Symbolic Algebra / 349 Appendix B. Lucas Certificates Exist / 351 References / 355 Index of Mathematica Objects / 359 Subject Index / 363

shortTOC:
Fundamentals Congruences, equations, and powers Euler's function Prime numbers Some applications Quadratic residues Continued fractions Prime testing with Lucas sequences Prime imaginaries and imaginary primes Appendix A. Mathematica basics Appendix B. Lucas certificates exist

rawshortTOC:
Fundamentals \\ Congruences, equations, and powers \\ Euler's function \\ Prime numbers \\ Some applications \\ Quadratic residues \\ Continued fractions \\ Prime testing with Lucas sequences \\ Prime imaginaries and imaginary primes \\ Appendix A. Mathematica basics \\ Appendix B. Lucas certificates exist

rawTOC:
Preface Vv \\ Notation Xi \\ Chapter 1. Fundamentals / 1 \\ 1.0 Introduction / 1 \\ 1.1 A Famous Sequence of Numbers / 2 \\ 1.2 The Euclidean Algorithm / 6 \\ The Oldest Algorithm \\ Reversing the Euclidean Algorithm \\ The Extended GCD Algorithm \\ The Fundamental Theorem of Arithmetic \\ Two Applications \\ 1.3 Modular Arithmetic / 25 \\ 1.4 Fast Powers / 30 \\ A Fast Algorithm for Exponentiation \\ Powers of Matrices, Big-O Notation \\ Chapter 2. Congruences, Equations, and Powers / 41 \\ 2.0 Introduction / / 41 \\ 2.1 Solving Linear Congruences / 41 \\ Linear Diophantine Equations in Two Variables \\ Linear Equations in Several Variables \\ Linear Congruences \\ The Conductor \\ An Important Quadratic Congruence \\ 2.2 The Chinese Remainder Theorem / 49 \\ 2.3 PowerMod Patterns / 55 \\ Fermat's Little Theorem \\ More Patterns in Powers \\ 2.4 Pseudoprimes / 59 \\ Using the Pseudoprime Test \\ Chapter 3. Euler's $\phi$ Function / 65 \\ 3.0 Introduction / 65 \\ 3.1 Euler's $\phi$ Function / 656 \\ 3.2 Perfect Numbers and Their Relatives / 12 \\ The Sum of Divisors Function \\ Perfect Numbers \\ Amicable, Abundant, and Deficient Numbers \\ 3.3 Euler's Theorem / 81 \\ 3.4 Primitive Roots for Primes / 84 \\ The Order of an Integer \\ Primes Have Primitive Roots \\ Repeating Decimals \\ 3.5 Primitive Roots for Composites / 70 \\ 3.6 The Universal Exponent / 73 \\ Universal Exponents \\ Power Towers \\ The Form of Carmichael Numbers \\ Chapter 4. Prime Numbers / 99 \\ 4.0 Introduction / 99 \\ 4.1 The number of Primes / 100 \\ We'll Never Run Out of Primes \\ The Sieve of Eratosthenes \\ Chebyshev's Theorem and Bertrand's Postulate \\ 4.2 Prime Testing and Certification / 114 \\ Strong Pseudoprimes \\ Industrial-Grade Primes \\ Prime Certification Via Primitive Roots \\ An Improvement \\ Pratt Certificates \\ 4.3 Refinements and Other Directions / 131 \\ Other Primality Tests \\ Strong Liars Are Scarce \\ Finding the $n$th Prime \\ 4.4 A Dozen Prime Mysteries / 141 \\ 5.0 Introduction / 145 \\ 5.1 Coding Secrets / 145 \\ Tossing a Coin into a Well \\ The RSA Cryptosystem \\ Digital Signatures \\ 5.2 The Yao Millionaire Problem / 155 \\ 5.3 Check Digits .158 \\ Basic Check Digit Schemes \\ A Perfect Check Digit Method \\ Beyond Perfection: Correcting Errors \\ 5.4 Factoring Algorithms / 167 \\ Trial Division \\ Fermat's Algorithm \\ Pollard Rho \\ Pollard $p - 1$ \\ The Current Scene \\ Chapter 6. Quadratic Residues / 179 \\ 6.0 Introduction / 179 \\ 6.1 P{\'e}pin's Test / 119 \\ Quadratic Residues \\ P{\'e}pin's Test \\ Primes Congruent to 1 (Mod 4) \\ 6.2 Proof of Quadratic Reciprocity / 185 \\ Gauss's Lemma \\ Proof of Quadratic Reciprocity \\ Jacobi's Extension \\ An Application to Factoring \\ 6.3 Quadratic Equations / 194 \\ Chapter 7. Continued Fractions / 201 \\ 7.0 Introduction / 201 \\ 7.1 Finite Continued Fractions / 202 \\ 7.2 Infinite Continued Fractions / 207 \\ 7.3 Periodic Continued Fractions / 213 \\ 7.4 Pell's Equation / 227 \\ 7.5 Archimedes and the Sun God's Cattle / 232 \\ Wurm's Version: Using Rectangular Bulls \\ The Real Cattle Problem \\ 7.6 Factoring via Continued Fractions / 238 \\ Chapter 8. Prime Testing with Lucas Sequences / 247 \\ 8.0 Introduction / 247 \\ 8.1 Divisibility Properties of Lucas Sequences / 248 \\ 8.2 Prime Tests Using Lucas Sequences / 259 \\ Lucas Certification \\ The Lucas--Lehmer Algorithm Explained \\ Lucas Pseudoprimes \\ Strong Quadratic Pseudoprimes \\ Primality Testing's Holy Grail \\ Chapter 9. Prime Imaginaries and Imaginary Primes / 279 \\ 9.0 Introduction / 279 \\ 9.1 Sums of Two Squares / 279 \\ Primes \\ The General Problem \\ How Many Ways \\ Number Theory and Salt \\ 9.2 The Gaussian Integers / 302 \\ Complex Number Theory \\ Gaussian Primes \\ The Moat Problem \\ The Gaussian Zoo \\ 9.3 Higher Reciprocity / 325 \\ Appendix A. Mathematica Basics / 333 \\ A.0 Introduction / 333 \\ A.1 Plotting / 336 \\ A.2 Typesetting / 338 \\ Sending Files By E-Mail \\ A.3 Types of Functions / 341 \\ A.4 Programs / 345 \\ A.6 Solving Equations / 347 \\ A.7 Symbolic Algebra / 349 \\ Appendix B. Lucas Certificates Exist / 351 \\ References / 355 \\ Index of Mathematica Objects / 359 \\ Subject Index / 363

entry:
@Book{Bressoud:2000:CCN,
  author =       "David M. Bressoud and S. Wagon",
  title =        "A Course in Computational Number Theory",
  publisher =    "Key College Publishers in cooperation with Springer",
  address =      "New York, NY, USA",
  pages =        "xii + 367",
  year =         "2000",
  ISBN =         "1-930190-10-7",
  ISBN-13 =      "978-1-930190-10-8",
  LCCN =         "QA241 .B788 2000",
  bibdate =      "Fri Sep 26 14:29:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Fundamentals \\
                 Congruences, equations, and powers \\
                 Euler's function \\
                 Prime numbers \\
                 Some applications \\
                 Quadratic residues \\
                 Continued fractions \\
                 Prime testing with Lucas sequences \\
                 Prime imaginaries and imaginary primes \\
                 Appendix A. Mathematica basics \\
                 Appendix B. Lucas certificates exist",
  subject =      "Number theory; Algorithms",
  tableofcontents = "Preface Vv \\
                 Notation Xi \\
                 Chapter 1. Fundamentals / 1 \\
                 1.0 Introduction / 1 \\
                 1.1 A Famous Sequence of Numbers / 2 \\
                 1.2 The Euclidean Algorithm / 6 \\
                 The Oldest Algorithm \\
                 Reversing the Euclidean Algorithm \\
                 The Extended GCD Algorithm \\
                 The Fundamental Theorem of Arithmetic \\
                 Two Applications \\
                 1.3 Modular Arithmetic / 25 \\
                 1.4 Fast Powers / 30 \\
                 A Fast Algorithm for Exponentiation \\
                 Powers of Matrices, Big-O Notation \\
                 Chapter 2. Congruences, Equations, and Powers / 41 \\
                 2.0 Introduction / / 41 \\
                 2.1 Solving Linear Congruences / 41 \\
                 Linear Diophantine Equations in Two Variables \\
                 Linear Equations in Several Variables \\
                 Linear Congruences \\
                 The Conductor \\
                 An Important Quadratic Congruence \\
                 2.2 The Chinese Remainder Theorem / 49 \\
                 2.3 PowerMod Patterns / 55 \\
                 Fermat's Little Theorem \\
                 More Patterns in Powers \\
                 2.4 Pseudoprimes / 59 \\
                 Using the Pseudoprime Test \\
                 Chapter 3. Euler's $\phi$ Function / 65 \\
                 3.0 Introduction / 65 \\
                 3.1 Euler's $\phi$ Function / 656 \\
                 3.2 Perfect Numbers and Their Relatives / 12 \\
                 The Sum of Divisors Function \\
                 Perfect Numbers \\
                 Amicable, Abundant, and Deficient Numbers \\
                 3.3 Euler's Theorem / 81 \\
                 3.4 Primitive Roots for Primes / 84 \\
                 The Order of an Integer \\
                 Primes Have Primitive Roots \\
                 Repeating Decimals \\
                 3.5 Primitive Roots for Composites / 70 \\
                 3.6 The Universal Exponent / 73 \\
                 Universal Exponents \\
                 Power Towers \\
                 The Form of Carmichael Numbers \\
                 Chapter 4. Prime Numbers / 99 \\
                 4.0 Introduction / 99 \\
                 4.1 The number of Primes / 100 \\
                 We'll Never Run Out of Primes \\
                 The Sieve of Eratosthenes \\
                 Chebyshev's Theorem and Bertrand's Postulate \\
                 4.2 Prime Testing and Certification / 114 \\
                 Strong Pseudoprimes \\
                 Industrial-Grade Primes \\
                 Prime Certification Via Primitive Roots \\
                 An Improvement \\
                 Pratt Certificates \\
                 4.3 Refinements and Other Directions / 131 \\
                 Other Primality Tests \\
                 Strong Liars Are Scarce \\
                 Finding the $n$th Prime \\
                 4.4 A Dozen Prime Mysteries / 141 \\
                 5.0 Introduction / 145 \\
                 5.1 Coding Secrets / 145 \\
                 Tossing a Coin into a Well \\
                 The RSA Cryptosystem \\
                 Digital Signatures \\
                 5.2 The Yao Millionaire Problem / 155 \\
                 5.3 Check Digits .158 \\
                 Basic Check Digit Schemes \\
                 A Perfect Check Digit Method \\
                 Beyond Perfection: Correcting Errors \\
                 5.4 Factoring Algorithms / 167 \\
                 Trial Division \\
                 Fermat's Algorithm \\
                 Pollard Rho \\
                 Pollard $p - 1$ \\
                 The Current Scene \\
                 Chapter 6. Quadratic Residues / 179 \\
                 6.0 Introduction / 179 \\
                 6.1 P{\'e}pin's Test / 119 \\
                 Quadratic Residues \\
                 P{\'e}pin's Test \\
                 Primes Congruent to 1 (Mod 4) \\
                 6.2 Proof of Quadratic Reciprocity / 185 \\
                 Gauss's Lemma \\
                 Proof of Quadratic Reciprocity \\
                 Jacobi's Extension \\
                 An Application to Factoring \\
                 6.3 Quadratic Equations / 194 \\
                 Chapter 7. Continued Fractions / 201 \\
                 7.0 Introduction / 201 \\
                 7.1 Finite Continued Fractions / 202 \\
                 7.2 Infinite Continued Fractions / 207 \\
                 7.3 Periodic Continued Fractions / 213 \\
                 7.4 Pell's Equation / 227 \\
                 7.5 Archimedes and the Sun God's Cattle / 232 \\
                 Wurm's Version: Using Rectangular Bulls \\
                 The Real Cattle Problem \\
                 7.6 Factoring via Continued Fractions / 238 \\
                 Chapter 8. Prime Testing with Lucas Sequences / 247 \\
                 8.0 Introduction / 247 \\
                 8.1 Divisibility Properties of Lucas Sequences / 248
                 \\
                 8.2 Prime Tests Using Lucas Sequences / 259 \\
                 Lucas Certification \\
                 The Lucas--Lehmer Algorithm Explained \\
                 Lucas Pseudoprimes \\
                 Strong Quadratic Pseudoprimes \\
                 Primality Testing's Holy Grail \\
                 Chapter 9. Prime Imaginaries and Imaginary Primes / 279
                 \\
                 9.0 Introduction / 279 \\
                 9.1 Sums of Two Squares / 279 \\
                 Primes \\
                 The General Problem \\
                 How Many Ways \\
                 Number Theory and Salt \\
                 9.2 The Gaussian Integers / 302 \\
                 Complex Number Theory \\
                 Gaussian Primes \\
                 The Moat Problem \\
                 The Gaussian Zoo \\
                 9.3 Higher Reciprocity / 325 \\
                 Appendix A. Mathematica Basics / 333 \\
                 A.0 Introduction / 333 \\
                 A.1 Plotting / 336 \\
                 A.2 Typesetting / 338 \\
                 Sending Files By E-Mail \\
                 A.3 Types of Functions / 341 \\
                 A.4 Programs / 345 \\
                 A.6 Solving Equations / 347 \\
                 A.7 Symbolic Algebra / 349 \\
                 Appendix B. Lucas Certificates Exist / 351 \\
                 References / 355 \\
                 Index of Mathematica Objects / 359 \\
                 Subject Index / 363",
}


bibtype: article
filename: elefunt.bib
label: Brezinski:2000:CAD
author: C. Brezinski
title: Convergence acceleration during the 20th century
journal: j-J-COMPUT-APPL-MATH
volume: 122
number: 1--2
pages: 1--21
month: oct
monthnumber: 10
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00360-5
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65-03 (01A60)
MRnumber: 1794649
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
note: Numerical analysis 2000, Vol. II: Interpolation and extrapolation
fjournal: Journal of Computational and Applied Mathematics
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: C. Brezinski
rawnote: Numerical analysis 2000, Vol. II: Interpolation and extrapolation
rawtitle: Convergence acceleration during the 20th century
entry:
@Article{Brezinski:2000:CAD,
  author =       "C. Brezinski",
  title =        "Convergence acceleration during the 20th century",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "122",
  number =       "1--2",
  pages =        "1--21",
  month =        oct,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00360-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65-03 (01A60)",
  MRnumber =     "1794649",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Numerical analysis 2000, Vol. II: Interpolation and
                 extrapolation",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Carlson:2000:RTE
author: B. C. Carlson and James FitzSimons
title: Reduction theorems for elliptic integrands with the square root of two quadratic factors
journal: j-J-COMPUT-APPL-MATH
volume: 118
number: 1--2
pages: 71--85
day: 1
month: jun
monthnumber: 6
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:35 MST 2017
bibtimestamp: 2017.02.25 12:43:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270000282X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. C. Carlson and James FitzSimons
rawtitle: Reduction theorems for elliptic integrands with the square root of two quadratic factors
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Carlson:2000:RTE,
  author =       "B. C. Carlson and James FitzSimons",
  title =        "Reduction theorems for elliptic integrands with the
                 square root of two quadratic factors",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "71--85",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270000282X",
  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: Cawley:2000:FCA
author: G. C. Cawley
title: On a Fast, Compact Approximation of the Exponential Function
journal: j-NEURAL-COMP
volume: 12
number: 9
pages: 2009--2012
day: 1
month: sep
monthnumber: 9
year: 2000
CODEN: NEUCEB
ISSN: 0899-7667 (print), 1530-888x (electronic) OR 08997667 (print), 1530888x (electronic)
ISSNL: 0899-7667 OR 08997667
bibdate: Fri Nov 8 05:39:32 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.11.08 05:39:32 MST
fjournal: Neural Computation
acknowledgement: ack-nhfb
journalURL: http://www.mitpressjournals.org/loi/neco
rawauthor: G. C. Cawley
rawtitle: On a Fast, Compact Approximation of the Exponential Function
entry:
@Article{Cawley:2000:FCA,
  author =       "G. C. Cawley",
  title =        "On a Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "12",
  number =       "9",
  pages =        "2009--2012",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "NEUCEB",
  ISSN =         "0899-7667 (print), 1530-888x (electronic)",
  ISSN-L =       "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Neural Computation",
  journal-URL =  "http://www.mitpressjournals.org/loi/neco",
  pagecount =    "4",
}


bibtype: article
filename: elefunt.bib
label: Cherri:2000:PCC
author: A. K. Cherri and M. S. Alam
title: Parallel computation of complex elementary functions using quaternary signed-digit arithmetic
journal: Optics and Laser Technology
volume: 32
number: 6
pages: 391--399
year: 2000
ISSN: 0030-3992 OR 00303992
bibdate: Sat Dec 7 09:21:28 MST 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2002.12.07 09:21:28 MST
acknowledgement: ack-nhfb
rawauthor: A. K. Cherri and M. S. Alam
rawtitle: Parallel computation of complex elementary functions using quaternary signed-digit arithmetic
entry:
@Article{Cherri:2000:PCC,
  author =       "A. K. Cherri and M. S. Alam",
  title =        "Parallel computation of complex elementary functions
                 using quaternary signed-digit arithmetic",
  journal =      "Optics and Laser Technology",
  volume =       "32",
  number =       "6",
  pages =        "391--399",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "0030-3992",
  bibdate =      "Sat Dec 7 09:21:28 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "9",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chu:2000:CPT
author: Wanming Chu and Yamin Li
booktitle: ACAC 2000: 5th Australasian Computer Architecture Conference
title: Cost / performance tradeoff of $n$-select square root implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 9--16
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Wanming Chu and Yamin Li
rawbooktitle: {ACAC 2000}: 5th Australasian Computer Architecture Conference
rawtitle: Cost\slash performance tradeoff of $n$-select square root implementations
entry:
@InProceedings{Chu:2000:CPT,
  author =       "Wanming Chu and Yamin Li",
  booktitle =    "{ACAC 2000}: 5th Australasian Computer Architecture
                 Conference",
  title =        "Cost\slash performance tradeoff of $n$-select square
                 root implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "9--16",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Hardware square-root units require large numbers of
                 gates even for iterative implementations. In this paper
                 we present four low-cost high-performance
                 fully-pipelined n-select implementations (nS-Root)
                 based on a non-restoring-remainder square root
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cohen:2000:CAA
author: Henri Cohen and Fernando Rodriguez Villegas and Don Zagier
title: Convergence Acceleration of Alternating Series
journal: j-EXP-MATH
volume: 9
number: 1
pages: 3--12
year: 2000
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11Y55 (65B05)
MRnumber: 1758796 (2001m:11222)
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 ???
URL: http://projecteuclid.org/euclid.em/1046889587; http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps
fjournal: Experimental Mathematics
keywords: convergence acceleration
ZMnumber: 0972.11115
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: Henri Cohen and Fernando {Rodriguez Villegas} and Don Zagier
rawtitle: Convergence Acceleration of Alternating Series
abstract:
We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $ sum ( - 1)^k a_k $ with an error of about $ 17.93^-n $ from the first $n$ terms for a wide class of sequences $ a_k $. Such methods are useful for high precision calculations frequently appearing in number theory.

rawabstract:
We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $ \sum ( - 1)^k a_k $ with an error of about $ 17.93^{-n} $ from the first $n$ terms for a wide class of sequences $ \{ a_k \} $. Such methods are useful for high precision calculations frequently appearing in number theory.

entry:
@Article{Cohen:2000:CAA,
  author =       "Henri Cohen and Fernando {Rodriguez Villegas} and Don
                 Zagier",
  title =        "Convergence Acceleration of Alternating Series",
  journal =      j-EXP-MATH,
  volume =       "9",
  number =       "1",
  pages =        "3--12",
  year =         "2000",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y55 (65B05)",
  MRnumber =     "1758796 (2001m:11222)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.em/1046889587;
                 http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps",
  ZMnumber =     "0972.11115",
  abstract =     "We discuss some linear acceleration methods for
                 alternating series which are in theory and in practice
                 much better than that of Euler--Van Wijngaarden. One of
                 the algorithms, for instance, allows one to calculate $
                 \sum ( - 1)^k a_k $ with an error of about $ 17.93^{-n}
                 $ from the first $n$ terms for a wide class of
                 sequences $ \{ a_k \} $. Such methods are useful for
                 high precision calculations frequently appearing in
                 number theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:2000:IGD
author: Milos D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei
title: Improving Goldschmidt Division, Square Root, and Square Root Reciprocal
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 759--763
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863046
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milos D. Ercegovac and Laurent Imbert and David W. Matula and Jean-Michel Muller and Guoheng Wei
rawtitle: Improving {Goldschmidt} Division, Square Root, and Square Root Reciprocal
entry:
@Article{Ercegovac:2000:IGD,
  author =       "Milos D. Ercegovac and Laurent Imbert and David W.
                 Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "759--763",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "The aim of this paper is to accelerate division,
                 square root, and square root reciprocal computations
                 when the Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Ercegovac:2000:RSR
author: Milos D. Ercegovac and Tomas Lang and Jean-Michel Muller and Arnaud Tisserand
journal: j-IEEE-TRANS-COMPUT
volume: 49
number: 7
pages: 628--637
month: jul
monthnumber: 7
year: 2000
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.863031
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
MRclass: 68M07 (65B15)
MRnumber: MR1783602 (2001e:68016)
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Institute of Electrical and Electronics Engineers. Transactions on Computers
remark: Selected papers from ARITH'14 cite Koren:1999:ISC.
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel Muller and Arnaud Tisserand
title:
Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers

rawtitle:
Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers

entry:
@Article{Ercegovac:2000:RSR,
  author =       "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel
                 Muller and Arnaud Tisserand",
  title =        "Reciprocation, Square Root, Inverse Square Root, and
                 Some Elementary Functions Using Small Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "628--637",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863031",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07 (65B15)",
  MRnumber =     "MR1783602 (2001e:68016)",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Institute of Electrical and Electronics Engineers.
                 Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "This paper deals with the computation of reciprocals,
                 square roots, inverse square roots, and some elementary
                 functions using small tables, small multipliers, and,
                 for some functions, a final ``large'' (almost
                 full-length) multiplication. \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Favati:2000:SAC
author: P. Favati and G. Lotti and O. Menchi and F. Romani
title: Separable asymptotic cost of evaluating elementary functions
journal: j-NUMER-ALGORITHMS
volume: 24
number: 3
pages: 255--274
year: 2000
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
MRclass: 65Y20
MRnumber: MR1780414 (2001d:65174)
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; Ingenta database
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: P. Favati and G. Lotti and O. Menchi and F. Romani
rawtitle: Separable asymptotic cost of evaluating elementary functions
entry:
@Article{Favati:2000:SAC,
  author =       "P. Favati and G. Lotti and O. Menchi and F. Romani",
  title =        "Separable asymptotic cost of evaluating elementary
                 functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "24",
  number =       "3",
  pages =        "255--274",
  year =         "2000",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65Y20",
  MRnumber =     "MR1780414 (2001d:65174)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  pagecount =    "20",
}


bibtype: article
filename: elefunt.bib
label: Galue:2000:MTG
author: L. Galue and H. G. Khajah and Shyam L. Kalla
title: Multiplication theorems for generalized and double-index Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 118
number: 1--2
pages: 143--150
day: 1
month: jun
monthnumber: 6
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:35 MST 2017
bibtimestamp: 2017.02.25 12:43:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700002855
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: L. Galu{\'e} and H. G. Khajah and Shyam L. Kalla
rawtitle: Multiplication theorems for generalized and double-index {Bessel} functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib

entry:
@Article{Galue:2000:MTG,
  author =       "L. Galu{\'e} and H. G. Khajah and Shyam L. Kalla",
  title =        "Multiplication theorems for generalized and
                 double-index {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "143--150",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002855",
  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: Harris:2000:SBE
author: Frank E. Harris
title: Spherical Bessel expansions of sine, cosine, and exponential integrals
journal: j-APPL-NUM-MATH
volume: 34
number: 1
pages: 95--98
month: jun
monthnumber: 6
year: 2000
CODEN: ANMAEL
DOI: https://doi.org/10.1016/S0168-9274(99)00031-8
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 33B10; 65D30 (33F05 65D20)
MRnumber: 1755696 (2001a:65027)
bibdate: Sat Oct 21 13:09:35 MDT 2000
bibtimestamp: 2000.10.21 13:09:35 MDT
fjournal: Applied Numerical Mathematics: Transactions of IMACS
ZMnumber: Zbl 0951.33002
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: Frank E. Harris
rawtitle: Spherical {Bessel} expansions of sine, cosine, and exponential integrals
bibsource:
http://www.elsevier.com/locate/issn/01689274; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/abstract.html; http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/article.pdf; http://www.sciencedirect.com/science/article/pii/S0168927499000318

entry:
@Article{Harris:2000:SBE,
  author =       "Frank E. Harris",
  title =        "Spherical {Bessel} expansions of sine, cosine, and
                 exponential integrals",
  journal =      j-APPL-NUM-MATH,
  volume =       "34",
  number =       "1",
  pages =        "95--98",
  month =        jun,
  year =         "2000",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/S0168-9274(99)00031-8",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "33B10; 65D30 (33F05 65D20)",
  MRnumber =     "1755696 (2001a:65027)",
  bibdate =      "Sat Oct 21 13:09:35 MDT 2000",
  bibsource =    "http://www.elsevier.com/locate/issn/01689274;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/abstract.html;
                 http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/article.pdf;
                 http://www.sciencedirect.com/science/article/pii/S0168927499000318",
  ZMnumber =     "Zbl 0951.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hasan:2000:FPI
author: M. A. Hasan and A. A. Hasan and S. Rahman
booktitle: Proceedings of the 39th IEEE Conference on Decision and Control
title: Fixed point iterations for computing square roots and the matrix sign function of complex matrices
volume: 5
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 4253--4258
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. A. Hasan and A. A. Hasan and S. Rahman
rawbooktitle: Proceedings of the 39th {IEEE} Conference on Decision and Control
rawtitle: Fixed point iterations for computing square roots and the matrix sign function of complex matrices
entry:
@InProceedings{Hasan:2000:FPI,
  author =       "M. A. Hasan and A. A. Hasan and S. Rahman",
  booktitle =    "Proceedings of the 39th {IEEE} Conference on Decision
                 and Control",
  title =        "Fixed point iterations for computing square roots and
                 the matrix sign function of complex matrices",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4253--4258",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this work has been the development of
                 new set of rational iterations for computing square
                 roots and the matrix sign function of complex matrices.
                 Given any positive integer r{\&}ges;2, we presented a
                 systematic way of deriving rth order \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hassibi:2000:ESR
author: B. Hassibi
title: An efficient square-root algorithm for BLAST
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: II737--II740
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: B. Hassibi
rawtitle: An efficient square-root algorithm for {BLAST}
booktitle:
Proceedings. 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing: ICASSP '00, 5--9 June 2000

rawbooktitle:
Proceedings. 2000 {IEEE} International Conference on Acoustics, Speech, and Signal Processing: {ICASSP '00}, 5--9 June 2000

entry:
@InProceedings{Hassibi:2000:ESR,
  author =       "B. Hassibi",
  booktitle =    "Proceedings. 2000 {IEEE} International Conference on
                 Acoustics, Speech, and Signal Processing: {ICASSP '00},
                 5--9 June 2000",
  title =        "An efficient square-root algorithm for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II737--II740",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Hassibi:2000:FSR
author: B. Hassibi
booktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
title: A fast square-root implementation for BLAST
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1255--1259
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: B. Hassibi
rawtitle: A fast square-root implementation for {BLAST}
rawbooktitle:
{Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000}

entry:
@InProceedings{Hassibi:2000:FSR,
  author =       "B. Hassibi",
  booktitle =    "{Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000}",
  title =        "A fast square-root implementation for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1255--1259",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Holmgren:2000:CAL
author: Sverker Holmgren and Henrik Branden and Erik Sterner
journal: j-SIAM-J-SCI-COMP
volume: 21
number: 4
pages: 1524--1550
month: jul
monthnumber: 7
year: 2000
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827597317983
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
bibdate: Fri Oct 27 13:32:22 MDT 2000
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.10.27 13:32:22 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/31798
fjournal: SIAM Journal on Scientific Computing
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sisc
rawauthor: Sverker Holmgren and Henrik Brand{\'e}n and Erik Sterner
title:
Convergence Acceleration for the Linearized Navier--Stokes Equations using Semicirculant Approximations

rawtitle:
Convergence Acceleration for the Linearized {Navier--Stokes} Equations using Semicirculant Approximations

entry:
@Article{Holmgren:2000:CAL,
  author =       "Sverker Holmgren and Henrik Brand{\'e}n and Erik
                 Sterner",
  title =        "Convergence Acceleration for the Linearized
                 {Navier--Stokes} Equations using Semicirculant
                 Approximations",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "21",
  number =       "4",
  pages =        "1524--1550",
  month =        jul,
  year =         "2000",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827597317983",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Oct 27 13:32:22 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31798",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "convergence acceleration",
}


bibtype: misc
filename: elefunt.bib
label: Intel:2000:DSR
author: Intel
title: Divide, Square Root, and Remainder Algorithms for the Itanium Architecture
pages: 1524--1550
month: jul
monthnumber: 7
year: 2000
bibdate: Fri Sep 22 17:06:23 2023
bibtimestamp: 2023.09.22 17:06:23 ???
URL: https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64
acknowledgement: ack-nhfb
howpublished: Intel Software Development Products
rawauthor: {Intel}
rawtitle: Divide, Square Root, and Remainder Algorithms for the {Itanium} Architecture
entry:
@Misc{Intel:2000:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  month =        jul,
  year =         "2000",
  bibdate =      "Fri Sep 22 17:06:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Jeffrey:2000:HMF
author: Alan Jeffrey
title: Handbook of Mathematical Formulas and Integrals
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
edition: Second
pages: xxvi + 433
year: 2000
ISBN: 0-12-382251-3 OR 0123822513
ISBN13: 978-0-12-382251-2 OR 9780123822512
LCCN: QA47 .J38 2000
bibdate: Wed Jun 12 14:47:49 MDT 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.06.12 14:47:49 MDT
subject: Mathematics; Tables; Formulae; Mathematics.
acknowledgement: ack-nhfb
rawauthor: Alan Jeffrey
rawtitle: Handbook of Mathematical Formulas and Integrals
TOC:
0: Quick Reference List of Frequently Used Data 0.1: Useful Identities / 1 0.2: Complex Relationships / 2 0.3: Constants / 2 0.4: Derivatives of Elementary Functions / 3 0.5: Rules of Differentiation and Integration / 3 0.6: Standard Integrals / 4 0.7: Standard Series / 11 0.8: Geometry / 13 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 1.1: Algebraic Results Involving Real and Complex Numbers / 25 1.2: Finite Sums / 29 1.3: Bernoulli and Euler Numbers and Polynomials / 37 1.4: Determinants / 47 1.5: Matrices / 55 1.6: Permutations and Combinations / 62 1.7: Partial Fraction Decomposition / 63 1.8: Convergence of Series / 66 1.9: Infinite Products / 71 1.10: Functional Series / 73 1.11: Power Series / 74 1.12: Taylor Series / 79 4.13: Fourier Series / 81 4.14: Asymptotic Expansions / 85 1.15: Basic Results from the Calculus / 86 2: Functions and Identities 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 2.2: Logarithms and Exponentials / 112 2.3: Exponential Function / 114 2.4: Trigonometric Identities / 115 2.5: Hyperbolic Identities / 121 2.6: Logarithm / 126 2.7: Inverse Trigonometric and Hyperbolic Functions 128 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 3: Derivatives of Elementary Functions 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 3.2: Derivatives of Trigonometric Functions / 140 3.3: Derivatives of Inverse Trigonometric Functions 140 3.4: Derivatives of Hyperbolic Functions / 141 3.5: Derivatives of Inverse Hyperbolic Functions 142 4: Indefinite Integrals of Algebraic Functions 4.1: Algebraic and Transcendental Functions / 145 4.2: Indefinite Integrals of Rational Functions / 146 4.3: Nonrational Algebraic Functions / 158 5: Indefinite Integrals of Exponential Functions 5.1: Basic Results / 167 6: Indefinite Integrals of Logarithmic Functions 6.1: Combinations of Logarithms and Polynomials / 173 7: Indefinite Integrals of Hyperbolic Functions 7.1: Basic Results / 179 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 7.9: Integrands Involving tanh kx and coth kx / 188 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 8.1: Basic Results / 191 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) / 194 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 9: Indefinite Integrals of Trigonometric Functions 9.1: Basic Results / 197 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 9.3: Integrands Involving tan x and/or cot x / 205 9.4: Integrands Involving sin x and cos x / 207 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 10: Indefinite Integrals of Inverse Trigonometric Functions 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions 215 --. 11: Gamma, Beta, Pi, and Psi Functions 11.1: Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 12: Elliptic Integrals and Functions 12.1: Elliptic Integrals / 229 12.2: Jacobian Elliptic Functions / 235 12.3: Derivatives and Integrals / 237 12.4: Inverse Jacobian Elliptic Functions / 237 13: Probability Integrals and the Error Function 13.1: Normal Distribution / 239 13.2: Error Function / 242 14: Fresnel Integrals, Sine and Cosine Integrals 14.1: Definitions, Series Representations, and Values at Infinity / 245 14.2: Definitions, Series Representations, and Values at Infinity / 247 15: Definite Integrals 15.1: Integrands Involving Powers of x / 249 15.2: Integrands Involving Trigonometric Functions 251 15.3: Integrands Involving the Exponential Function 254 15.4: Integrands Involving the Hyperbolic Function 256 15.5: Integrands Involving the Logarithmic Function 256 16: Different Forms of Fourier Series 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 259 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 260 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 16.10: Representative Examples of Fourier Series 261 16.11: Fourier Series and Discontinuous Functions 265 17: Bessel Functions 17.1: Bessel's Differential Equation / 269 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 17.3: Bessel Functions of Fractional Order / 272 17.4: Asymptotic Representations for Bessel Functions / 273 17.5: Zeros of Bessel Functions / 273 17.6: Bessel's Modified Equation / 274 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 17.8: Modified Bessel Functions of Fractional Order 277 17.9: Asymptotic Representations of Modified Bessel Functions / 278 17.10: Relationships between Bessel Functions / 278 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 17.12: Indefinite Integrals of Bessel Functions / 281 17.13: Definite Integrals Involving Bessel Functions / 282 17.14: Spherical Bessel Functions / 283 18: Orthogonal Polynomials 18.2: Legendre Polynomials P[subscript n](x) / 286 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 18.4: Laguerre Polynomials L[subscript n](x) / 294 18.5: Hermite Polynomials H[subscript n](x) / 296 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 21.1: Classical Methods / 315 22: Solutions of Standard Ordinary Differential Equations 22.2: Separation of Variables / 323 22.3: Linear First-Order Equations / 323 22.4: Bernoulli's Equation / 324 22.5: Exact Equations / 325 22.6: Homogeneous Equations / 325 22.7: Linear Differential Equations / 326 22.8: Constant Coefficient Linear Differential Equations--Homogeneous Case / 327 22.9: Linear Homogeneous Second-Order Equation / 330 22.10: Constant Coefficient Linear Differential Equations--Inhomogeneous Case / 331 22.11: Linear Inhomogeneous Second-Order Equation 333 22.12: Determination of Particular Integrals by the Method of- Undetermined Coefficients / 334 22.13: Cauchy-Euler Equation / 336 22.14: Legendre's Equation / 337 22.15: Bessel's Equations / 337 22.16: Power Series and Frobenius Methods / 339 22.17: Hypergeometric Equation / 344 22.18: Numerical Methods / 345 23: Vector Analysis 23.1: Scalars and Vectors / 353 23.2: Scalar Products / 358 23.3: Vector Products / 359 23.4: Triple Products / 360 23.5: Products of Four Vectors / 361 23.6: Derivatives of Vector Functions of a Scalar t 361 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 23.9: Line Integrals / 364 23.10: Vector Integral Theorems / 366 23.11: A Vector Rate of Change Theorem / 368 23.12: Useful Vector Identities and Results / 368 24: Systems of Orthogonal Coordinates 24.1: Curvilinear Coordinates / 369 24.2: Vector Operators in Orthogonal Coordinates 371 24.3: Systems of Orthogonal Coordinates / 371 25: Partial Differential Equations and Special Functions 25.1: Fundamental Ideas / 381 25.2: Method of Separation of Variables / 385 25.3: Sturm--Liouville Problem and Special Functions 387 25.4: A First-Order System and the Wave Equation 390 25.5: Conservation Equations (Laws) / 391 25.6: Method of Characteristics / 392 25.7: Discontinuous Solutions (Shocks) / 396 25.8: Similarity Solutions / 398 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 26: Z-Transform 26.1: Z-Transform and Transform Pairs / 403 27: Numerical Approximation 27.2: Economization of Series / 411 27.3: Pade Approximation / 413 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

shortTOC:
0: Quick Reference List of Frequently Used Data 1: Numerical, Algebraic, and Analytical Results for Series and Calculus 2: Functions and Identities 3: Derivatives of Elementary Functions 4: Indefinite Integrals of Algebraic Functions 5: Indefinite Integrals of Exponential Functions 6: Indefinite Integrals of Logarithmic Functions 7: Indefinite Integrals of Hyperbolic Functions 8: Indefinite Integrals Involving Inverse Hyperbolic Functions 9: Indefinite Integrals of Trigonometric Functions 10: Indefinite Integrals of Inverse Trigonometric Functions 11: The Gamma, Beta, Pi, and Psi Functions 12: Elliptic Integrals and Functions 13: Probability Integrals and the Error Function 14: Fresnel Integrals 15: Definite Integrals 16: Different Forms of Fourier Series 17: Bessel Functions 18: Orthogonal Polynomials 19: Laplace Transformation 20: Fourier Transforms 21: Numerical Integration 22: Solutions of Standard Ordinary Differential Equations 23: Vector Analysis 24: Systems of Orthogonal Coordinates 25: Partial Differential Equations and Special Functions

rawshortTOC:
0: Quick Reference List of Frequently Used Data \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 2: Functions and Identities \\ 3: Derivatives of Elementary Functions \\ 4: Indefinite Integrals of Algebraic Functions \\ 5: Indefinite Integrals of Exponential Functions \\ 6: Indefinite Integrals of Logarithmic Functions \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 9: Indefinite Integrals of Trigonometric Functions \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 11: The Gamma, Beta, Pi, and Psi Functions \\ 12: Elliptic Integrals and Functions \\ 13: Probability Integrals and the Error Function \\ 14: Fresnel Integrals \\ 15: Definite Integrals \\ 16: Different Forms of Fourier Series \\ 17: Bessel Functions \\ 18: Orthogonal Polynomials \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 22: Solutions of Standard Ordinary Differential Equations \\ 23: Vector Analysis \\ 24: Systems of Orthogonal Coordinates \\ 25: Partial Differential Equations and Special Functions

rawTOC:
0: Quick Reference List of Frequently Used Data \\ 0.1: Useful Identities / 1 \\ 0.2: Complex Relationships / 2 \\ 0.3: Constants / 2 \\ 0.4: Derivatives of Elementary Functions / 3 \\ 0.5: Rules of Differentiation and Integration / 3 \\ 0.6: Standard Integrals / 4 \\ 0.7: Standard Series / 11 \\ 0.8: Geometry / 13 \\ 1: Numerical, Algebraic, and Analytical Results for Series and Calculus \\ 1.1: Algebraic Results Involving Real and Complex Numbers / 25 \\ 1.2: Finite Sums / 29 \\ 1.3: Bernoulli and Euler Numbers and Polynomials / 37 \\ 1.4: Determinants / 47 \\ 1.5: Matrices / 55 \\ 1.6: Permutations and Combinations / 62 \\ 1.7: Partial Fraction Decomposition / 63 \\ 1.8: Convergence of Series / 66 \\ 1.9: Infinite Products / 71 \\ 1.10: Functional Series / 73 \\ 1.11: Power Series / 74 \\ 1.12: Taylor Series / 79 \\ 4.13: Fourier Series / 81 \\ 4.14: Asymptotic Expansions / 85 \\ 1.15: Basic Results from the Calculus / 86 \\ 2: Functions and Identities \\ 2.1: Complex Numbers and Trigonometric and Hyperbolic Functions / 101 \\ 2.2: Logarithms and Exponentials / 112 \\ 2.3: Exponential Function / 114 \\ 2.4: Trigonometric Identities / 115 \\ 2.5: Hyperbolic Identities / 121 \\ 2.6: Logarithm / 126 \\ 2.7: Inverse Trigonometric and Hyperbolic Functions 128 \\ 2.8: Series Representations of Trigonometric and Hyperbolic Functions / 133 \\ 2.9: Useful Limiting Values and Inequalities Involving Elementary Functions / 136 \\ 3: Derivatives of Elementary Functions \\ 3.1: Derivatives of Algebraic, Logarithmic, and Exponential Functions / 139 \\ 3.2: Derivatives of Trigonometric Functions / 140 \\ 3.3: Derivatives of Inverse Trigonometric Functions 140 \\ 3.4: Derivatives of Hyperbolic Functions / 141 \\ 3.5: Derivatives of Inverse Hyperbolic Functions 142 \\ 4: Indefinite Integrals of Algebraic Functions \\ 4.1: Algebraic and Transcendental Functions / 145 \\ 4.2: Indefinite Integrals of Rational Functions / 146 \\ 4.3: Nonrational Algebraic Functions / 158 \\ 5: Indefinite Integrals of Exponential Functions \\ 5.1: Basic Results / 167 \\ 6: Indefinite Integrals of Logarithmic Functions \\ 6.1: Combinations of Logarithms and Polynomials / 173 \\ 7: Indefinite Integrals of Hyperbolic Functions \\ 7.1: Basic Results / 179 \\ 7.2: Integrands Involving Powers of sinh(bx) or cosh(bx) / 180 \\ 7.3: Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) / 181 \\ 7.4: Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x / 183 \\ 7.5: Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x / 183 \\ 7.6: Integrands Involving (1 [plus or minus] cosh x)[superscript -m] / 185 \\ 7.7: Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x / 185 \\ 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d) / 186 \\ 7.9: Integrands Involving tanh kx and coth kx / 188 \\ 7.10: Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx / 189 \\ 8: Indefinite Integrals Involving Inverse Hyperbolic Functions \\ 8.1: Basic Results / 191 \\ 8.2: Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193 \\ 8.3: Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) / 194 \\ 8.4: Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195 \\ 9: Indefinite Integrals of Trigonometric Functions \\ 9.1: Basic Results / 197 \\ 9.2: Integrands Involving Powers of x and Powers of sin x or cos x / 197 \\ 9.3: Integrands Involving tan x and/or cot x / 205 \\ 9.4: Integrands Involving sin x and cos x / 207 \\ 9.5: Integrands Involving Sines and Cosines with Linear Arguments and Powers of x / 211 \\ 10: Indefinite Integrals of Inverse Trigonometric Functions \\ 10.1: Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions 215 --. 11: Gamma, Beta, Pi, and Psi Functions \\ 11.1: Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) / 221 \\ 12: Elliptic Integrals and Functions \\ 12.1: Elliptic Integrals / 229 \\ 12.2: Jacobian Elliptic Functions / 235 \\ 12.3: Derivatives and Integrals / 237 \\ 12.4: Inverse Jacobian Elliptic Functions / 237 \\ 13: Probability Integrals and the Error Function \\ 13.1: Normal Distribution / 239 \\ 13.2: Error Function / 242 \\ 14: Fresnel Integrals, Sine and Cosine Integrals \\ 14.1: Definitions, Series Representations, and Values at Infinity / 245 \\ 14.2: Definitions, Series Representations, and Values at Infinity / 247 \\ 15: Definite Integrals \\ 15.1: Integrands Involving Powers of x / 249 \\ 15.2: Integrands Involving Trigonometric Functions 251 \\ 15.3: Integrands Involving the Exponential Function 254 \\ 15.4: Integrands Involving the Hyperbolic Function 256 \\ 15.5: Integrands Involving the Logarithmic Function 256 \\ 16: Different Forms of Fourier Series \\ 16.1: Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 257 \\ 16.2: Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L / 258 \\ 16.3: Fourier Series for f(x) on a [less than or equal] x [less than or equal] b / 258 \\ 16.4: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 \\ 16.5: Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 259 \\ 16.6: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 \\ 16.7: Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L / 260 \\ 16.8: Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] / 260 \\ 16.9: Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 \\ 16.10: Representative Examples of Fourier Series 261 \\ 16.11: Fourier Series and Discontinuous Functions 265 \\ 17: Bessel Functions \\ 17.1: Bessel's Differential Equation / 269 \\ 17.2: Series Expansions for J[subscript v](x) and Y[subscript v](x) / 270 \\ 17.3: Bessel Functions of Fractional Order / 272 \\ 17.4: Asymptotic Representations for Bessel Functions / 273 \\ 17.5: Zeros of Bessel Functions / 273 \\ 17.6: Bessel's Modified Equation / 274 \\ 17.7: Series Expansions for I[subscript v](x) and K[subscript v](x) / 276 \\ 17.8: Modified Bessel Functions of Fractional Order 277 \\ 17.9: Asymptotic Representations of Modified Bessel Functions / 278 \\ 17.10: Relationships between Bessel Functions / 278 \\ 17.11: Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) / 281 \\ 17.12: Indefinite Integrals of Bessel Functions / 281 \\ 17.13: Definite Integrals Involving Bessel Functions / 282 \\ 17.14: Spherical Bessel Functions / 283 \\ 18: Orthogonal Polynomials \\ 18.2: Legendre Polynomials P[subscript n](x) / 286 \\ 18.3: Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) / 290 \\ 18.4: Laguerre Polynomials L[subscript n](x) / 294 \\ 18.5: Hermite Polynomials H[subscript n](x) / 296 \\ 19: Laplace Transformation \\ 20: Fourier Transforms \\ 21: Numerical Integration \\ 21.1: Classical Methods / 315 \\ 22: Solutions of Standard Ordinary Differential Equations \\ 22.2: Separation of Variables / 323 \\ 22.3: Linear First-Order Equations / 323 \\ 22.4: Bernoulli's Equation / 324 \\ 22.5: Exact Equations / 325 \\ 22.6: Homogeneous Equations / 325 \\ 22.7: Linear Differential Equations / 326 \\ 22.8: Constant Coefficient Linear Differential Equations--Homogeneous Case / 327 \\ 22.9: Linear Homogeneous Second-Order Equation / 330 \\ 22.10: Constant Coefficient Linear Differential Equations--Inhomogeneous Case / 331 \\ 22.11: Linear Inhomogeneous Second-Order Equation 333 \\ 22.12: Determination of Particular Integrals by the Method of- Undetermined Coefficients / 334 \\ 22.13: Cauchy-Euler Equation / 336 \\ 22.14: Legendre's Equation / 337 \\ 22.15: Bessel's Equations / 337 \\ 22.16: Power Series and Frobenius Methods / 339 \\ 22.17: Hypergeometric Equation / 344 \\ 22.18: Numerical Methods / 345 \\ 23: Vector Analysis \\ 23.1: Scalars and Vectors / 353 \\ 23.2: Scalar Products / 358 \\ 23.3: Vector Products / 359 \\ 23.4: Triple Products / 360 \\ 23.5: Products of Four Vectors / 361 \\ 23.6: Derivatives of Vector Functions of a Scalar t 361 \\ 23.7: Derivatives of Vector Functions of Several Scalar Variables / 362 \\ 23.8: Integrals of Vector Functions of a Scalar Variable t / 363 \\ 23.9: Line Integrals / 364 \\ 23.10: Vector Integral Theorems / 366 \\ 23.11: A Vector Rate of Change Theorem / 368 \\ 23.12: Useful Vector Identities and Results / 368 \\ 24: Systems of Orthogonal Coordinates \\ 24.1: Curvilinear Coordinates / 369 \\ 24.2: Vector Operators in Orthogonal Coordinates 371 \\ 24.3: Systems of Orthogonal Coordinates / 371 \\ 25: Partial Differential Equations and Special Functions \\ 25.1: Fundamental Ideas / 381 \\ 25.2: Method of Separation of Variables / 385 \\ 25.3: Sturm--Liouville Problem and Special Functions 387 \\ 25.4: A First-Order System and the Wave Equation 390 \\ 25.5: Conservation Equations (Laws) / 391 \\ 25.6: Method of Characteristics / 392 \\ 25.7: Discontinuous Solutions (Shocks) / 396 \\ 25.8: Similarity Solutions / 398 \\ 25.9: Burgers's Equation, the KdV Equation, and the KdVB Equation / 400 \\ 26: Z-Transform \\ 26.1: Z-Transform and Transform Pairs / 403 \\ 27: Numerical Approximation \\ 27.2: Economization of Series / 411 \\ 27.3: Pade Approximation / 413 \\ 27.4: Finite Difference Approximations to Ordinary and Partial Derivatives / 415

entry:
@Book{Jeffrey:2000:HMF,
  author =       "Alan Jeffrey",
  title =        "Handbook of Mathematical Formulas and Integrals",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  edition =      "Second",
  pages =        "xxvi + 433",
  year =         "2000",
  ISBN =         "0-12-382251-3",
  ISBN-13 =      "978-0-12-382251-2",
  LCCN =         "QA47 .J38 2000",
  bibdate =      "Wed Jun 12 14:47:49 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "0: Quick Reference List of Frequently Used
                 Data \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 2: Functions and Identities \\
                 3: Derivatives of Elementary Functions \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 5: Indefinite Integrals of Exponential Functions \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 11: The Gamma, Beta, Pi, and Psi Functions \\
                 12: Elliptic Integrals and Functions \\
                 13: Probability Integrals and the Error Function \\
                 14: Fresnel Integrals \\
                 15: Definite Integrals \\
                 16: Different Forms of Fourier Series \\
                 17: Bessel Functions \\
                 18: Orthogonal Polynomials \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 23: Vector Analysis \\
                 24: Systems of Orthogonal Coordinates \\
                 25: Partial Differential Equations and Special
                 Functions",
  subject =      "Mathematics; Tables; Formulae; Mathematics.",
  tableofcontents = "0: Quick Reference List of Frequently Used Data \\
                 0.1: Useful Identities / 1 \\
                 0.2: Complex Relationships / 2 \\
                 0.3: Constants / 2 \\
                 0.4: Derivatives of Elementary Functions / 3 \\
                 0.5: Rules of Differentiation and Integration / 3 \\
                 0.6: Standard Integrals / 4 \\
                 0.7: Standard Series / 11 \\
                 0.8: Geometry / 13 \\
                 1: Numerical, Algebraic, and Analytical Results for
                 Series and Calculus \\
                 1.1: Algebraic Results Involving Real and Complex
                 Numbers / 25 \\
                 1.2: Finite Sums / 29 \\
                 1.3: Bernoulli and Euler Numbers and Polynomials / 37
                 \\
                 1.4: Determinants / 47 \\
                 1.5: Matrices / 55 \\
                 1.6: Permutations and Combinations / 62 \\
                 1.7: Partial Fraction Decomposition / 63 \\
                 1.8: Convergence of Series / 66 \\
                 1.9: Infinite Products / 71 \\
                 1.10: Functional Series / 73 \\
                 1.11: Power Series / 74 \\
                 1.12: Taylor Series / 79 \\
                 4.13: Fourier Series / 81 \\
                 4.14: Asymptotic Expansions / 85 \\
                 1.15: Basic Results from the Calculus / 86 \\
                 2: Functions and Identities \\
                 2.1: Complex Numbers and Trigonometric and Hyperbolic
                 Functions / 101 \\
                 2.2: Logarithms and Exponentials / 112 \\
                 2.3: Exponential Function / 114 \\
                 2.4: Trigonometric Identities / 115 \\
                 2.5: Hyperbolic Identities / 121 \\
                 2.6: Logarithm / 126 \\
                 2.7: Inverse Trigonometric and Hyperbolic Functions 128
                 \\
                 2.8: Series Representations of Trigonometric and
                 Hyperbolic Functions / 133 \\
                 2.9: Useful Limiting Values and Inequalities Involving
                 Elementary Functions / 136 \\
                 3: Derivatives of Elementary Functions \\
                 3.1: Derivatives of Algebraic, Logarithmic, and
                 Exponential Functions / 139 \\
                 3.2: Derivatives of Trigonometric Functions / 140 \\
                 3.3: Derivatives of Inverse Trigonometric Functions 140
                 \\
                 3.4: Derivatives of Hyperbolic Functions / 141 \\
                 3.5: Derivatives of Inverse Hyperbolic Functions 142
                 \\
                 4: Indefinite Integrals of Algebraic Functions \\
                 4.1: Algebraic and Transcendental Functions / 145 \\
                 4.2: Indefinite Integrals of Rational Functions / 146
                 \\
                 4.3: Nonrational Algebraic Functions / 158 \\
                 5: Indefinite Integrals of Exponential Functions \\
                 5.1: Basic Results / 167 \\
                 6: Indefinite Integrals of Logarithmic Functions \\
                 6.1: Combinations of Logarithms and Polynomials / 173
                 \\
                 7: Indefinite Integrals of Hyperbolic Functions \\
                 7.1: Basic Results / 179 \\
                 7.2: Integrands Involving Powers of sinh(bx) or
                 cosh(bx) / 180 \\
                 7.3: Integrands Involving (a [plus or minus]
                 bx)[superscript m] sinh(cx) or (a + bx)[superscript m]
                 cosh(cx) / 181 \\
                 7.4: Integrands Involving x[superscript m]
                 sinh[superscript n] x or x[superscript m]
                 cosh[superscript n] x / 183 \\
                 7.5: Integrands Involving x[superscript m]
                 sinh[superscript -n] x or x[superscript m]
                 cosh[superscript -n] x / 183 \\
                 7.6: Integrands Involving (1 [plus or minus] cosh
                 x)[superscript -m] / 185 \\
                 7.7: Integrands Involving sinh(ax)cosh[superscript -n]
                 x or cosh(ax)sinh[superscript -n] x / 185 \\
                 7.8: Integrands Involving sinh(ax + b) and cosh(cx + d)
                 / 186 \\
                 7.9: Integrands Involving tanh kx and coth kx / 188 \\
                 7.10: Integrands Involving (a + bx)[superscript m] sinh
                 kx or (a + bx)[superscript m] cosh kx / 189 \\
                 8: Indefinite Integrals Involving Inverse Hyperbolic
                 Functions \\
                 8.1: Basic Results / 191 \\
                 8.2: Integrands Involving x[superscript -n]
                 arcsinh(x/a) or x[superscript -n] arccosh(x/a) / 193
                 \\
                 8.3: Integrands Involving x[superscript n] arctanh(x/a)
                 or x[superscript n] arccoth(x/a) / 194 \\
                 8.4: Integrands Involving x[superscript -n]
                 arctanh(x/a) or x[superscript -n] arccoth(x/a) / 195
                 \\
                 9: Indefinite Integrals of Trigonometric Functions \\
                 9.1: Basic Results / 197 \\
                 9.2: Integrands Involving Powers of x and Powers of sin
                 x or cos x / 197 \\
                 9.3: Integrands Involving tan x and/or cot x / 205 \\
                 9.4: Integrands Involving sin x and cos x / 207 \\
                 9.5: Integrands Involving Sines and Cosines with Linear
                 Arguments and Powers of x / 211 \\
                 10: Indefinite Integrals of Inverse Trigonometric
                 Functions \\
                 10.1: Integrands Involving Powers of x and Powers of
                 Inverse Trigonometric Functions 215 --. 11: Gamma,
                 Beta, Pi, and Psi Functions \\
                 11.1: Euler Integral and Limit and Infinite Product
                 Representations for [Gamma] (x) / 221 \\
                 12: Elliptic Integrals and Functions \\
                 12.1: Elliptic Integrals / 229 \\
                 12.2: Jacobian Elliptic Functions / 235 \\
                 12.3: Derivatives and Integrals / 237 \\
                 12.4: Inverse Jacobian Elliptic Functions / 237 \\
                 13: Probability Integrals and the Error Function \\
                 13.1: Normal Distribution / 239 \\
                 13.2: Error Function / 242 \\
                 14: Fresnel Integrals, Sine and Cosine Integrals \\
                 14.1: Definitions, Series Representations, and Values
                 at Infinity / 245 \\
                 14.2: Definitions, Series Representations, and Values
                 at Infinity / 247 \\
                 15: Definite Integrals \\
                 15.1: Integrands Involving Powers of x / 249 \\
                 15.2: Integrands Involving Trigonometric Functions 251
                 \\
                 15.3: Integrands Involving the Exponential Function 254
                 \\
                 15.4: Integrands Involving the Hyperbolic Function 256
                 \\
                 15.5: Integrands Involving the Logarithmic Function 256
                 \\
                 16: Different Forms of Fourier Series \\
                 16.1: Fourier Series for f(x) on -[pi] [less than or
                 equal] x [less than or equal] [pi] / 257 \\
                 16.2: Fourier Series for f(x) on -L [less than or
                 equal] x [less than or equal] L / 258 \\
                 16.3: Fourier Series for f(x) on a [less than or equal]
                 x [less than or equal] b / 258 \\
                 16.4: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 259
                 \\
                 16.5: Half-Range Fourier Cosine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L / 259 \\
                 16.6: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] [pi] 260
                 \\
                 16.7: Half-Range Fourier Sine Series for f(x) on 0
                 [less than or equal] x [less than or equal] L / 260 \\
                 16.8: Complex (Exponential) Fourier Series for f(x) on
                 -[pi] [less than or equal] x [less than or equal] [pi]
                 / 260 \\
                 16.9: Complex (Exponential) Fourier Series for f(x) on
                 -L [less than or equal] x [less than or equal] L 261
                 \\
                 16.10: Representative Examples of Fourier Series 261
                 \\
                 16.11: Fourier Series and Discontinuous Functions 265
                 \\
                 17: Bessel Functions \\
                 17.1: Bessel's Differential Equation / 269 \\
                 17.2: Series Expansions for J[subscript v](x) and
                 Y[subscript v](x) / 270 \\
                 17.3: Bessel Functions of Fractional Order / 272 \\
                 17.4: Asymptotic Representations for Bessel Functions /
                 273 \\
                 17.5: Zeros of Bessel Functions / 273 \\
                 17.6: Bessel's Modified Equation / 274 \\
                 17.7: Series Expansions for I[subscript v](x) and
                 K[subscript v](x) / 276 \\
                 17.8: Modified Bessel Functions of Fractional Order 277
                 \\
                 17.9: Asymptotic Representations of Modified Bessel
                 Functions / 278 \\
                 17.10: Relationships between Bessel Functions / 278 \\
                 17.11: Integral Representations of J[subscript n](x),
                 I[subscript n](x), and K[subscript n](x) / 281 \\
                 17.12: Indefinite Integrals of Bessel Functions / 281
                 \\
                 17.13: Definite Integrals Involving Bessel Functions /
                 282 \\
                 17.14: Spherical Bessel Functions / 283 \\
                 18: Orthogonal Polynomials \\
                 18.2: Legendre Polynomials P[subscript n](x) / 286 \\
                 18.3: Chebyshev Polynomials T[subscript n](x) and
                 U[subscript n](x) / 290 \\
                 18.4: Laguerre Polynomials L[subscript n](x) / 294 \\
                 18.5: Hermite Polynomials H[subscript n](x) / 296 \\
                 19: Laplace Transformation \\
                 20: Fourier Transforms \\
                 21: Numerical Integration \\
                 21.1: Classical Methods / 315 \\
                 22: Solutions of Standard Ordinary Differential
                 Equations \\
                 22.2: Separation of Variables / 323 \\
                 22.3: Linear First-Order Equations / 323 \\
                 22.4: Bernoulli's Equation / 324 \\
                 22.5: Exact Equations / 325 \\
                 22.6: Homogeneous Equations / 325 \\
                 22.7: Linear Differential Equations / 326 \\
                 22.8: Constant Coefficient Linear Differential
                 Equations--Homogeneous Case / 327 \\
                 22.9: Linear Homogeneous Second-Order Equation / 330
                 \\
                 22.10: Constant Coefficient Linear Differential
                 Equations--Inhomogeneous Case / 331 \\
                 22.11: Linear Inhomogeneous Second-Order Equation 333
                 \\
                 22.12: Determination of Particular Integrals by the
                 Method of- Undetermined Coefficients / 334 \\
                 22.13: Cauchy-Euler Equation / 336 \\
                 22.14: Legendre's Equation / 337 \\
                 22.15: Bessel's Equations / 337 \\
                 22.16: Power Series and Frobenius Methods / 339 \\
                 22.17: Hypergeometric Equation / 344 \\
                 22.18: Numerical Methods / 345 \\
                 23: Vector Analysis \\
                 23.1: Scalars and Vectors / 353 \\
                 23.2: Scalar Products / 358 \\
                 23.3: Vector Products / 359 \\
                 23.4: Triple Products / 360 \\
                 23.5: Products of Four Vectors / 361 \\
                 23.6: Derivatives of Vector Functions of a Scalar t 361
                 \\
                 23.7: Derivatives of Vector Functions of Several Scalar
                 Variables / 362 \\
                 23.8: Integrals of Vector Functions of a Scalar
                 Variable t / 363 \\
                 23.9: Line Integrals / 364 \\
                 23.10: Vector Integral Theorems / 366 \\
                 23.11: A Vector Rate of Change Theorem / 368 \\
                 23.12: Useful Vector Identities and Results / 368 \\
                 24: Systems of Orthogonal Coordinates \\
                 24.1: Curvilinear Coordinates / 369 \\
                 24.2: Vector Operators in Orthogonal Coordinates 371
                 \\
                 24.3: Systems of Orthogonal Coordinates / 371 \\
                 25: Partial Differential Equations and Special
                 Functions \\
                 25.1: Fundamental Ideas / 381 \\
                 25.2: Method of Separation of Variables / 385 \\
                 25.3: Sturm--Liouville Problem and Special Functions
                 387 \\
                 25.4: A First-Order System and the Wave Equation 390
                 \\
                 25.5: Conservation Equations (Laws) / 391 \\
                 25.6: Method of Characteristics / 392 \\
                 25.7: Discontinuous Solutions (Shocks) / 396 \\
                 25.8: Similarity Solutions / 398 \\
                 25.9: Burgers's Equation, the KdV Equation, and the
                 KdVB Equation / 400 \\
                 26: Z-Transform \\
                 26.1: Z-Transform and Transform Pairs / 403 \\
                 27: Numerical Approximation \\
                 27.2: Economization of Series / 411 \\
                 27.3: Pade Approximation / 413 \\
                 27.4: Finite Difference Approximations to Ordinary and
                 Partial Derivatives / 415",
}


bibtype: article
filename: elefunt.bib
label: Kilbas:2000:CFI
author: A. A. Kilbas and J. J. Trujillo
title: Computation of fractional integrals via functions of hypergeometric and Bessel type
journal: j-J-COMPUT-APPL-MATH
volume: 118
number: 1--2
pages: 223--239
day: 1
month: jun
monthnumber: 6
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:35 MST 2017
bibtimestamp: 2017.02.25 12:43:35 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700002910
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. A. Kilbas and J. J. Trujillo
rawtitle: Computation of fractional integrals via functions of hypergeometric and {Bessel} type
entry:
@Article{Kilbas:2000:CFI,
  author =       "A. A. Kilbas and J. J. Trujillo",
  title =        "Computation of fractional integrals via functions of
                 hypergeometric and {Bessel} type",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "223--239",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002910",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lefevre:2000:CRF
author: V. D. Lefevre and J.-M. Muller
booktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
title: Correctly rounded functions for better arithmetic
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 875--878
year: 2000
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
acknowledgement: ack-nhfb
rawauthor: V. D. Lefevre and J.-M. Muller
rawbooktitle: Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, 2000
rawtitle: Correctly rounded functions for better arithmetic
entry:
@InProceedings{Lefevre:2000:CRF,
  author =       "V. D. Lefevre and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Correctly rounded functions for better arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "875--878",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The IEEE 754 standard for floating-point arithmetic
                 requires that the four arithmetic operations and the
                 square root should be correctly rounded. This has
                 improved the accuracy, reliability and portability of
                 numerical software. Unfortunately, such \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lopez:2000:AES
author: Jose L. Lopez
title: Asymptotic Expansions of Symmetric Standard Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 31
number: 4
pages: 754--775
year: 2000
CODEN: SJMAAH
DOI: https://doi.org/10.1137/S0036141099351176
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Fri Oct 27 08:17:04 MDT 2000
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.10.27 08:17:04 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/35117
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: Jos{\'e} L. L{\'o}pez
rawtitle: Asymptotic Expansions of Symmetric Standard Elliptic Integrals
entry:
@Article{Lopez:2000:AES,
  author =       "Jos{\'e} L. L{\'o}pez",
  title =        "Asymptotic Expansions of Symmetric Standard Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "31",
  number =       "4",
  pages =        "754--775",
  year =         "2000",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/S0036141099351176",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Oct 27 08:17:04 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/35117",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lozier:2000:DPN
author: Daniel W. Lozier
title: The DLMF Project: a New Initiative in Classical Special Functions
crossref: Dunkl:2000:PIW
pages: 207--220
year: 2000
bibdate: Fri Jul 09 06:31:32 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:31:32 ???
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawtitle: The {DLMF Project}: a New Initiative in Classical Special Functions
entry:
@InProceedings{Lozier:2000:DPN,
  author =       "Daniel W. Lozier",
  title =        "The {DLMF Project}: a New Initiative in Classical
                 Special Functions",
  crossref =     "Dunkl:2000:PIW",
  pages =        "207--220",
  year =         "2000",
  bibdate =      "Fri Jul 09 06:31:32 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Markstein:2000:IEF
author: Peter Markstein
title: IA-64 and elementary functions: speed and precision
publisher: pub-PH
address: pub-PH:adr
pages: xix + 298
year: 2000
ISBN: 0-13-018348-2 OR 0130183482
ISBN13: 978-0-13-018348-4 OR 9780130183484
LCCN: QA76.9.A73 M365 2000
bibdate: Fri Jan 5 08:00:52 MST 2001
bibtimestamp: 2001.01.05 08:00:52 MST
series: Hewlett--Packard professional books
URL: http://www.markstein.org/
keywords: IA-64 (computer architecture)
acknowledgement: ack-nhfb
rawauthor: Peter Markstein
rawtitle: {IA-64} and elementary functions: speed and precision
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/intel-ia-64.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/microchip.bib; University of California MELVYL catalog.

remark:
Besides recipes for accurate computation of elementary functions, this book also contains algorithms for the correctly-rounded computation of floating-point division and square-root, and of integer division, starting from low-precision reciprocal approximations. There is also a wealth of information on the tradeoffs between integer and floating-point instruction use in a pipelined parallel architecture.

TOC:
IA-64 Architecture New Architecture Objectives VLIW Memory Enhancements Software Pipelining Floating Point Enhancements Summary IA-64 Instructions And Registers Instructions Register Sets Accessing Memory Assembly Language Problems Increasing Instruction Level Parallelism Branching Speculation Problems Floating Point Architecture Floating Point Status Register Precision Fused Multiply-Add Division and Square Root Assists Floating Comparisons Communication between Floating Point and General Purpose Registers Fixed Point Multiplication SIMD Arithmetic Problems Programming For IA-64 Compiler Options Pragmas Floating Point Data Types In-Line Assembly The fenv.h Header Extended Examples Quad Precision Problems Computation of Elementary Functions Mathematical Preliminaries Floating Point Approximation and Error Analysis The Exclusion Theorem Ulps Problems Approximation Of Functions Taylor Series Lagrangian Interpolation Chebychev Approximation Remez Approximation Practical Considerations Function Evaluation Table Construction Problems Division Approximations for the Reciprocal Computing the Quotient Division Using Only Final Precision Results Fast Variants of Division Remainder Integer Division An Implementation of Division Problems Square Root Approximations Rounding the Square Root Computing the Square Root Calculating the Reciprocal Square Root An Implementation of Square Root Problems Exponential Functions Definitions and Formulas Argument Reduction Error Containment Computing the Exponential The Function expm Problems Logarithmic Functions General Relations Argument Reductions Error Analysis The Function log1p Computing the Logarithm Problems The Power Function Definition Single Precision Double Precision Double-Extended Precision Quad Precision Computing the Power Function Problems Trigonometric Functions Formulas and Identities Argument Reduction Error Analysis Computing the Trigonometric Functions Problems Inverse Sine And Cosine Definitions and Formulas Argument Reduction Error Analysis Computing the arcsin Problems Inverse Tangent Functions Definitions and Formulas Argument Reduction Error Analysis Computing the arctan Problems Hyperbolic Functions Definitions and Formulas Argument Reduction Error Analysis Computing the Hyperbolic Functions Problems Inverse Hyperbolic Functions Definitions and Formulas. arcsinh. arccosh. arctanh Problems Odds And Ends Correctly Rounded Functions Monotonicity Alternative Algorithms Testing New Architectural Directions Problems In-Line Assembly Solutions To Problems Bibliography Subject Index

rawTOC:
IA-64 Architecture \\ New Architecture Objectives \\ VLIW \\ Memory Enhancements \\ Software Pipelining \\ Floating Point Enhancements \\ Summary \\ IA-64 Instructions And Registers \\ Instructions \\ Register Sets \\ Accessing Memory \\ Assembly Language \\ Problems \\ Increasing Instruction Level Parallelism \\ Branching \\ Speculation \\ Problems \\ Floating Point Architecture \\ Floating Point Status Register \\ Precision \\ Fused Multiply-Add \\ Division and Square Root Assists \\ Floating Comparisons \\ Communication between Floating Point and General Purpose Registers \\ Fixed Point Multiplication \\ SIMD Arithmetic \\ Problems \\ Programming For IA-64 \\ Compiler Options \\ Pragmas \\ Floating Point Data Types \\ In-Line Assembly \\ The fenv.h Header \\ Extended Examples \\ Quad Precision \\ Problems \\ Computation of Elementary Functions \\ Mathematical Preliminaries \\ Floating Point \\ Approximation and Error Analysis \\ The Exclusion Theorem \\ Ulps \\ Problems \\ Approximation Of Functions \\ Taylor Series \\ Lagrangian Interpolation \\ Chebychev Approximation \\ Remez Approximation \\ Practical Considerations \\ Function Evaluation \\ Table Construction \\ Problems \\ Division \\ Approximations for the Reciprocal \\ Computing the Quotient \\ Division Using Only Final Precision Results \\ Fast Variants of Division \\ Remainder \\ Integer Division \\ An Implementation of Division \\ Problems \\ Square Root \\ Approximations \\ Rounding the Square Root \\ Computing the Square Root \\ Calculating the Reciprocal Square Root \\ An Implementation of Square Root \\ Problems \\ Exponential Functions \\ Definitions and Formulas \\ Argument Reduction \\ Error Containment \\ Computing the Exponential \\ The Function expm \\ Problems \\ Logarithmic Functions \\ General Relations \\ Argument Reductions \\ Error Analysis \\ The Function log1p \\ Computing the Logarithm \\ Problems \\ The Power Function \\ Definition \\ Single Precision \\ Double Precision \\ Double-Extended Precision \\ Quad Precision \\ Computing the Power Function \\ Problems \\ Trigonometric Functions \\ Formulas and Identities \\ Argument Reduction \\ Error Analysis \\ Computing the Trigonometric Functions \\ Problems \\ Inverse Sine And Cosine \\ Definitions and Formulas \\ Argument Reduction \\ Error Analysis \\ Computing the arcsin \\ Problems \\ Inverse Tangent Functions \\ Definitions and Formulas \\ Argument Reduction \\ Error Analysis \\ Computing the arctan \\ Problems \\ Hyperbolic Functions \\ Definitions and Formulas \\ Argument Reduction \\ Error Analysis \\ Computing the Hyperbolic Functions \\ Problems \\ Inverse Hyperbolic Functions \\ Definitions and Formulas. arcsinh. arccosh. arctanh \\ Problems \\ Odds And Ends \\ Correctly Rounded Functions \\ Monotonicity \\ Alternative Algorithms \\ Testing \\ New Architectural Directions \\ Problems \\ In-Line Assembly \\ Solutions To Problems \\ Bibliography \\ Subject Index

entry:
@Book{Markstein:2000:IEF,
  author =       "Peter Markstein",
  title =        "{IA-64} and elementary functions: speed and
                 precision",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 298",
  year =         "2000",
  ISBN =         "0-13-018348-2",
  ISBN-13 =      "978-0-13-018348-4",
  LCCN =         "QA76.9.A73 M365 2000",
  bibdate =      "Fri Jan 5 08:00:52 MST 2001",
  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/intel-ia-64.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib;
                 University of California MELVYL catalog.",
  series =       "Hewlett--Packard professional books",
  URL =          "http://www.markstein.org/",
  acknowledgement = ack-nhfb,
  keywords =     "IA-64 (computer architecture)",
  remark =       "Besides recipes for accurate computation of elementary
                 functions, this book also contains algorithms for the
                 correctly-rounded computation of floating-point
                 division and square-root, and of integer division,
                 starting from low-precision reciprocal approximations.
                 There is also a wealth of information on the tradeoffs
                 between integer and floating-point instruction use in a
                 pipelined parallel architecture.",
  tableofcontents = "IA-64 Architecture \\
                 New Architecture Objectives \\
                 VLIW \\
                 Memory Enhancements \\
                 Software Pipelining \\
                 Floating Point Enhancements \\
                 Summary \\
                 IA-64 Instructions And Registers \\
                 Instructions \\
                 Register Sets \\
                 Accessing Memory \\
                 Assembly Language \\
                 Problems \\
                 Increasing Instruction Level Parallelism \\
                 Branching \\
                 Speculation \\
                 Problems \\
                 Floating Point Architecture \\
                 Floating Point Status Register \\
                 Precision \\
                 Fused Multiply-Add \\
                 Division and Square Root Assists \\
                 Floating Comparisons \\
                 Communication between Floating Point and General
                 Purpose Registers \\
                 Fixed Point Multiplication \\
                 SIMD Arithmetic \\
                 Problems \\
                 Programming For IA-64 \\
                 Compiler Options \\
                 Pragmas \\
                 Floating Point Data Types \\
                 In-Line Assembly \\
                 The fenv.h Header \\
                 Extended Examples \\
                 Quad Precision \\
                 Problems \\
                 Computation of Elementary Functions \\
                 Mathematical Preliminaries \\
                 Floating Point \\
                 Approximation and Error Analysis \\
                 The Exclusion Theorem \\
                 Ulps \\
                 Problems \\
                 Approximation Of Functions \\
                 Taylor Series \\
                 Lagrangian Interpolation \\
                 Chebychev Approximation \\
                 Remez Approximation \\
                 Practical Considerations \\
                 Function Evaluation \\
                 Table Construction \\
                 Problems \\
                 Division \\
                 Approximations for the Reciprocal \\
                 Computing the Quotient \\
                 Division Using Only Final Precision Results \\
                 Fast Variants of Division \\
                 Remainder \\
                 Integer Division \\
                 An Implementation of Division \\
                 Problems \\
                 Square Root \\
                 Approximations \\
                 Rounding the Square Root \\
                 Computing the Square Root \\
                 Calculating the Reciprocal Square Root \\
                 An Implementation of Square Root \\
                 Problems \\
                 Exponential Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Containment \\
                 Computing the Exponential \\
                 The Function expm \\
                 Problems \\
                 Logarithmic Functions \\
                 General Relations \\
                 Argument Reductions \\
                 Error Analysis \\
                 The Function log1p \\
                 Computing the Logarithm \\
                 Problems \\
                 The Power Function \\
                 Definition \\
                 Single Precision \\
                 Double Precision \\
                 Double-Extended Precision \\
                 Quad Precision \\
                 Computing the Power Function \\
                 Problems \\
                 Trigonometric Functions \\
                 Formulas and Identities \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Trigonometric Functions \\
                 Problems \\
                 Inverse Sine And Cosine \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arcsin \\
                 Problems \\
                 Inverse Tangent Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arctan \\
                 Problems \\
                 Hyperbolic Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Hyperbolic Functions \\
                 Problems \\
                 Inverse Hyperbolic Functions \\
                 Definitions and Formulas. arcsinh. arccosh. arctanh \\
                 Problems \\
                 Odds And Ends \\
                 Correctly Rounded Functions \\
                 Monotonicity \\
                 Alternative Algorithms \\
                 Testing \\
                 New Architectural Directions \\
                 Problems \\
                 In-Line Assembly \\
                 Solutions To Problems \\
                 Bibliography \\
                 Subject Index",
}


bibtype: article
filename: elefunt.bib
label: Paliouras:2000:FPP
author: V. Paliouras and K. Karagianni and T. Stouraitis
title: A floating-point processor for fast and accurate sine / cosine evaluation
journal: j-IEEE-TRANS-CIRCUITS-SYST-2
volume: 47
number: 5
pages: 441--451
month: may
monthnumber: 5
year: 2000
CODEN: ICSPE5
DOI: https://doi.org/10.1109/82.842112
ISSN: 1057-7130 (print), 1558-125X (electronic) OR 10577130 (print), 1558125X (electronic)
ISSNL: 1057-7130 OR 10577130
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Transactions on Circuits and Systems. 2, Analog and Digital Signal Processing
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82
rawauthor: V. Paliouras and K. Karagianni and T. Stouraitis
rawtitle: A floating-point processor for fast and accurate sine\slash cosine evaluation
entry:
@Article{Paliouras:2000:FPP,
  author =       "V. Paliouras and K. Karagianni and T. Stouraitis",
  title =        "A floating-point processor for fast and accurate
                 sine\slash cosine evaluation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "5",
  pages =        "441--451",
  month =        may,
  year =         "2000",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.842112",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A VLSI architecture for fast and accurate
                 floating-point sine/cosine evaluation is presented,
                 combining floating-point and simple fixed-point
                 arithmetic. The algorithm implemented by the
                 architecture is based on second order polynomial
                 interpolation \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Simon:2000:DCF
author: Marvin Kenneth Simon and Mohamed-Slim Alouini
title: Digital Communication over Fading Channels: a Unified Approach to Performance Analysis
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xix + 544
year: 2000
ISBN: 0-471-31779-9 OR 0471317799
ISBN13: 978-0-471-31779-1 OR 9780471317791
LCCN: TK5103.7 .S523 2000
bibdate: Sat Dec 16 17:34:06 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.12.16 17:34:06 MST
series: Wiley series in telecommunications and signal processing
subject: Digital communications; Reliability; Mathematics; Radio; Transmitters and transmission; Fading
acknowledgement: ack-nhfb
authordates: 1939--
rawauthor: Marvin Kenneth Simon and Mohamed-Slim Alouini
rawtitle: Digital Communication over Fading Channels: a Unified Approach to Performance Analysis
URL:
http://www.loc.gov/catdir/bios/wiley043/99056352.html; http://www.loc.gov/catdir/description/wiley035/99056352.html; http://www.loc.gov/catdir/toc/onix06/99056352.html

TOC:
1.1: System Performance Measures 4 1.1.1: Average Signal-to-Noise Ratio 4 1.1.2: Outage Probability 5 1.1.3: Average Bit Error Probability 6 Chapter 2: Fading Channel Characterization and Modeling 15 2.1: Main Characteristics of Fading Channels 15 2.1.1: Envelope and Phase Fluctuations 15 2.1.2: Slow and Fast Fading 16 2.1.3: Frequency-Flat and Frequency-Selective Fading 16 2.2: Modeling of Flat Fading Channels 17 2.2.1: Multipath Fading 18 2.2.2: Log-Normal Shadowing 23 2.2.3: Composite Multipath/Shadowing 24 2.2.4: Combined (Time-Shared) Shadowed/Unshadowed Fading 25 2.3: Modeling of Frequency-Selective Fading Channels 26 Chapter 3: Types of Communication 31 3.1: Ideal Coherent Detection 31 3.1.1: Multiple Amplitude-Shift-Keying or Multiple Amplitude Modulation 33 3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature Amplitude Modulation 34 3.1.3: M-ary Phase-Shift-Keying 35 3.1.4: Differentially Encoded M-ary Phase-Shift-Keying 39 3.1.5: Offset QPSK or Staggered QPSK 41 3.1.6: M-ary Frequency-Shift-Keying 43 3.1.7: Minimum-Shift-Keying 45 3.2: Nonideal Coherent Detection 47 3.3: Noncoherent Detection 53 3.4: Partially Coherent Detection 55 3.4.1: Conventional Detection: One-Symbol Observation 55 3.4.2: Multiple Symbol Detection 57 3.5: Differentially Coherent Detection 59 3.5.1: M-ary Differential Phase Shift Keying 59 3.5.2: [pi]/4-Differential QPSK 65 Part 2: Mathematical Tools Chapter 4: Alternative Representations of Classical Functions 69 4.1: Gaussian $Q$-Function 70 4.1.1: One-Dimensional Case 70 4.1.2: Two-Dimensional Case 72 4.2: Marcum $Q$-Function 74 4.2.1: First-Order Marcum $Q$-Function 74 4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81 4.3: Other Functions 90 Appendix 4A: Derivation of Eq. (4.2) 95 Chapter 5: Useful Expressions for Evaluating Average Error Probability Performance 99 5.1: Integrals Involving the Gaussian $Q$-Function 99 5.1.1: Rayleigh Fading Channel 101 5.1.2: Nakagami-q (Hoyt) Fading Channel 101 5.1.3: Nakagami-n (Rice) Fading Channel 102 5.1.4: Nakagami-m Fading Channel 102 5.1.5: Log-Normal Shadowing Channel 104 5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 104 5.2: Integrals Involving the Marcum $Q$-Function 107 5.2.1: Rayleigh Fading Channel 108 5.2.2: Nakagami-q (Hoyt) Fading Channel 109 5.2.3: Nakagami-n (Rice) Fading Channel 109 5.2.4: Nakagami-m Fading Channel 109 5.2.5: Log-Normal Shadowing Channel 109 5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 110 5.3: Integrals Involving the Incomplete Gamma Function 111 5.3.1: Rayleigh Fading Channel 112 5.3.2: Nakagami-q (Hoyt) Fading Channel 112 5.3.3: Nakagami-n (Rice) Fading Channel 112 5.3.4: Nakagami-m Fading Channel 113 5.3.5: Log-Normal Shadowing Channel 114 5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 114 5.4: Integrals Involving Other Functions 114 5.4.1: M-PSK Error Probability Integral 114 5.4.2: Arbitrary Two-Dimensional Signal Constellation Error Probability Integral 116 5.4.3: Integer Powers of the Gaussian $Q$-Function 117 5.4.4: Integer Powers of M-PSK Error Probability Integrals 121 Appendix 5A: Evaluation of Definite Integrals Associated with Rayleigh and Nakagami-$m$ Fading 124 Chapter 6: New Representations of Some PDF's and CDF's for Correlative Fading Applications 141 6.1: Bivariate Rayleigh PDF and CDF 142 6.2: PDF and CDF for Maximum of Two Rayleigh Random Variables 146 6.3: PDF and CDF for Maximum of Two Nakagami-m Random Variables 149 Part 3: Optimum Reception and Performance Evaluation Chapter 7: Optimum Receivers for Fading Channels 157 7.1: Case of Known Amplitudes, Phases, and Delays: Coherent, Detection 159 7.2: Case of Known Phases and Delays, Unknown Amplitudes 163 7.2.1: Rayleigh Fading 163 7.2.2: Nakagami-m Fading 164 7.3: Case of Known Amplitudes and Delays, Unknown Phases 166 7.4: Case of Known Delays and Unknown Amplitudes and Phases 168 7.4.1: One-Symbol Observation: Noncoherent Detection 168 7.4.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 181 7.4.3: N-Symbol Observation: Multiple Symbol Differentially Coherent Detection 186 7.5: Case of Unknown Amplitudes, Phases, and Delays 188 7.5.1: One-Symbol Observation: Noncoherent Detection 188 7.5.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 190 Chapter 8: Performance of Single Channel Receives 193 8.1: Performance Over the AWGN Channel 193 8.1.1: Ideal Coherent Detection 194 8.1.2: Nonideal Coherent Detection 206 8.1.3: Noncoherent Detection 209 8.1.4: Partially Coherent Detection 210 8.1.5: Differentially Coherent Detection 213 8.1.6: Generic Results for Binary Signaling 218 8.2: Performance Over Fading Channels 219 8.2.1: Ideal Coherent Detection 220 8.2.2: Nonideal Coherent Detection 234 8.2.3: Noncoherent Detection 239 8.2.4: Partially Coherent Detection 242 8.2.5: Differentially Coherent Detection 243 Appendix 8A: Stein's Unified Analysis of the Error Probability Performance of Certain Communication Systems 253 Chapter 9: Performance of Multichannel Receivers 259 9.1: Diversity Combining 260 9.1.1: Diversity Concept 260 9.1.2: Mathematical Modeling 260 9.1.3: Brief Survey of Diversity Combining Techniques 261 9.1.4: Complexity-Performance Trade-offs 264 9.2: Maximal-Ratio Combining 265 9.2.1: Receiver Structure 265 9.2.2: PDF-Based Approach 267 9.2.3: MGF-Based Approach 268 9.2.4: Bounds and Asymptotic SER Expressions 275 9.3: Coherent Equal Gain Combining 278 9.3.1: Receiver Structure 279 9.3.2: Average Output SNR 279 9.3.3: Exact Error Rate Analysis 281 9.3.4: Approximate Error Rate Analysis 288 9.3.5: Asymptotic Error Rate Analysis 289 9.4: Noncoherent Equal-Gain Combining 290 9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 9.4.2: M-ary Orthogonal FSK 304 9.5: Outage Probability Performance 311 9.5.1: MRC and Noncoherent EGC 312 9.5.2: Coherent EGC 313 9.5.3: Numerical Examples 314 9.6: Impact of Fading Correlation 316 9.6.1: Model A: Two Correlated Branches with Nonidentical Fading 320 9.6.2: Model B: D Identically Distributed Branches with Constant Correlation 323 9.6.3: Model C: D Identically Distributed Branches with Exponential Correlation 324 9.6.4: Model D: D Nonidentically Distributed Branches with Arbitrary Correlation 325 9.6.5: Numerical Examples 329 9.7: Selection Combining 333 9.7.1: MGF of Output SNR 335 9.7.2: Average Output SNR 336 9.7.3: Outage Probability 338 9.7.4: Average Probability of Error 340 9.8: Switched Diversity 348 9.8.1: Performance of SSC over Independent Identically Distributed Branches 348 9.8.2: Effect of Branch Unbalance 362 9.8.3: Effect of Branch Correlation 366 9.9: Performance in the Presence of Outdated or Imperfect Channel Estimates 370 9.9.1: Maximal-Ratio Combining 370 9.9.2: Noncoherent EGC over Rician Fast Fading 371 9.9.3: Selection Combining 373 9.9.4: Switched Diversity 374 9.9.5: Numerical Results 377 9.10: Hybrid Diversity Schemes 378 9.10.1: Generalized Selection Combining 378 9.10.2: Generalized Switched Diversity 403 9.10.3: Two-Dimensional Diversity Schemes 408 Appendix 9A: Alternative Forms of the Bit Error Probability for a Decision Statistic that is a Quadratic Form of Complex Gaussian Random Variables 421 Appendix 9B: Simple Numerical Techniques for thee Inversion of the Laplace Transform of Cumulative Distribution Functions 427 9B.1: Euler Summation-Based Technique 427 9B.2: Gauss-Chebyshev Quadrature-Based Technique 428 Appendix 9C: Proof of Theorem 1 430 Appendix 9D: Direct Proof of Eq. (9.331) 431 Appendix 9E: Special Definite Integrals 432 Part 4: Application in Practical Communication Systems Chapter 10: Optimum Combining: A Diversity Technique for Communication Over Fading Channels in the Presence of Interference 437 10.1: Performance of Optimum Combining Receivers 438 10.1.1: Single Interferer, Independent Identically Distributed Fading 438 10.1.2: Multiple Interferers, Independent Identically Distributed Fading 454 10.1.3: Comparison with Results for MRC in the Presence of Interference 466 Chapter 11: Direct-Sequence Code-Division Multiple Access 473 11.1: Single-Carrier DS-CDMA Systems 474 11.1.1: System and Channel Models 474 11.1.2: Performance Analysis 477 11.2: Multicarrier DS-CDMA Systems 479 11.2.1: System and Channel Models 480 11.2.2: Performance Analysis 483 11.2.3: Numerical Examples 489 Part 5: Further Extensions Chapter 12: Coded Communication Over Fading Channels 497 12.1: Coherent Detection 499 12.1.1: System Model 499 12.1.2: Evaluation of Pairwise Error Probability 502 12.1.3: Transfer Function Bound on Average Bit Error Probability 510 12.1.4: Alternative Formulation of the Transfer Function Bound 513 12.2: Differentially Coherent Detection 520 12.2.1: System Model 520 12.2.2: Performance Evaluation 522 12.3: Numerical Results: Comparison of the True Upper Bounds and Union-Chernoff Bounds 526 Appendix 12A: Evaluation of a Moment Generating Function Associated with Differential Detection of M-PSK Sequences 532

rawTOC:
1.1: System Performance Measures 4 \\ 1.1.1: Average Signal-to-Noise Ratio 4 \\ 1.1.2: Outage Probability 5 \\ 1.1.3: Average Bit Error Probability 6 \\ Chapter 2: Fading Channel Characterization and Modeling 15 \\ 2.1: Main Characteristics of Fading Channels 15 \\ 2.1.1: Envelope and Phase Fluctuations 15 \\ 2.1.2: Slow and Fast Fading 16 \\ 2.1.3: Frequency-Flat and Frequency-Selective Fading 16 \\ 2.2: Modeling of Flat Fading Channels 17 \\ 2.2.1: Multipath Fading 18 \\ 2.2.2: Log-Normal Shadowing 23 \\ 2.2.3: Composite Multipath/Shadowing 24 \\ 2.2.4: Combined (Time-Shared) Shadowed/Unshadowed Fading 25 \\ 2.3: Modeling of Frequency-Selective Fading Channels 26 \\ Chapter 3: Types of Communication 31 \\ 3.1: Ideal Coherent Detection 31 \\ 3.1.1: Multiple Amplitude-Shift-Keying or Multiple Amplitude Modulation 33 \\ 3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature Amplitude Modulation 34 \\ 3.1.3: M-ary Phase-Shift-Keying 35 \\ 3.1.4: Differentially Encoded M-ary Phase-Shift-Keying 39 \\ 3.1.5: Offset QPSK or Staggered QPSK 41 \\ 3.1.6: M-ary Frequency-Shift-Keying 43 \\ 3.1.7: Minimum-Shift-Keying 45 \\ 3.2: Nonideal Coherent Detection 47 \\ 3.3: Noncoherent Detection 53 \\ 3.4: Partially Coherent Detection 55 \\ 3.4.1: Conventional Detection: One-Symbol Observation 55 \\ 3.4.2: Multiple Symbol Detection 57 \\ 3.5: Differentially Coherent Detection 59 \\ 3.5.1: M-ary Differential Phase Shift Keying 59 \\ 3.5.2: [pi]/4-Differential QPSK 65 \\ Part 2: Mathematical Tools \\ Chapter 4: Alternative Representations of Classical Functions 69 \\ 4.1: Gaussian $Q$-Function 70 \\ 4.1.1: One-Dimensional Case 70 \\ 4.1.2: Two-Dimensional Case 72 \\ 4.2: Marcum $Q$-Function 74 \\ 4.2.1: First-Order Marcum $Q$-Function 74 \\ 4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81 \\ 4.3: Other Functions 90 \\ Appendix 4A: Derivation of Eq. (4.2) 95 \\ Chapter 5: Useful Expressions for Evaluating Average Error Probability Performance 99 \\ 5.1: Integrals Involving the Gaussian $Q$-Function 99 \\ 5.1.1: Rayleigh Fading Channel 101 \\ 5.1.2: Nakagami-q (Hoyt) Fading Channel 101 \\ 5.1.3: Nakagami-n (Rice) Fading Channel 102 \\ 5.1.4: Nakagami-m Fading Channel 102 \\ 5.1.5: Log-Normal Shadowing Channel 104 \\ 5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 104 \\ 5.2: Integrals Involving the Marcum $Q$-Function 107 \\ 5.2.1: Rayleigh Fading Channel 108 \\ 5.2.2: Nakagami-q (Hoyt) Fading Channel 109 \\ 5.2.3: Nakagami-n (Rice) Fading Channel 109 \\ 5.2.4: Nakagami-m Fading Channel 109 \\ 5.2.5: Log-Normal Shadowing Channel 109 \\ 5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 110 \\ 5.3: Integrals Involving the Incomplete Gamma Function 111 \\ 5.3.1: Rayleigh Fading Channel 112 \\ 5.3.2: Nakagami-q (Hoyt) Fading Channel 112 \\ 5.3.3: Nakagami-n (Rice) Fading Channel 112 \\ 5.3.4: Nakagami-m Fading Channel 113 \\ 5.3.5: Log-Normal Shadowing Channel 114 \\ 5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading Channel 114 \\ 5.4: Integrals Involving Other Functions 114 \\ 5.4.1: M-PSK Error Probability Integral 114 \\ 5.4.2: Arbitrary Two-Dimensional Signal Constellation Error Probability Integral 116 \\ 5.4.3: Integer Powers of the Gaussian $Q$-Function 117 \\ 5.4.4: Integer Powers of M-PSK Error Probability Integrals 121 \\ Appendix 5A: Evaluation of Definite Integrals Associated with Rayleigh and Nakagami-$m$ Fading 124 \\ Chapter 6: New Representations of Some PDF's and CDF's for Correlative Fading Applications 141 \\ 6.1: Bivariate Rayleigh PDF and CDF 142 \\ 6.2: PDF and CDF for Maximum of Two Rayleigh Random Variables 146 \\ 6.3: PDF and CDF for Maximum of Two Nakagami-m Random Variables 149 \\ Part 3: Optimum Reception and Performance Evaluation \\ Chapter 7: Optimum Receivers for Fading Channels 157 \\ 7.1: Case of Known Amplitudes, Phases, and Delays: Coherent, Detection 159 \\ 7.2: Case of Known Phases and Delays, Unknown Amplitudes 163 \\ 7.2.1: Rayleigh Fading 163 \\ 7.2.2: Nakagami-m Fading 164 \\ 7.3: Case of Known Amplitudes and Delays, Unknown Phases 166 \\ 7.4: Case of Known Delays and Unknown Amplitudes and Phases 168 \\ 7.4.1: One-Symbol Observation: Noncoherent Detection 168 \\ 7.4.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 181 \\ 7.4.3: N-Symbol Observation: Multiple Symbol Differentially Coherent Detection 186 \\ 7.5: Case of Unknown Amplitudes, Phases, and Delays 188 \\ 7.5.1: One-Symbol Observation: Noncoherent Detection 188 \\ 7.5.2: Two-Symbol Observation: Conventional Differentially Coherent Detection 190 \\ Chapter 8: Performance of Single Channel Receives 193 \\ 8.1: Performance Over the AWGN Channel 193 \\ 8.1.1: Ideal Coherent Detection 194 \\ 8.1.2: Nonideal Coherent Detection 206 \\ 8.1.3: Noncoherent Detection 209 \\ 8.1.4: Partially Coherent Detection 210 \\ 8.1.5: Differentially Coherent Detection 213 \\ 8.1.6: Generic Results for Binary Signaling 218 \\ 8.2: Performance Over Fading Channels 219 \\ 8.2.1: Ideal Coherent Detection 220 \\ 8.2.2: Nonideal Coherent Detection 234 \\ 8.2.3: Noncoherent Detection 239 \\ 8.2.4: Partially Coherent Detection 242 \\ 8.2.5: Differentially Coherent Detection 243 \\ Appendix 8A: Stein's Unified Analysis of the Error Probability Performance of Certain Communication Systems 253 \\ Chapter 9: Performance of Multichannel Receivers 259 \\ 9.1: Diversity Combining 260 \\ 9.1.1: Diversity Concept 260 \\ 9.1.2: Mathematical Modeling 260 \\ 9.1.3: Brief Survey of Diversity Combining Techniques 261 \\ 9.1.4: Complexity-Performance Trade-offs 264 \\ 9.2: Maximal-Ratio Combining 265 \\ 9.2.1: Receiver Structure 265 \\ 9.2.2: PDF-Based Approach 267 \\ 9.2.3: MGF-Based Approach 268 \\ 9.2.4: Bounds and Asymptotic SER Expressions 275 \\ 9.3: Coherent Equal Gain Combining 278 \\ 9.3.1: Receiver Structure 279 \\ 9.3.2: Average Output SNR 279 \\ 9.3.3: Exact Error Rate Analysis 281 \\ 9.3.4: Approximate Error Rate Analysis 288 \\ 9.3.5: Asymptotic Error Rate Analysis 289 \\ 9.4: Noncoherent Equal-Gain Combining 290 \\ 9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 \\ 9.4.2: M-ary Orthogonal FSK 304 \\ 9.5: Outage Probability Performance 311 \\ 9.5.1: MRC and Noncoherent EGC 312 \\ 9.5.2: Coherent EGC 313 \\ 9.5.3: Numerical Examples 314 \\ 9.6: Impact of Fading Correlation 316 \\ 9.6.1: Model A: Two Correlated Branches with Nonidentical Fading 320 \\ 9.6.2: Model B: D Identically Distributed Branches with Constant Correlation 323 \\ 9.6.3: Model C: D Identically Distributed Branches with Exponential Correlation 324 \\ 9.6.4: Model D: D Nonidentically Distributed Branches with Arbitrary Correlation 325 \\ 9.6.5: Numerical Examples 329 \\ 9.7: Selection Combining 333 \\ 9.7.1: MGF of Output SNR 335 \\ 9.7.2: Average Output SNR 336 \\ 9.7.3: Outage Probability 338 \\ 9.7.4: Average Probability of Error 340 \\ 9.8: Switched Diversity 348 \\ 9.8.1: Performance of SSC over Independent Identically Distributed Branches 348 \\ 9.8.2: Effect of Branch Unbalance 362 \\ 9.8.3: Effect of Branch Correlation 366 \\ 9.9: Performance in the Presence of Outdated or Imperfect Channel Estimates 370 \\ 9.9.1: Maximal-Ratio Combining 370 \\ 9.9.2: Noncoherent EGC over Rician Fast Fading 371 \\ 9.9.3: Selection Combining 373 \\ 9.9.4: Switched Diversity 374 \\ 9.9.5: Numerical Results 377 \\ 9.10: Hybrid Diversity Schemes 378 \\ 9.10.1: Generalized Selection Combining 378 \\ 9.10.2: Generalized Switched Diversity 403 \\ 9.10.3: Two-Dimensional Diversity Schemes 408 \\ Appendix 9A: Alternative Forms of the Bit Error Probability for a Decision Statistic that is a Quadratic Form of Complex Gaussian Random Variables 421 \\ Appendix 9B: Simple Numerical Techniques for thee Inversion of the Laplace Transform of Cumulative Distribution Functions 427 \\ 9B.1: Euler Summation-Based Technique 427 \\ 9B.2: Gauss-Chebyshev Quadrature-Based Technique 428 \\ Appendix 9C: Proof of Theorem 1 430 \\ Appendix 9D: Direct Proof of Eq. (9.331) 431 \\ Appendix 9E: Special Definite Integrals 432 \\ Part 4: Application in Practical Communication Systems \\ Chapter 10: Optimum Combining: A Diversity Technique for Communication Over Fading Channels in the Presence of Interference 437 \\ 10.1: Performance of Optimum Combining Receivers 438 \\ 10.1.1: Single Interferer, Independent Identically Distributed Fading 438 \\ 10.1.2: Multiple Interferers, Independent Identically Distributed Fading 454 \\ 10.1.3: Comparison with Results for MRC in the Presence of Interference 466 \\ Chapter 11: Direct-Sequence Code-Division Multiple Access 473 \\ 11.1: Single-Carrier DS-CDMA Systems 474 \\ 11.1.1: System and Channel Models 474 \\ 11.1.2: Performance Analysis 477 \\ 11.2: Multicarrier DS-CDMA Systems 479 \\ 11.2.1: System and Channel Models 480 \\ 11.2.2: Performance Analysis 483 \\ 11.2.3: Numerical Examples 489 \\ Part 5: Further Extensions \\ Chapter 12: Coded Communication Over Fading Channels 497 \\ 12.1: Coherent Detection 499 \\ 12.1.1: System Model 499 \\ 12.1.2: Evaluation of Pairwise Error Probability 502 \\ 12.1.3: Transfer Function Bound on Average Bit Error Probability 510 \\ 12.1.4: Alternative Formulation of the Transfer Function Bound 513 \\ 12.2: Differentially Coherent Detection 520 \\ 12.2.1: System Model 520 \\ 12.2.2: Performance Evaluation 522 \\ 12.3: Numerical Results: Comparison of the True Upper Bounds and Union-Chernoff Bounds 526 \\ Appendix 12A: Evaluation of a Moment Generating Function Associated with Differential Detection of M-PSK Sequences 532

entry:
@Book{Simon:2000:DCF,
  author =       "Marvin Kenneth Simon and Mohamed-Slim Alouini",
  title =        "Digital Communication over Fading Channels: a Unified
                 Approach to Performance Analysis",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 544",
  year =         "2000",
  ISBN =         "0-471-31779-9",
  ISBN-13 =      "978-0-471-31779-1",
  LCCN =         "TK5103.7 .S523 2000",
  bibdate =      "Sat Dec 16 17:34:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in telecommunications and signal
                 processing",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/99056352.html;
                 http://www.loc.gov/catdir/description/wiley035/99056352.html;
                 http://www.loc.gov/catdir/toc/onix06/99056352.html",
  acknowledgement = ack-nhfb,
  author-dates = "1939--",
  subject =      "Digital communications; Reliability; Mathematics;
                 Radio; Transmitters and transmission; Fading",
  tableofcontents = "1.1: System Performance Measures 4 \\
                 1.1.1: Average Signal-to-Noise Ratio 4 \\
                 1.1.2: Outage Probability 5 \\
                 1.1.3: Average Bit Error Probability 6 \\
                 Chapter 2: Fading Channel Characterization and Modeling
                 15 \\
                 2.1: Main Characteristics of Fading Channels 15 \\
                 2.1.1: Envelope and Phase Fluctuations 15 \\
                 2.1.2: Slow and Fast Fading 16 \\
                 2.1.3: Frequency-Flat and Frequency-Selective Fading 16
                 \\
                 2.2: Modeling of Flat Fading Channels 17 \\
                 2.2.1: Multipath Fading 18 \\
                 2.2.2: Log-Normal Shadowing 23 \\
                 2.2.3: Composite Multipath/Shadowing 24 \\
                 2.2.4: Combined (Time-Shared) Shadowed/Unshadowed
                 Fading 25 \\
                 2.3: Modeling of Frequency-Selective Fading Channels 26
                 \\
                 Chapter 3: Types of Communication 31 \\
                 3.1: Ideal Coherent Detection 31 \\
                 3.1.1: Multiple Amplitude-Shift-Keying or Multiple
                 Amplitude Modulation 33 \\
                 3.1.2: Quadrature Amplitude-Shift-Keying or Quadrature
                 Amplitude Modulation 34 \\
                 3.1.3: M-ary Phase-Shift-Keying 35 \\
                 3.1.4: Differentially Encoded M-ary Phase-Shift-Keying
                 39 \\
                 3.1.5: Offset QPSK or Staggered QPSK 41 \\
                 3.1.6: M-ary Frequency-Shift-Keying 43 \\
                 3.1.7: Minimum-Shift-Keying 45 \\
                 3.2: Nonideal Coherent Detection 47 \\
                 3.3: Noncoherent Detection 53 \\
                 3.4: Partially Coherent Detection 55 \\
                 3.4.1: Conventional Detection: One-Symbol Observation
                 55 \\
                 3.4.2: Multiple Symbol Detection 57 \\
                 3.5: Differentially Coherent Detection 59 \\
                 3.5.1: M-ary Differential Phase Shift Keying 59 \\
                 3.5.2: [pi]/4-Differential QPSK 65 \\
                 Part 2: Mathematical Tools \\
                 Chapter 4: Alternative Representations of Classical
                 Functions 69 \\
                 4.1: Gaussian $Q$-Function 70 \\
                 4.1.1: One-Dimensional Case 70 \\
                 4.1.2: Two-Dimensional Case 72 \\
                 4.2: Marcum $Q$-Function 74 \\
                 4.2.1: First-Order Marcum $Q$-Function 74 \\
                 4.2.2: Generalized ($m$th-Order) Marcum $Q$-Function 81
                 \\
                 4.3: Other Functions 90 \\
                 Appendix 4A: Derivation of Eq. (4.2) 95 \\
                 Chapter 5: Useful Expressions for Evaluating Average
                 Error Probability Performance 99 \\
                 5.1: Integrals Involving the Gaussian $Q$-Function 99
                 \\
                 5.1.1: Rayleigh Fading Channel 101 \\
                 5.1.2: Nakagami-q (Hoyt) Fading Channel 101 \\
                 5.1.3: Nakagami-n (Rice) Fading Channel 102 \\
                 5.1.4: Nakagami-m Fading Channel 102 \\
                 5.1.5: Log-Normal Shadowing Channel 104 \\
                 5.1.6: Composite Log-Normal Shadowing/Nakagami-m Fading
                 Channel 104 \\
                 5.2: Integrals Involving the Marcum $Q$-Function 107
                 \\
                 5.2.1: Rayleigh Fading Channel 108 \\
                 5.2.2: Nakagami-q (Hoyt) Fading Channel 109 \\
                 5.2.3: Nakagami-n (Rice) Fading Channel 109 \\
                 5.2.4: Nakagami-m Fading Channel 109 \\
                 5.2.5: Log-Normal Shadowing Channel 109 \\
                 5.2.6: Composite Log-Normal Shadowing/Nakagami-m Fading
                 Channel 110 \\
                 5.3: Integrals Involving the Incomplete Gamma Function
                 111 \\
                 5.3.1: Rayleigh Fading Channel 112 \\
                 5.3.2: Nakagami-q (Hoyt) Fading Channel 112 \\
                 5.3.3: Nakagami-n (Rice) Fading Channel 112 \\
                 5.3.4: Nakagami-m Fading Channel 113 \\
                 5.3.5: Log-Normal Shadowing Channel 114 \\
                 5.3.6: Composite Log-Normal Shadowing/Nakagami-m Fading
                 Channel 114 \\
                 5.4: Integrals Involving Other Functions 114 \\
                 5.4.1: M-PSK Error Probability Integral 114 \\
                 5.4.2: Arbitrary Two-Dimensional Signal Constellation
                 Error Probability Integral 116 \\
                 5.4.3: Integer Powers of the Gaussian $Q$-Function 117
                 \\
                 5.4.4: Integer Powers of M-PSK Error Probability
                 Integrals 121 \\
                 Appendix 5A: Evaluation of Definite Integrals
                 Associated with Rayleigh and Nakagami-$m$ Fading 124
                 \\
                 Chapter 6: New Representations of Some PDF's and CDF's
                 for Correlative Fading Applications 141 \\
                 6.1: Bivariate Rayleigh PDF and CDF 142 \\
                 6.2: PDF and CDF for Maximum of Two Rayleigh Random
                 Variables 146 \\
                 6.3: PDF and CDF for Maximum of Two Nakagami-m Random
                 Variables 149 \\
                 Part 3: Optimum Reception and Performance Evaluation
                 \\
                 Chapter 7: Optimum Receivers for Fading Channels 157
                 \\
                 7.1: Case of Known Amplitudes, Phases, and Delays:
                 Coherent, Detection 159 \\
                 7.2: Case of Known Phases and Delays, Unknown
                 Amplitudes 163 \\
                 7.2.1: Rayleigh Fading 163 \\
                 7.2.2: Nakagami-m Fading 164 \\
                 7.3: Case of Known Amplitudes and Delays, Unknown
                 Phases 166 \\
                 7.4: Case of Known Delays and Unknown Amplitudes and
                 Phases 168 \\
                 7.4.1: One-Symbol Observation: Noncoherent Detection
                 168 \\
                 7.4.2: Two-Symbol Observation: Conventional
                 Differentially Coherent Detection 181 \\
                 7.4.3: N-Symbol Observation: Multiple Symbol
                 Differentially Coherent Detection 186 \\
                 7.5: Case of Unknown Amplitudes, Phases, and Delays 188
                 \\
                 7.5.1: One-Symbol Observation: Noncoherent Detection
                 188 \\
                 7.5.2: Two-Symbol Observation: Conventional
                 Differentially Coherent Detection 190 \\
                 Chapter 8: Performance of Single Channel Receives 193
                 \\
                 8.1: Performance Over the AWGN Channel 193 \\
                 8.1.1: Ideal Coherent Detection 194 \\
                 8.1.2: Nonideal Coherent Detection 206 \\
                 8.1.3: Noncoherent Detection 209 \\
                 8.1.4: Partially Coherent Detection 210 \\
                 8.1.5: Differentially Coherent Detection 213 \\
                 8.1.6: Generic Results for Binary Signaling 218 \\
                 8.2: Performance Over Fading Channels 219 \\
                 8.2.1: Ideal Coherent Detection 220 \\
                 8.2.2: Nonideal Coherent Detection 234 \\
                 8.2.3: Noncoherent Detection 239 \\
                 8.2.4: Partially Coherent Detection 242 \\
                 8.2.5: Differentially Coherent Detection 243 \\
                 Appendix 8A: Stein's Unified Analysis of the Error
                 Probability Performance of Certain Communication
                 Systems 253 \\
                 Chapter 9: Performance of Multichannel Receivers 259
                 \\
                 9.1: Diversity Combining 260 \\
                 9.1.1: Diversity Concept 260 \\
                 9.1.2: Mathematical Modeling 260 \\
                 9.1.3: Brief Survey of Diversity Combining Techniques
                 261 \\
                 9.1.4: Complexity-Performance Trade-offs 264 \\
                 9.2: Maximal-Ratio Combining 265 \\
                 9.2.1: Receiver Structure 265 \\
                 9.2.2: PDF-Based Approach 267 \\
                 9.2.3: MGF-Based Approach 268 \\
                 9.2.4: Bounds and Asymptotic SER Expressions 275 \\
                 9.3: Coherent Equal Gain Combining 278 \\
                 9.3.1: Receiver Structure 279 \\
                 9.3.2: Average Output SNR 279 \\
                 9.3.3: Exact Error Rate Analysis 281 \\
                 9.3.4: Approximate Error Rate Analysis 288 \\
                 9.3.5: Asymptotic Error Rate Analysis 289 \\
                 9.4: Noncoherent Equal-Gain Combining 290 \\
                 9.4.1: DPSK, DQPSK, and BFSK: Exact and Bounds 290 \\
                 9.4.2: M-ary Orthogonal FSK 304 \\
                 9.5: Outage Probability Performance 311 \\
                 9.5.1: MRC and Noncoherent EGC 312 \\
                 9.5.2: Coherent EGC 313 \\
                 9.5.3: Numerical Examples 314 \\
                 9.6: Impact of Fading Correlation 316 \\
                 9.6.1: Model A: Two Correlated Branches with
                 Nonidentical Fading 320 \\
                 9.6.2: Model B: D Identically Distributed Branches with
                 Constant Correlation 323 \\
                 9.6.3: Model C: D Identically Distributed Branches with
                 Exponential Correlation 324 \\
                 9.6.4: Model D: D Nonidentically Distributed Branches
                 with Arbitrary Correlation 325 \\
                 9.6.5: Numerical Examples 329 \\
                 9.7: Selection Combining 333 \\
                 9.7.1: MGF of Output SNR 335 \\
                 9.7.2: Average Output SNR 336 \\
                 9.7.3: Outage Probability 338 \\
                 9.7.4: Average Probability of Error 340 \\
                 9.8: Switched Diversity 348 \\
                 9.8.1: Performance of SSC over Independent Identically
                 Distributed Branches 348 \\
                 9.8.2: Effect of Branch Unbalance 362 \\
                 9.8.3: Effect of Branch Correlation 366 \\
                 9.9: Performance in the Presence of Outdated or
                 Imperfect Channel Estimates 370 \\
                 9.9.1: Maximal-Ratio Combining 370 \\
                 9.9.2: Noncoherent EGC over Rician Fast Fading 371 \\
                 9.9.3: Selection Combining 373 \\
                 9.9.4: Switched Diversity 374 \\
                 9.9.5: Numerical Results 377 \\
                 9.10: Hybrid Diversity Schemes 378 \\
                 9.10.1: Generalized Selection Combining 378 \\
                 9.10.2: Generalized Switched Diversity 403 \\
                 9.10.3: Two-Dimensional Diversity Schemes 408 \\
                 Appendix 9A: Alternative Forms of the Bit Error
                 Probability for a Decision Statistic that is a
                 Quadratic Form of Complex Gaussian Random Variables 421
                 \\
                 Appendix 9B: Simple Numerical Techniques for thee
                 Inversion of the Laplace Transform of Cumulative
                 Distribution Functions 427 \\
                 9B.1: Euler Summation-Based Technique 427 \\
                 9B.2: Gauss-Chebyshev Quadrature-Based Technique 428
                 \\
                 Appendix 9C: Proof of Theorem 1 430 \\
                 Appendix 9D: Direct Proof of Eq. (9.331) 431 \\
                 Appendix 9E: Special Definite Integrals 432 \\
                 Part 4: Application in Practical Communication Systems
                 \\
                 Chapter 10: Optimum Combining: A Diversity Technique
                 for Communication Over Fading Channels in the Presence
                 of Interference 437 \\
                 10.1: Performance of Optimum Combining Receivers 438
                 \\
                 10.1.1: Single Interferer, Independent Identically
                 Distributed Fading 438 \\
                 10.1.2: Multiple Interferers, Independent Identically
                 Distributed Fading 454 \\
                 10.1.3: Comparison with Results for MRC in the Presence
                 of Interference 466 \\
                 Chapter 11: Direct-Sequence Code-Division Multiple
                 Access 473 \\
                 11.1: Single-Carrier DS-CDMA Systems 474 \\
                 11.1.1: System and Channel Models 474 \\
                 11.1.2: Performance Analysis 477 \\
                 11.2: Multicarrier DS-CDMA Systems 479 \\
                 11.2.1: System and Channel Models 480 \\
                 11.2.2: Performance Analysis 483 \\
                 11.2.3: Numerical Examples 489 \\
                 Part 5: Further Extensions \\
                 Chapter 12: Coded Communication Over Fading Channels
                 497 \\
                 12.1: Coherent Detection 499 \\
                 12.1.1: System Model 499 \\
                 12.1.2: Evaluation of Pairwise Error Probability 502
                 \\
                 12.1.3: Transfer Function Bound on Average Bit Error
                 Probability 510 \\
                 12.1.4: Alternative Formulation of the Transfer
                 Function Bound 513 \\
                 12.2: Differentially Coherent Detection 520 \\
                 12.2.1: System Model 520 \\
                 12.2.2: Performance Evaluation 522 \\
                 12.3: Numerical Results: Comparison of the True Upper
                 Bounds and Union-Chernoff Bounds 526 \\
                 Appendix 12A: Evaluation of a Moment Generating
                 Function Associated with Differential Detection of
                 M-PSK Sequences 532",
}


bibtype: inproceedings
filename: elefunt.bib
label: Takahashi:2000:IMP
author: D. Takahashi
booktitle: Proceedings of the 2000 International Workshops on Parallel Processing
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 229--235
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: D. Takahashi
rawbooktitle: Proceedings of the 2000 International Workshops on Parallel Processing
title:
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers

rawtitle:
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers

entry:
@InProceedings{Takahashi:2000:IMP,
  author =       "D. Takahashi",
  booktitle =    "Proceedings of the 2000 International Workshops on
                 Parallel Processing",
  title =        "Implementation of multiple-precision parallel division
                 and square root on distributed-memory parallel
                 computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--235",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present efficient parallel algorithms for
                 multiple-precision division and square root operation
                 of more than several million decimal digits on
                 distributed-memory parallel computers. It is well known
                 that multiple-precision division and square \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tchoumatchenko:2000:FBS
author: V. Tchoumatchenko and T. Vassileva and P. Gurov
title: A FPGA based square-root coprocessor
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 520--525
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: V. Tchoumatchenko and T. Vassileva and P. Gurov
rawtitle: A {FPGA} based square-root coprocessor
booktitle:
Proceedings of the 22nd EUROMICRO Conference EUROMICRO 96. 'Beyond 2000: Hardware and Software Design Strategies'

rawbooktitle:
{Proceedings of the 22nd EUROMICRO Conference EUROMICRO 96. 'Beyond 2000: Hardware and Software Design Strategies'}

entry:
@InProceedings{Tchoumatchenko:2000:FBS,
  author =       "V. Tchoumatchenko and T. Vassileva and P. Gurov",
  booktitle =    "{Proceedings of the 22nd EUROMICRO Conference
                 EUROMICRO 96. 'Beyond 2000: Hardware and Software
                 Design Strategies'}",
  title =        "A {FPGA} based square-root coprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "520--525",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present an FPGA implementation of a non-restoring
                 integer square-root algorithm, that uses estimates for
                 result-digit selection and radix-$2$ redundant addition
                 in recurrence. On-the-fly conversion of the
                 result-digit and signed-digit adder/ \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Temme:2000:NAA
author: Nico M. Temme
title: Numerical and asymptotic aspects of parabolic cylinder functions
journal: j-J-COMPUT-APPL-MATH
volume: 121
number: 1--2
pages: 221--246
day: 1
month: sep
monthnumber: 9
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:36 MST 2017
bibtimestamp: 2017.02.25 12:43:36 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700003472
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Nico M. Temme
rawtitle: Numerical and asymptotic aspects of parabolic cylinder functions
entry:
@Article{Temme:2000:NAA,
  author =       "Nico M. Temme",
  title =        "Numerical and asymptotic aspects of parabolic cylinder
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "221--246",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:36 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003472",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tommiska:2000:AEI
author: M. T. Tommiska
title: Area-efficient implementation of a fast square root algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: S18/1--S18/4
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. T. Tommiska
rawtitle: Area-efficient implementation of a fast square root algorithm
booktitle:
Proceedings of the 2000 Third IEEE International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000

rawbooktitle:
Proceedings of the 2000 Third {IEEE} International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000

entry:
@InProceedings{Tommiska:2000:AEI,
  author =       "M. T. Tommiska",
  booktitle =    "Proceedings of the 2000 Third {IEEE} International
                 Caracas Conference on Devices, Circuits and Systems,
                 15--17 March 2000",
  title =        "Area-efficient implementation of a fast square root
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "S18/1--S18/4",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An area-efficient implementation of a fast-converging
                 square-root algorithm is presented. The design of
                 special arithmetic operations differs in many ways from
                 the traditional tasks that digital designers are used
                 to, and the role of \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Wachspress:2000:EEF
author: E. L. Wachspress
title: Evaluating elliptic functions and their inverses
journal: j-COMPUT-MATH-APPL
volume: 39
number: 3--4
pages: 131--136
month: feb
monthnumber: 2
year: 2000
CODEN: CMAPDK
DOI: https://doi.org/10.1016/S0898-1221(99)00339-9
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:06 MST 2017
bibtimestamp: 2017.03.01 21:49:06 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122199003399
fjournal: Computers and Mathematics with Applications
keywords: arithmetic-geometric mean (AGM)
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: E. L. Wachspress
rawtitle: Evaluating elliptic functions and their inverses
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Wachspress:2000:EEF,
  author =       "E. L. Wachspress",
  title =        "Evaluating elliptic functions and their inverses",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "3--4",
  pages =        "131--136",
  month =        feb,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/S0898-1221(99)00339-9",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122199003399",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "arithmetic-geometric mean (AGM)",
}


bibtype: book
filename: elefunt.bib
label: Wall:2000:ATC
author: H. S. Wall
title: Analytic Theory of Continued Fractions
publisher: pub-AMS
address: pub-AMS:adr
pages: xiii + 433
year: 2000
ISBN: 0-8218-2106-7 OR 0821821067
ISBN13: 978-0-8218-2106-0 OR 9780821821060
LCCN: QA295 .W28 2000
bibdate: Thu Apr 3 20:24:06 MDT 2008
bibtimestamp: 2008.04.03 20:24:06 MDT
note: This is a reprint of the definitive, and widely cited, treatise first published in 1948.
remark: Originally published: New York: D. Van Nostrand Co., 1948.
subject: Continued fractions
acknowledgement: ack-nhfb
rawauthor: H. S. Wall
rawnote: This is a reprint of the definitive, and widely cited, treatise first published in 1948.
rawtitle: Analytic Theory of Continued Fractions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; z3950.loc.gov:7090/Voyager

TOC:
Preface / vi Introduction / 1 Part I: Convergence Theory I: The Continued fraction as a Product of Linear Fractional Transformations 1. Definitions and Formulas / 13 2. Continued Fractions and Series / 17 3. Equivalence Transformations / 19 4. Even and Odd Parts of a Continued Fraction / 20 II: Convergence Theorems 5. Some General Remarks on the Convergence Problem / 25 6. Necessary Conditions for Convergence / 27 7. A Sufficient Condition for Convergence / 33 8. Convergence of Periodic Continued Fractions / 35 III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity 9. The First Interpretation of the Fundamental Inequalities / 40 10. Worpitzky's Theorem / 42 11. Convergence of Continued Fractions Whose Partial Quotients Are of the Form $(1 - g_p - 1) g_p x_p / 1$ / 45 12. A Convergence Theorem of von Koch / 50 13. Second Interpretation of the Fundamental Inequalities / 52 14. The Parabola Theorem / 56 15. ``Convergence Neighborhoods'' of a Point (1) / 62 IV: Introduction to the Theory of Positive Definite Continued Fractions 16. Definition of a Positive Definite Continued Fraction / 64 17. The Nest of Circles / 170 18. Positive Definite Continued Fractions and the Parabola Theorem / 175 19. Chain Sequences / 19 20. Quadratic Forms and Chain Sequences / 86 V: Some General Convergence Theorems 21. Schwarz's Inequality / 95 22. The Theorem of Invariability / 96 23. The Indeterminate Case / 99 24. Convergence Continuation Theorem / 104 25. The Determinate Case / 109 26. Bounded J-fractions / 110 27. Real J-fractions / 114 VI: Stieltjes Type Continued Fractions 28. Convergence and Divergence of the Continued Fraction of Stieltjes / 118 29. The Condition (H) / 122 30. Three Convergence Theorems / 131 VII: Extensions of the Parabola Theorem 31. A Family of Parabolic Domains / 135 32. ``Convergence Neighborhoods'' of a Point (2) / 137 33. A Theorem of Van Vleck / 138 34. The Cardioid Theorem / 140 35. An Extension of a Theorem of Szasz / 143 VIII: The Value Region Problem 36. A Sufficient Condition / 147 37. The Two-Circle Theorem / 148 38. Circular Element Regions with Centers at the Origin / 150 39. A Family of Parabolic Element Regions / 152 Part II: Function Theory IX: J-Fraction Expansions for Rational Functions 40. The Expansion Algorithm / 161 41. Conditions Involving Determinants / 164 42. Relationship Between the J-fraction and the Power Series for $f_1 / f_0$ / 166 43. Rational Fractions with Simple Poles and Positive Residues / 167 44, Expansion of Rational Functions into Stieltjes Type Continued Fractions / 170 X: Theory of Equations 45. The Test-Fraction / 174 46. Polygonal Bounds for the Roots of a Polynomial / 176 47. Polynomials Whose Roots Are in a Given Half-Plane / 178 48. Determination of the Number of Roots of P(z) in Each of the Half Planes R(z) 20 / 182 49. Computation of the Roots of Polynomials / 185 XI: J-Fraction Expansions for Power Series 50. Polynomials Orthogonal Relative to a Sequence / 192 51. Algorithm for Expanding a Power Series into a J-fraction / 196 52. Stieltjes Type Continued Fraction Expansions for Power Series / 200 53. Stieltjes' Expansion Theorem / 202 54. Convergence Questions 208 XII: Matrix Theory of Continued Fractions 55. Linear Forms / 214 56. Bilinear Forms / 216 57. Bounded Matrices / 218 58. Bounded Reciprocals of Bounded Matrices / 223 59. The Bounded Reciprocal of a Bounded J-matrix / 226 60. Reciprocals of an Arbitrary J-matrix / 228 61. Reciprocals of the J-matrix Associated with a Positive Definite J-fraction / 230 62. Estimates for the Equivalent Functions / 235 XIII: Continued Fractions and Definite Integrals 63. The Stieltjes Integral / 239 64. Sequences of Stieltjes Integrals / 245 65. The Stieltjes Inversion Formula / 247 66. Representation of an Equivalent Function of a Positive Definite J-fraction as a Stieltjes Transform / 250 67. Proper Equivalent Functions / 254 XIV: The Moment Problem for a Finite Interval 68. Formulation of the Problem / 258 69. Solution of the Moment Problem by Means of S-fractions / 260 70. Some Geometry / 263 71. Totally Monotone Sequences / 267 72. Composition of Moment Sequences / 269 XV: Bounded Analytic Functions 73. Integral Formulas for Bounded Analytic Functions / 275 74. Continued Fraction Expansions for Real Analytic Functions / 278 75. Continued Fraction Expansions for $1/G(z)$ and for $G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$ / 280 76. Condition for $G(z)/sqrt 1 + z$ to Be Bounded in the Unit Circle / 283 77. Analytic Functions Bounded in the Unit Circle / 285 78. Continued Fraction Expansions for Arbitrary Functions Which Are Analytic and Have Positive Real Parts in $Ext (-1, -infty )$ / 288 XVI: Hausdorff Summability 79. Hausdorff Matrices / 302 80. A Theorem on $(A, d_n)$-Transformations / 304 81. Hausdorff Means / 306 82. Examples of Hausdorff Means / 309 83. The Hausdorff Inclusion Problem / 310 XVII: The Moment Problem for an Infinite Interval 84. Asymptotic Expressions for J-fractions / 316 85. A Theorem of Hamburger / 321 86. The Moment Problem for the Interval $(-infty , +infty )$ / 325 87. The Stieltjes Moment Problem / 327 88. A Theorem of Carleman / 330 XVIII: The Continued Fraction of Gauss 89. General Properties / 335 90. Elementary Functions / 342 91. Certain Meromorphic Functions / 347 92. A Class of Divergent Series / 349 XIX: Stieltjes Summability 93. Definition and Illustrative Examples / 362 94. List of Expansion Formulas / 369 XX: The Pade Table 95. Definitions / 37 96. The Normal Pade Table / 379 97. The Pade Table for the Series of Stieltjes / 389 98. General Theorems on the Pade Table / 393 99. C-fractions / 399 100. Regular C-fractions and Power Series / 405 101. $alpha $-regular C-fractions / 409 102. Concluding Remarks on the Pade Table / 410 Bibliography / 417 Index / 427

shortTOC:
Preface Introduction Part I: Convergence Theory I: The Continued fraction as a Product of Linear Fractional Transformations II: Convergence Theorems III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity IV: Introduction to the Theory of Positive Definite Continued Fractions V: Some General Convergence Theorems VI: Stieltjes Type Continued Fractions VII: Extensions of the Parabola Theorem VIII: The Value Region Problem Part II: Function Theory IX: J-Fraction Expansions for Rational Functions X: Theory of Equations XI: J-Fraction Expansions for Power Series XII: Matrix Theory of Continued Fractions XIII: Continued Fractions and Definite Integrals XIV: The Moment Problem for a Finite Interval XV: Bounded Analytic Functions XVI: Hausdorff Summability XVII: The Moment Problem for an Infinite Interval XVIII: The Continued Fraction of Gauss XIX: Stieltjes Summability XX: The Pade Table Bibliography Index

rawshortTOC:
Preface \\ Introduction \\ Part I: Convergence Theory \\ I: The Continued fraction as a Product of Linear Fractional Transformations \\ II: Convergence Theorems \\ III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity \\ IV: Introduction to the Theory of Positive Definite Continued Fractions \\ V: Some General Convergence Theorems \\ VI: Stieltjes Type Continued Fractions \\ VII: Extensions of the Parabola Theorem \\ VIII: The Value Region Problem \\ Part II: Function Theory \\ IX: J-Fraction Expansions for Rational Functions \\ X: Theory of Equations \\ XI: J-Fraction Expansions for Power Series \\ XII: Matrix Theory of Continued Fractions \\ XIII: Continued Fractions and Definite Integrals \\ XIV: The Moment Problem for a Finite Interval \\ XV: Bounded Analytic Functions \\ XVI: Hausdorff Summability \\ XVII: The Moment Problem for an Infinite Interval \\ XVIII: The Continued Fraction of Gauss \\ XIX: Stieltjes Summability \\ XX: The Pad{\'e} Table \\ Bibliography \\ Index

rawTOC:
Preface / vi \\ Introduction / 1 \\ Part I: Convergence Theory \\ \\ I: The Continued fraction as a Product of Linear Fractional Transformations \\ 1. Definitions and Formulas / 13 \\ 2. Continued Fractions and Series / 17 \\ 3. Equivalence Transformations / 19 \\ 4. Even and Odd Parts of a Continued Fraction / 20 \\ \\ II: Convergence Theorems \\ 5. Some General Remarks on the Convergence Problem / 25 \\ 6. Necessary Conditions for Convergence / 27 \\ 7. A Sufficient Condition for Convergence / 33 \\ 8. Convergence of Periodic Continued Fractions / 35 \\ \\ III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity \\ 9. The First Interpretation of the Fundamental Inequalities / 40 \\ 10. Worpitzky's Theorem / 42 \\ 11. Convergence of Continued Fractions Whose Partial Quotients Are of the Form $(1 - g_{p - 1}) g_p x_p / 1$ / 45 \\ 12. A Convergence Theorem of von Koch / 50 \\ 13. Second Interpretation of the Fundamental Inequalities / 52 \\ 14. The Parabola Theorem / 56 \\ 15. ``Convergence Neighborhoods'' of a Point (1) / 62 \\ \\ IV: Introduction to the Theory of Positive Definite Continued Fractions \\ 16. Definition of a Positive Definite Continued Fraction / 64 \\ 17. The Nest of Circles / 170 \\ 18. Positive Definite Continued Fractions and the Parabola Theorem / 175 \\ 19. Chain Sequences / 19 \\ 20. Quadratic Forms and Chain Sequences / 86 \\ \\ V: Some General Convergence Theorems \\ 21. Schwarz's Inequality / 95 \\ 22. The Theorem of Invariability / 96 \\ 23. The Indeterminate Case / 99 \\ 24. Convergence Continuation Theorem / 104 \\ 25. The Determinate Case / 109 \\ 26. Bounded J-fractions / 110 \\ 27. Real J-fractions / 114 \\ \\ VI: Stieltjes Type Continued Fractions \\ 28. Convergence and Divergence of the Continued Fraction of Stieltjes / 118 \\ 29. The Condition (H) / 122 \\ 30. Three Convergence Theorems / 131 \\ \\ VII: Extensions of the Parabola Theorem \\ 31. A Family of Parabolic Domains / 135 \\ 32. ``Convergence Neighborhoods'' of a Point (2) / 137 \\ 33. A Theorem of Van Vleck / 138 \\ 34. The Cardioid Theorem / 140 \\ 35. An Extension of a Theorem of Sz{\'a}sz / 143 \\ \\ VIII: The Value Region Problem \\ 36. A Sufficient Condition / 147 \\ 37. The Two-Circle Theorem / 148 \\ 38. Circular Element Regions with Centers at the Origin / 150 \\ 39. A Family of Parabolic Element Regions / 152 \\ \\ Part II: Function Theory \\ \\ IX: J-Fraction Expansions for Rational Functions \\ 40. The Expansion Algorithm / 161 \\ 41. Conditions Involving Determinants / 164 \\ 42. Relationship Between the J-fraction and the Power Series for $f_1 / f_0$ / 166 \\ 43. Rational Fractions with Simple Poles and Positive Residues / 167 \\ 44, Expansion of Rational Functions into Stieltjes Type Continued Fractions / 170 \\ \\ X: Theory of Equations \\ 45. The Test-Fraction / 174 \\ 46. Polygonal Bounds for the Roots of a Polynomial / 176 \\ 47. Polynomials Whose Roots Are in a Given Half-Plane / 178 \\ 48. Determination of the Number of Roots of P(z) in Each of the Half Planes R(z) 20 / 182 \\ 49. Computation of the Roots of Polynomials / 185 \\ \\ XI: J-Fraction Expansions for Power Series \\ 50. Polynomials Orthogonal Relative to a Sequence / 192 \\ 51. Algorithm for Expanding a Power Series into a J-fraction / 196 \\ 52. Stieltjes Type Continued Fraction Expansions for Power Series / 200 \\ 53. Stieltjes' Expansion Theorem / 202 \\ 54. Convergence Questions 208 \\ \\ XII: Matrix Theory of Continued Fractions \\ 55. Linear Forms / 214 \\ 56. Bilinear Forms / 216 \\ 57. Bounded Matrices / 218 \\ 58. Bounded Reciprocals of Bounded Matrices / 223 \\ 59. The Bounded Reciprocal of a Bounded J-matrix / 226 \\ 60. Reciprocals of an Arbitrary J-matrix / 228 \\ 61. Reciprocals of the J-matrix Associated with a Positive Definite J-fraction / 230 \\ 62. Estimates for the Equivalent Functions / 235 \\ XIII: Continued Fractions and Definite Integrals \\ 63. The Stieltjes Integral / 239 \\ 64. Sequences of Stieltjes Integrals / 245 \\ 65. The Stieltjes Inversion Formula / 247 \\ 66. Representation of an Equivalent Function of a Positive Definite J-fraction as a Stieltjes Transform / 250 \\ 67. Proper Equivalent Functions / 254 \\ \\ XIV: The Moment Problem for a Finite Interval \\ 68. Formulation of the Problem / 258 \\ 69. Solution of the Moment Problem by Means of S-fractions / 260 \\ 70. Some Geometry / 263 \\ 71. Totally Monotone Sequences / 267 \\ 72. Composition of Moment Sequences / 269 \\ \\ XV: Bounded Analytic Functions \\ 73. Integral Formulas for Bounded Analytic Functions / 275 \\ 74. Continued Fraction Expansions for Real Analytic Functions / 278 \\ 75. Continued Fraction Expansions for $1/G(z)$ and for $G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$ / 280 \\ 76. Condition for $G(z)/\sqrt{1 + z}$ to Be Bounded in the Unit Circle / 283 \\ 77. Analytic Functions Bounded in the Unit Circle / 285 \\ 78. Continued Fraction Expansions for Arbitrary Functions Which Are Analytic and Have Positive Real Parts in $\Ext(-1, -\infty)$ / 288 \\ \\ XVI: Hausdorff Summability \\ 79. Hausdorff Matrices / 302 \\ 80. A Theorem on $(A, d_n)$-Transformations / 304 \\ 81. Hausdorff Means / 306 \\ 82. Examples of Hausdorff Means / 309 \\ 83. The Hausdorff Inclusion Problem / 310 \\ \\ XVII: The Moment Problem for an Infinite Interval \\ 84. Asymptotic Expressions for J-fractions / 316 \\ 85. A Theorem of Hamburger / 321 \\ 86. The Moment Problem for the Interval $(-\infty, +\infty)$ / 325 \\ 87. The Stieltjes Moment Problem / 327 \\ 88. A Theorem of Carleman / 330 \\ \\ XVIII: The Continued Fraction of Gauss \\ 89. General Properties / 335 \\ 90. Elementary Functions / 342 \\ 91. Certain Meromorphic Functions / 347 \\ 92. A Class of Divergent Series / 349 \\ \\ XIX: Stieltjes Summability \\ 93. Definition and Illustrative Examples / 362 \\ 94. List of Expansion Formulas / 369 \\ \\ XX: The Pad{\'e} Table \\ 95. Definitions / 37 \\ 96. The Normal Pad{\'e} Table / 379 \\ 97. The Pad{\'e} Table for the Series of Stieltjes / 389 \\ 98. General Theorems on the Pad{\'e} Table / 393 \\ 99. C-fractions / 399 \\ 100. Regular C-fractions and Power Series / 405 \\ 101. $\alpha$-regular C-fractions / 409 \\ 102. Concluding Remarks on the Pad{\'e} Table / 410 \\ \\ Bibliography / 417 \\ Index / 427

entry:
@Book{Wall:2000:ATC,
  author =       "H. S. Wall",
  title =        "Analytic Theory of Continued Fractions",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xiii + 433",
  year =         "2000",
  ISBN =         "0-8218-2106-7",
  ISBN-13 =      "978-0-8218-2106-0",
  LCCN =         "QA295 .W28 2000",
  bibdate =      "Thu Apr 3 20:24:06 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "This is a reprint of the definitive, and widely cited,
                 treatise first published in 1948.",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York: D. Van Nostrand Co.,
                 1948.",
  shorttableofcontents = "Preface \\
                 Introduction \\
                 Part I: Convergence Theory \\
                 I: The Continued fraction as a Product of Linear
                 Fractional Transformations \\
                 II: Convergence Theorems \\
                 III: Convergence of Continued Fractions Whose Partial
                 Denominators Are Equal to Unity \\
                 IV: Introduction to the Theory of Positive Definite
                 Continued Fractions \\
                 V: Some General Convergence Theorems \\
                 VI: Stieltjes Type Continued Fractions \\
                 VII: Extensions of the Parabola Theorem \\
                 VIII: The Value Region Problem \\
                 Part II: Function Theory \\
                 IX: J-Fraction Expansions for Rational Functions \\
                 X: Theory of Equations \\
                 XI: J-Fraction Expansions for Power Series \\
                 XII: Matrix Theory of Continued Fractions \\
                 XIII: Continued Fractions and Definite Integrals \\
                 XIV: The Moment Problem for a Finite Interval \\
                 XV: Bounded Analytic Functions \\
                 XVI: Hausdorff Summability \\
                 XVII: The Moment Problem for an Infinite Interval \\
                 XVIII: The Continued Fraction of Gauss \\
                 XIX: Stieltjes Summability \\
                 XX: The Pad{\'e} Table \\
                 Bibliography \\
                 Index",
  subject =      "Continued fractions",
  tableofcontents = "Preface / vi \\
                 Introduction / 1 \\
                 Part I: Convergence Theory \\
                 \\
                 I: The Continued fraction as a Product of Linear
                 Fractional Transformations \\
                 1. Definitions and Formulas / 13 \\
                 2. Continued Fractions and Series / 17 \\
                 3. Equivalence Transformations / 19 \\
                 4. Even and Odd Parts of a Continued Fraction / 20 \\
                 \\
                 II: Convergence Theorems \\
                 5. Some General Remarks on the Convergence Problem / 25
                 \\
                 6. Necessary Conditions for Convergence / 27 \\
                 7. A Sufficient Condition for Convergence / 33 \\
                 8. Convergence of Periodic Continued Fractions / 35 \\
                 \\
                 III: Convergence of Continued Fractions Whose Partial
                 Denominators Are Equal to Unity \\
                 9. The First Interpretation of the Fundamental
                 Inequalities / 40 \\
                 10. Worpitzky's Theorem / 42 \\
                 11. Convergence of Continued Fractions Whose Partial
                 Quotients Are of the Form $(1 - g_{p - 1}) g_p x_p / 1$
                 / 45 \\
                 12. A Convergence Theorem of von Koch / 50 \\
                 13. Second Interpretation of the Fundamental
                 Inequalities / 52 \\
                 14. The Parabola Theorem / 56 \\
                 15. ``Convergence Neighborhoods'' of a Point (1) / 62
                 \\
                 \\
                 IV: Introduction to the Theory of Positive Definite
                 Continued Fractions \\
                 16. Definition of a Positive Definite Continued
                 Fraction / 64 \\
                 17. The Nest of Circles / 170 \\
                 18. Positive Definite Continued Fractions and the
                 Parabola Theorem / 175 \\
                 19. Chain Sequences / 19 \\
                 20. Quadratic Forms and Chain Sequences / 86 \\
                 \\
                 V: Some General Convergence Theorems \\
                 21. Schwarz's Inequality / 95 \\
                 22. The Theorem of Invariability / 96 \\
                 23. The Indeterminate Case / 99 \\
                 24. Convergence Continuation Theorem / 104 \\
                 25. The Determinate Case / 109 \\
                 26. Bounded J-fractions / 110 \\
                 27. Real J-fractions / 114 \\
                 \\
                 VI: Stieltjes Type Continued Fractions \\
                 28. Convergence and Divergence of the Continued
                 Fraction of Stieltjes / 118 \\
                 29. The Condition (H) / 122 \\
                 30. Three Convergence Theorems / 131 \\
                 \\
                 VII: Extensions of the Parabola Theorem \\
                 31. A Family of Parabolic Domains / 135 \\
                 32. ``Convergence Neighborhoods'' of a Point (2) / 137
                 \\
                 33. A Theorem of Van Vleck / 138 \\
                 34. The Cardioid Theorem / 140 \\
                 35. An Extension of a Theorem of Sz{\'a}sz / 143 \\
                 \\
                 VIII: The Value Region Problem \\
                 36. A Sufficient Condition / 147 \\
                 37. The Two-Circle Theorem / 148 \\
                 38. Circular Element Regions with Centers at the Origin
                 / 150 \\
                 39. A Family of Parabolic Element Regions / 152 \\
                 \\
                 Part II: Function Theory \\
                 \\
                 IX: J-Fraction Expansions for Rational Functions \\
                 40. The Expansion Algorithm / 161 \\
                 41. Conditions Involving Determinants / 164 \\
                 42. Relationship Between the J-fraction and the Power
                 Series for $f_1 / f_0$ / 166 \\
                 43. Rational Fractions with Simple Poles and Positive
                 Residues / 167 \\
                 44, Expansion of Rational Functions into Stieltjes Type
                 Continued Fractions / 170 \\
                 \\
                 X: Theory of Equations \\
                 45. The Test-Fraction / 174 \\
                 46. Polygonal Bounds for the Roots of a Polynomial /
                 176 \\
                 47. Polynomials Whose Roots Are in a Given Half-Plane /
                 178 \\
                 48. Determination of the Number of Roots of P(z) in
                 Each of the Half Planes R(z) 20 / 182 \\
                 49. Computation of the Roots of Polynomials / 185 \\
                 \\
                 XI: J-Fraction Expansions for Power Series \\
                 50. Polynomials Orthogonal Relative to a Sequence / 192
                 \\
                 51. Algorithm for Expanding a Power Series into a
                 J-fraction / 196 \\
                 52. Stieltjes Type Continued Fraction Expansions for
                 Power Series / 200 \\
                 53. Stieltjes' Expansion Theorem / 202 \\
                 54. Convergence Questions 208 \\
                 \\
                 XII: Matrix Theory of Continued Fractions \\
                 55. Linear Forms / 214 \\
                 56. Bilinear Forms / 216 \\
                 57. Bounded Matrices / 218 \\
                 58. Bounded Reciprocals of Bounded Matrices / 223 \\
                 59. The Bounded Reciprocal of a Bounded J-matrix / 226
                 \\
                 60. Reciprocals of an Arbitrary J-matrix / 228 \\
                 61. Reciprocals of the J-matrix Associated with a
                 Positive Definite J-fraction / 230 \\
                 62. Estimates for the Equivalent Functions / 235 \\
                 XIII: Continued Fractions and Definite Integrals \\
                 63. The Stieltjes Integral / 239 \\
                 64. Sequences of Stieltjes Integrals / 245 \\
                 65. The Stieltjes Inversion Formula / 247 \\
                 66. Representation of an Equivalent Function of a
                 Positive Definite J-fraction as a Stieltjes Transform /
                 250 \\
                 67. Proper Equivalent Functions / 254 \\
                 \\
                 XIV: The Moment Problem for a Finite Interval \\
                 68. Formulation of the Problem / 258 \\
                 69. Solution of the Moment Problem by Means of
                 S-fractions / 260 \\
                 70. Some Geometry / 263 \\
                 71. Totally Monotone Sequences / 267 \\
                 72. Composition of Moment Sequences / 269 \\
                 \\
                 XV: Bounded Analytic Functions \\
                 73. Integral Formulas for Bounded Analytic Functions /
                 275 \\
                 74. Continued Fraction Expansions for Real Analytic
                 Functions / 278 \\
                 75. Continued Fraction Expansions for $1/G(z)$ and for
                 $G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$
                 / 280 \\
                 76. Condition for $G(z)/\sqrt{1 + z}$ to Be Bounded in
                 the Unit Circle / 283 \\
                 77. Analytic Functions Bounded in the Unit Circle / 285
                 \\
                 78. Continued Fraction Expansions for Arbitrary
                 Functions Which Are Analytic and Have Positive Real
                 Parts in $\Ext(-1, -\infty)$ / 288 \\
                 \\
                 XVI: Hausdorff Summability \\
                 79. Hausdorff Matrices / 302 \\
                 80. A Theorem on $(A, d_n)$-Transformations / 304 \\
                 81. Hausdorff Means / 306 \\
                 82. Examples of Hausdorff Means / 309 \\
                 83. The Hausdorff Inclusion Problem / 310 \\
                 \\
                 XVII: The Moment Problem for an Infinite Interval \\
                 84. Asymptotic Expressions for J-fractions / 316 \\
                 85. A Theorem of Hamburger / 321 \\
                 86. The Moment Problem for the Interval $(-\infty,
                 +\infty)$ / 325 \\
                 87. The Stieltjes Moment Problem / 327 \\
                 88. A Theorem of Carleman / 330 \\
                 \\
                 XVIII: The Continued Fraction of Gauss \\
                 89. General Properties / 335 \\
                 90. Elementary Functions / 342 \\
                 91. Certain Meromorphic Functions / 347 \\
                 92. A Class of Divergent Series / 349 \\
                 \\
                 XIX: Stieltjes Summability \\
                 93. Definition and Illustrative Examples / 362 \\
                 94. List of Expansion Formulas / 369 \\
                 \\
                 XX: The Pad{\'e} Table \\
                 95. Definitions / 37 \\
                 96. The Normal Pad{\'e} Table / 379 \\
                 97. The Pad{\'e} Table for the Series of Stieltjes /
                 389 \\
                 98. General Theorems on the Pad{\'e} Table / 393 \\
                 99. C-fractions / 399 \\
                 100. Regular C-fractions and Power Series / 405 \\
                 101. $\alpha$-regular C-fractions / 409 \\
                 102. Concluding Remarks on the Pad{\'e} Table / 410 \\
                 \\
                 Bibliography / 417 \\
                 Index / 427",
  xxauthor =     "H. S. (Hubert Stanley) Wall",
}


bibtype: techreport
filename: elefunt.bib
label: Zimmermann:2000:PGF
author: Paul Zimmermann
title: A proof of GMP fast division and square root implementations
type: Technical report
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 14
month: sep
monthnumber: 9
year: 2000
bibdate: Sun Sep 10 08:48:46 2006
bibtimestamp: 2006.09.10 08:48:46 ???
URL: http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
rawtitle: A proof of {GMP} fast division and square root implementations
abstract:
This short note gives a detailed correctness proof of fast (i.e., subquadratic) versions of the GNU MP tt mpn_bz_divrem_n and tt mpn_sqrtrem functions, together with complete GMP code. The tt mpn_bz_divrem_n function divides (with remainder) a number of $ 2 n $ limbs by a divisor of $n$ limbs in $ 2 K(n) $, where $ K(n) $ is the time spent in a $ (n times n) $ multiplication, using the Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm. The tt mpn_sqrtrem computes the square root and the remainder of a number of $ 2 n $ limbs (square root and remainder have about $n$ limbs each) in time $ 3 K(n) / 2 $; it uses Karatsuba Square Root.

rawabstract:
This short note gives a detailed correctness proof of fast (i.e., subquadratic) versions of the GNU MP {\tt mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions, together with complete GMP code. The {\tt mpn\_bz\_divrem\_n} function divides (with remainder) a number of $ 2 n $ limbs by a divisor of $n$ limbs in $ 2 K(n) $, where $ K(n) $ is the time spent in a $ (n \times n) $ multiplication, using the Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm. The {\tt mpn\_sqrtrem} computes the square root and the remainder of a number of $ 2 n $ limbs (square root and remainder have about $n$ limbs each) in time $ 3 K(n) / 2 $; it uses Karatsuba Square Root.

entry:
@TechReport{Zimmermann:2000:PGF,
  author =       "Paul Zimmermann",
  title =        "A proof of {GMP} fast division and square root
                 implementations",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "14",
  month =        sep,
  year =         "2000",
  bibdate =      "Sun Sep 10 08:48:46 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
  abstract =     "This short note gives a detailed correctness proof of
                 fast (i.e., subquadratic) versions of the GNU MP {\tt
                 mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
                 together with complete GMP code. The {\tt
                 mpn\_bz\_divrem\_n} function divides (with remainder) a
                 number of $ 2 n $ limbs by a divisor of $n$ limbs in $
                 2 K(n) $, where $ K(n) $ is the time spent in a $ (n
                 \times n) $ multiplication, using the
                 Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
                 The {\tt mpn\_sqrtrem} computes the square root and the
                 remainder of a number of $ 2 n $ limbs (square root and
                 remainder have about $n$ limbs each) in time $ 3 K(n) /
                 2 $; it uses Karatsuba Square Root.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Arfken:2001:MMP
author: George B. (George Brown) Arfken and Hans-Jurgen Weber
title: Mathematical methods for physicists
publisher: Harcourt/Academic Press
address: San Diego, CA, USA
edition: Fifth
pages: xiv + 1112
year: 2001
ISBN: 0-12-059825-6, 0-12-059826-4 OR 0120598256, 0120598264
ISBN13: 978-0-12-059825-0, 978-0-12-059826-7 OR 9780120598250, 9780120598267
LCCN: QA37.3 .A74 2001
MRclass: 00A06, 15-01, 26-01, 30-01, 34-01, 35-01, 65-01
bibdate: Wed Mar 15 06:50:49 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 06:50:49 MDT
URL: http://catalog.hathitrust.org/api/volumes/oclc/45705658.html
acknowledgement: ack-nhfb
authordates: 1922--
rawauthor: George B. (George Brown) Arfken and Hans-Jurgen Weber
rawtitle: Mathematical methods for physicists
subject:
Mathematics; Mathematical physics; Matematicas; Fisica matematica; Mathematical physics; Mathematics; Wiskundige methoden; Natuurkunde; Matematica; Fisica; Mathematiques; Physique mathematique

TOC:
1: Vector Analysis / 1 1.2: Rotation of the Coordinate Axes / 8 1.3: Scalar or Dot Product / 13 1.4: Vector or Cross Product / 19 1.5: Triple Scalar Product, Triple Vector Product / 27 1.6: Gradient, [down triangle, open] / 35 1.7: Divergence, [down triangle, open] / 40 1.8: Curl, [down triangle, open] x / 44 1.9: Successive Applications of [down triangle, open] / 51 1.10: Vector Integration / 55 1.11: Gauss's Theorem / 61 1.12: Stokes's Theorem / 65 1.13: Potential Theory / 69 1.14: Gauss's Law, Poisson's Equation / 80 1.15: Dirac Delta Function / 84 1.16: Helmholtz's Theorem / 96 2: Curved Coordinates, Tensors / 103 2.1: Orthogonal Coordinates / 103 2.2: Differential Vector Operators / 108 2.3: Special Coordinate Systems: Introduction / 113 2.4: Circular Cylindrical Coordinates / 114 2.5: Spherical Polar Coordinates / 121 2.6: Tensor Analysis / 131 2.7: Contraction, Direct Product / 137 2.8: Quotient Rule / 139 2.9: Pseudotensors, Dual Tensors / 141 2.10: Non-Cartesian Tensors / 150 2.11: Tensor Derivative Operators / 160 3: Determinants and Matrices / 165 3.1: Determinants / 165 3.2: Matrices / 174 3.3: Orthogonal Matrices / 192 3.4: Hermitian Matrices, Unitary Matrices / 206 3.5: Diagonalization of Matrices / 213 3.6: Normal Matrices / 227 4: Group Theory / 237 4.1: Introduction to Group Theory / 237 4.2: Generators of Continuous Groups / 242 4.3: Orbital Angular Momentum / 258 4.4: Angular Momentum Coupling / 263 4.5: Homogeneous Lorentz Group / 275 4.6: Lorentz Covariance of Maxwell's Equations / 278 4.7: Discrete Groups / 286 5: Infinite Series / 303 5.2: Convergence Tests / 306 5.3: Alternating Series / 322 5.4: Algebra of Series / 325 5.5: Series of Functions / 329 5.6: Taylor's Expansion / 334 5.7: Power Series / 346 5.8: Elliptic Integrals / 354 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360 5.10: Asymptotic Series / 373 5.11: Infinite Products / 381 6: Functions of a Complex Variable I / 389 6.1: Complex Algebra / 390 6.2: Cauchy--Riemann Conditions / 399 6.3: Cauchy's Integral Theorem / 404 6.4: Cauchy's Integral Formula / 411 6.5: Laurent Expansion / 416 6.6: Mapping / 425 6.7: Conformal Mapping / 434 7: Functions of a Complex Variable II / 439 7.1: Singularities / 439 7.2: Calculus of Residues / 444 7.3: Dispersion Relations / 469 7.4: Method of Steepest Descents / 477 8: Differential Equations / 487 8.1: Partial Differential Equations / 487 8.2: First-Order Differential Equations / 496 8.3: Separation of Variables / 506 8.4: Singular Points / 516 8.5: Series Solutions--Frobenius's Method / 518 8.6: A Second Solution / 533 8.7: Nonhomogeneous Equation--Green's Function / 548 8.8: Numerical Solutions / 567 9: Sturm--Liouville Theory / 575 9.1: Self-Adjoint ODEs / 575 9.2: Hermitian Operators / 588 9.3: Gram--Schmidt Orthogonalization / 596 9.4: Completeness of Eigenfunctions / 604 9.5: Green's Function--Eigenfunction Expansion / 616 10: Gamma-Factorial Function / 631 10.1: Definitions, Simple Properties / 631 10.2: Digamma and Polygamma Functions / 643 10.3: Stirling's Series / 649 10.4: Beta Function / 654 10.5: Incomplete Gamma Function / 660 11: Bessel Functions / 669 11.1: Bessel Functions of the First Kind J[subscript v](x) / 669 11.2: Orthogonality / 688 11.3: Neumann Functions, Bessel Functions of the Second Kind / 694 11.4: Hankel Functions / 702 11.5: Modified Bessel Functions I[subscript v](x) and K[subscript v](x) / 709 11.6: Asymptotic Expansions / 716 11.7: Spherical Bessel Functions / 722 12: Legendre Functions / 739 12.1: Generating Function / 739 12.2: Recurrence Relations / 748 12.3: Orthogonality / 755 12.4: Alternate Definitions / 767 12.5: Associated Legendre Functions / 771 12.6G: Spherical Harmonics / 786 12.7: Orbital Angular Momentum Operators / 792 12.8: Addition Theorem for Spherical Harmonics / 796 12.9: Integrals of Three Ys / 802 12.10: Legendre Functions of the Second Kind / 806 12.11: Vector Spherical Harmonics / 813 13: Special Functions / 817 13.1: Hermite Functions / 817 13.2: Laguerre Functions / 828 13.3: Chebyshev Polynomials / 839 13.4: Hypergeometric Functions / 850 13.5: Confluent Hypergeometric Functions / 855 14: Fourier Series / 863 14.1: General Properties / 863 14.2: Advantages, Uses of Fouries Series / 870 14.3: Applications of Fourier Series / 874 14.4: Properties of Fourier Series / 886 14.5: Gibbs Phenomenon / 893 14.6: Discrete Fourier Transform / 898 15: Integral Transforms / 905 15.1: Integral Transforms / 905 15.2: Development of the Fourier Integral / 909 15.3: Fourier Transforms--Inversion Theorem / 911 15.4: Fourier Transform of Derivatives / 920 15.5: Convolution Theorem / 924 15.6: Momentum Representation / 928 15.7: Transfer Functions / 935 15.8: Laplace Transforms / 938 15.9: Laplace Transform of Derivatives / 946 15.10: Other Properties / 953 15.11: Convolution or Faltungs Theorem / 965 15.12: Inverse Laplace Transform / 969 16: Integral Equations / 983 16.2: Integral Transforms, Generating Functions / 991 16.3: Neumann Series, Separable Kernels / 997 16.4: Hilbert--Schmidt Theory / 1009 17: Calculus of Variations / 1017 17.1: A Dependent and an Independent Variable / 1018 17.2: Applications of the Euler Equation / 1023 17.3: Several Dependent Variables / 1031 17.4: Several Independent Variables / 1036 17.5: Several Dependent and Independent Variables / 1038 17.6: Lagrangian Multipliers / 1039 17.7: Variation With Constraints / 1045 17.8: Rayleigh--Ritz Variational Technique / 1052 18: Nonlinear Methods and Chaos / 1059 18.2: Logistic Map / 1060 18.3: Sensitivity to Initial Conditions / 1064 18.4: Nonlinear Differential Equations / 1068 Appendix 1: Real Zeros of a Function / 1085 Appendix 2: Gaussian Quadrature / 1089

rawTOC:
1: Vector Analysis / 1 \\ 1.2: Rotation of the Coordinate Axes / 8 \\ 1.3: Scalar or Dot Product / 13 \\ 1.4: Vector or Cross Product / 19 \\ 1.5: Triple Scalar Product, Triple Vector Product / 27 \\ 1.6: Gradient, [down triangle, open] / 35 \\ 1.7: Divergence, [down triangle, open] / 40 \\ 1.8: Curl, [down triangle, open] x / 44 \\ 1.9: Successive Applications of [down triangle, open] / 51 \\ 1.10: Vector Integration / 55 \\ 1.11: Gauss's Theorem / 61 \\ 1.12: Stokes's Theorem / 65 \\ 1.13: Potential Theory / 69 \\ 1.14: Gauss's Law, Poisson's Equation / 80 \\ 1.15: Dirac Delta Function / 84 \\ 1.16: Helmholtz's Theorem / 96 \\ 2: Curved Coordinates, Tensors / 103 \\ 2.1: Orthogonal Coordinates / 103 \\ 2.2: Differential Vector Operators / 108 \\ 2.3: Special Coordinate Systems: Introduction / 113 \\ 2.4: Circular Cylindrical Coordinates / 114 \\ 2.5: Spherical Polar Coordinates / 121 \\ 2.6: Tensor Analysis / 131 \\ 2.7: Contraction, Direct Product / 137 \\ 2.8: Quotient Rule / 139 \\ 2.9: Pseudotensors, Dual Tensors / 141 \\ 2.10: Non-Cartesian Tensors / 150 \\ 2.11: Tensor Derivative Operators / 160 \\ 3: Determinants and Matrices / 165 \\ 3.1: Determinants / 165 \\ 3.2: Matrices / 174 \\ 3.3: Orthogonal Matrices / 192 \\ 3.4: Hermitian Matrices, Unitary Matrices / 206 \\ 3.5: Diagonalization of Matrices / 213 \\ 3.6: Normal Matrices / 227 \\ 4: Group Theory / 237 \\ 4.1: Introduction to Group Theory / 237 \\ 4.2: Generators of Continuous Groups / 242 \\ 4.3: Orbital Angular Momentum / 258 \\ 4.4: Angular Momentum Coupling / 263 \\ 4.5: Homogeneous Lorentz Group / 275 \\ 4.6: Lorentz Covariance of Maxwell's Equations / 278 \\ 4.7: Discrete Groups / 286 \\ 5: Infinite Series / 303 \\ 5.2: Convergence Tests / 306 \\ 5.3: Alternating Series / 322 \\ 5.4: Algebra of Series / 325 \\ 5.5: Series of Functions / 329 \\ 5.6: Taylor's Expansion / 334 \\ 5.7: Power Series / 346 \\ 5.8: Elliptic Integrals / 354 \\ 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360 \\ 5.10: Asymptotic Series / 373 \\ 5.11: Infinite Products / 381 \\ 6: Functions of a Complex Variable I / 389 \\ 6.1: Complex Algebra / 390 \\ 6.2: Cauchy--Riemann Conditions / 399 \\ 6.3: Cauchy's Integral Theorem / 404 \\ 6.4: Cauchy's Integral Formula / 411 \\ 6.5: Laurent Expansion / 416 \\ 6.6: Mapping / 425 \\ 6.7: Conformal Mapping / 434 \\ 7: Functions of a Complex Variable II / 439 \\ 7.1: Singularities / 439 \\ 7.2: Calculus of Residues / 444 \\ 7.3: Dispersion Relations / 469 \\ 7.4: Method of Steepest Descents / 477 \\ 8: Differential Equations / 487 \\ 8.1: Partial Differential Equations / 487 \\ 8.2: First-Order Differential Equations / 496 \\ 8.3: Separation of Variables / 506 \\ 8.4: Singular Points / 516 \\ 8.5: Series Solutions--Frobenius's Method / 518 \\ 8.6: A Second Solution / 533 \\ 8.7: Nonhomogeneous Equation--Green's Function / 548 \\ 8.8: Numerical Solutions / 567 \\ 9: Sturm--Liouville Theory / 575 \\ 9.1: Self-Adjoint ODEs / 575 \\ 9.2: Hermitian Operators / 588 \\ 9.3: Gram--Schmidt Orthogonalization / 596 \\ 9.4: Completeness of Eigenfunctions / 604 \\ 9.5: Green's Function--Eigenfunction Expansion / 616 \\ 10: Gamma-Factorial Function / 631 \\ 10.1: Definitions, Simple Properties / 631 \\ 10.2: Digamma and Polygamma Functions / 643 \\ 10.3: Stirling's Series / 649 \\ 10.4: Beta Function / 654 \\ 10.5: Incomplete Gamma Function / 660 \\ 11: Bessel Functions / 669 \\ 11.1: Bessel Functions of the First Kind J[subscript v](x) / 669 \\ 11.2: Orthogonality / 688 \\ 11.3: Neumann Functions, Bessel Functions of the Second Kind / 694 \\ 11.4: Hankel Functions / 702 \\ 11.5: Modified Bessel Functions I[subscript v](x) and K[subscript v](x) / 709 \\ 11.6: Asymptotic Expansions / 716 \\ 11.7: Spherical Bessel Functions / 722 \\ 12: Legendre Functions / 739 \\ 12.1: Generating Function / 739 \\ 12.2: Recurrence Relations / 748 \\ 12.3: Orthogonality / 755 \\ 12.4: Alternate Definitions / 767 \\ 12.5: Associated Legendre Functions / 771 \\ 12.6G: Spherical Harmonics / 786 \\ 12.7: Orbital Angular Momentum Operators / 792 \\ 12.8: Addition Theorem for Spherical Harmonics / 796 \\ 12.9: Integrals of Three Ys / 802 \\ 12.10: Legendre Functions of the Second Kind / 806 \\ 12.11: Vector Spherical Harmonics / 813 \\ 13: Special Functions / 817 \\ 13.1: Hermite Functions / 817 \\ 13.2: Laguerre Functions / 828 \\ 13.3: Chebyshev Polynomials / 839 \\ 13.4: Hypergeometric Functions / 850 \\ 13.5: Confluent Hypergeometric Functions / 855 \\ 14: Fourier Series / 863 \\ 14.1: General Properties / 863 \\ 14.2: Advantages, Uses of Fouries Series / 870 \\ 14.3: Applications of Fourier Series / 874 \\ 14.4: Properties of Fourier Series / 886 \\ 14.5: Gibbs Phenomenon / 893 \\ 14.6: Discrete Fourier Transform / 898 \\ 15: Integral Transforms / 905 \\ 15.1: Integral Transforms / 905 \\ 15.2: Development of the Fourier Integral / 909 \\ 15.3: Fourier Transforms--Inversion Theorem / 911 \\ 15.4: Fourier Transform of Derivatives / 920 \\ 15.5: Convolution Theorem / 924 \\ 15.6: Momentum Representation / 928 \\ 15.7: Transfer Functions / 935 \\ 15.8: Laplace Transforms / 938 \\ 15.9: Laplace Transform of Derivatives / 946 \\ 15.10: Other Properties / 953 \\ 15.11: Convolution or Faltungs Theorem / 965 \\ 15.12: Inverse Laplace Transform / 969 \\ 16: Integral Equations / 983 \\ 16.2: Integral Transforms, Generating Functions / 991 \\ 16.3: Neumann Series, Separable Kernels / 997 \\ 16.4: Hilbert--Schmidt Theory / 1009 \\ 17: Calculus of Variations / 1017 \\ 17.1: A Dependent and an Independent Variable / 1018 \\ 17.2: Applications of the Euler Equation / 1023 \\ 17.3: Several Dependent Variables / 1031 \\ 17.4: Several Independent Variables / 1036 \\ 17.5: Several Dependent and Independent Variables / 1038 \\ 17.6: Lagrangian Multipliers / 1039 \\ 17.7: Variation With Constraints / 1045 \\ 17.8: Rayleigh--Ritz Variational Technique / 1052 \\ 18: Nonlinear Methods and Chaos / 1059 \\ 18.2: Logistic Map / 1060 \\ 18.3: Sensitivity to Initial Conditions / 1064 \\ 18.4: Nonlinear Differential Equations / 1068 \\ Appendix 1: Real Zeros of a Function / 1085 \\ Appendix 2: Gaussian Quadrature / 1089

entry:
@Book{Arfken:2001:MMP,
  author =       "George B. (George Brown) Arfken and Hans-Jurgen
                 Weber",
  title =        "Mathematical methods for physicists",
  publisher =    "Harcourt/Academic Press",
  address =      "San Diego, CA, USA",
  edition =      "Fifth",
  pages =        "xiv + 1112",
  year =         "2001",
  ISBN =         "0-12-059825-6, 0-12-059826-4",
  ISBN-13 =      "978-0-12-059825-0, 978-0-12-059826-7",
  LCCN =         "QA37.3 .A74 2001",
  MRclass =      "00A06, 15-01, 26-01, 30-01, 34-01, 35-01, 65-01",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/45705658.html",
  acknowledgement = ack-nhfb,
  author-dates = "1922--",
  subject =      "Mathematics; Mathematical physics; Matem{\'a}ticas;
                 F{\'i}sica matem{\'a}tica; Mathematical physics;
                 Mathematics; Wiskundige methoden; Natuurkunde;
                 Matem{\'a}tica; F{\'i}sica; Math{\'e}matiques; Physique
                 math{\'e}matique",
  tableofcontents = "1: Vector Analysis / 1 \\
                 1.2: Rotation of the Coordinate Axes / 8 \\
                 1.3: Scalar or Dot Product / 13 \\
                 1.4: Vector or Cross Product / 19 \\
                 1.5: Triple Scalar Product, Triple Vector Product / 27
                 \\
                 1.6: Gradient, [down triangle, open] / 35 \\
                 1.7: Divergence, [down triangle, open] / 40 \\
                 1.8: Curl, [down triangle, open] x / 44 \\
                 1.9: Successive Applications of [down triangle, open] /
                 51 \\
                 1.10: Vector Integration / 55 \\
                 1.11: Gauss's Theorem / 61 \\
                 1.12: Stokes's Theorem / 65 \\
                 1.13: Potential Theory / 69 \\
                 1.14: Gauss's Law, Poisson's Equation / 80 \\
                 1.15: Dirac Delta Function / 84 \\
                 1.16: Helmholtz's Theorem / 96 \\
                 2: Curved Coordinates, Tensors / 103 \\
                 2.1: Orthogonal Coordinates / 103 \\
                 2.2: Differential Vector Operators / 108 \\
                 2.3: Special Coordinate Systems: Introduction / 113 \\
                 2.4: Circular Cylindrical Coordinates / 114 \\
                 2.5: Spherical Polar Coordinates / 121 \\
                 2.6: Tensor Analysis / 131 \\
                 2.7: Contraction, Direct Product / 137 \\
                 2.8: Quotient Rule / 139 \\
                 2.9: Pseudotensors, Dual Tensors / 141 \\
                 2.10: Non-Cartesian Tensors / 150 \\
                 2.11: Tensor Derivative Operators / 160 \\
                 3: Determinants and Matrices / 165 \\
                 3.1: Determinants / 165 \\
                 3.2: Matrices / 174 \\
                 3.3: Orthogonal Matrices / 192 \\
                 3.4: Hermitian Matrices, Unitary Matrices / 206 \\
                 3.5: Diagonalization of Matrices / 213 \\
                 3.6: Normal Matrices / 227 \\
                 4: Group Theory / 237 \\
                 4.1: Introduction to Group Theory / 237 \\
                 4.2: Generators of Continuous Groups / 242 \\
                 4.3: Orbital Angular Momentum / 258 \\
                 4.4: Angular Momentum Coupling / 263 \\
                 4.5: Homogeneous Lorentz Group / 275 \\
                 4.6: Lorentz Covariance of Maxwell's Equations / 278
                 \\
                 4.7: Discrete Groups / 286 \\
                 5: Infinite Series / 303 \\
                 5.2: Convergence Tests / 306 \\
                 5.3: Alternating Series / 322 \\
                 5.4: Algebra of Series / 325 \\
                 5.5: Series of Functions / 329 \\
                 5.6: Taylor's Expansion / 334 \\
                 5.7: Power Series / 346 \\
                 5.8: Elliptic Integrals / 354 \\
                 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360
                 \\
                 5.10: Asymptotic Series / 373 \\
                 5.11: Infinite Products / 381 \\
                 6: Functions of a Complex Variable I / 389 \\
                 6.1: Complex Algebra / 390 \\
                 6.2: Cauchy--Riemann Conditions / 399 \\
                 6.3: Cauchy's Integral Theorem / 404 \\
                 6.4: Cauchy's Integral Formula / 411 \\
                 6.5: Laurent Expansion / 416 \\
                 6.6: Mapping / 425 \\
                 6.7: Conformal Mapping / 434 \\
                 7: Functions of a Complex Variable II / 439 \\
                 7.1: Singularities / 439 \\
                 7.2: Calculus of Residues / 444 \\
                 7.3: Dispersion Relations / 469 \\
                 7.4: Method of Steepest Descents / 477 \\
                 8: Differential Equations / 487 \\
                 8.1: Partial Differential Equations / 487 \\
                 8.2: First-Order Differential Equations / 496 \\
                 8.3: Separation of Variables / 506 \\
                 8.4: Singular Points / 516 \\
                 8.5: Series Solutions--Frobenius's Method / 518 \\
                 8.6: A Second Solution / 533 \\
                 8.7: Nonhomogeneous Equation--Green's Function / 548
                 \\
                 8.8: Numerical Solutions / 567 \\
                 9: Sturm--Liouville Theory / 575 \\
                 9.1: Self-Adjoint ODEs / 575 \\
                 9.2: Hermitian Operators / 588 \\
                 9.3: Gram--Schmidt Orthogonalization / 596 \\
                 9.4: Completeness of Eigenfunctions / 604 \\
                 9.5: Green's Function--Eigenfunction Expansion / 616
                 \\
                 10: Gamma-Factorial Function / 631 \\
                 10.1: Definitions, Simple Properties / 631 \\
                 10.2: Digamma and Polygamma Functions / 643 \\
                 10.3: Stirling's Series / 649 \\
                 10.4: Beta Function / 654 \\
                 10.5: Incomplete Gamma Function / 660 \\
                 11: Bessel Functions / 669 \\
                 11.1: Bessel Functions of the First Kind J[subscript
                 v](x) / 669 \\
                 11.2: Orthogonality / 688 \\
                 11.3: Neumann Functions, Bessel Functions of the Second
                 Kind / 694 \\
                 11.4: Hankel Functions / 702 \\
                 11.5: Modified Bessel Functions I[subscript v](x) and
                 K[subscript v](x) / 709 \\
                 11.6: Asymptotic Expansions / 716 \\
                 11.7: Spherical Bessel Functions / 722 \\
                 12: Legendre Functions / 739 \\
                 12.1: Generating Function / 739 \\
                 12.2: Recurrence Relations / 748 \\
                 12.3: Orthogonality / 755 \\
                 12.4: Alternate Definitions / 767 \\
                 12.5: Associated Legendre Functions / 771 \\
                 12.6G: Spherical Harmonics / 786 \\
                 12.7: Orbital Angular Momentum Operators / 792 \\
                 12.8: Addition Theorem for Spherical Harmonics / 796
                 \\
                 12.9: Integrals of Three Ys / 802 \\
                 12.10: Legendre Functions of the Second Kind / 806 \\
                 12.11: Vector Spherical Harmonics / 813 \\
                 13: Special Functions / 817 \\
                 13.1: Hermite Functions / 817 \\
                 13.2: Laguerre Functions / 828 \\
                 13.3: Chebyshev Polynomials / 839 \\
                 13.4: Hypergeometric Functions / 850 \\
                 13.5: Confluent Hypergeometric Functions / 855 \\
                 14: Fourier Series / 863 \\
                 14.1: General Properties / 863 \\
                 14.2: Advantages, Uses of Fouries Series / 870 \\
                 14.3: Applications of Fourier Series / 874 \\
                 14.4: Properties of Fourier Series / 886 \\
                 14.5: Gibbs Phenomenon / 893 \\
                 14.6: Discrete Fourier Transform / 898 \\
                 15: Integral Transforms / 905 \\
                 15.1: Integral Transforms / 905 \\
                 15.2: Development of the Fourier Integral / 909 \\
                 15.3: Fourier Transforms--Inversion Theorem / 911 \\
                 15.4: Fourier Transform of Derivatives / 920 \\
                 15.5: Convolution Theorem / 924 \\
                 15.6: Momentum Representation / 928 \\
                 15.7: Transfer Functions / 935 \\
                 15.8: Laplace Transforms / 938 \\
                 15.9: Laplace Transform of Derivatives / 946 \\
                 15.10: Other Properties / 953 \\
                 15.11: Convolution or Faltungs Theorem / 965 \\
                 15.12: Inverse Laplace Transform / 969 \\
                 16: Integral Equations / 983 \\
                 16.2: Integral Transforms, Generating Functions / 991
                 \\
                 16.3: Neumann Series, Separable Kernels / 997 \\
                 16.4: Hilbert--Schmidt Theory / 1009 \\
                 17: Calculus of Variations / 1017 \\
                 17.1: A Dependent and an Independent Variable / 1018
                 \\
                 17.2: Applications of the Euler Equation / 1023 \\
                 17.3: Several Dependent Variables / 1031 \\
                 17.4: Several Independent Variables / 1036 \\
                 17.5: Several Dependent and Independent Variables /
                 1038 \\
                 17.6: Lagrangian Multipliers / 1039 \\
                 17.7: Variation With Constraints / 1045 \\
                 17.8: Rayleigh--Ritz Variational Technique / 1052 \\
                 18: Nonlinear Methods and Chaos / 1059 \\
                 18.2: Logistic Map / 1060 \\
                 18.3: Sensitivity to Initial Conditions / 1064 \\
                 18.4: Nonlinear Differential Equations / 1068 \\
                 Appendix 1: Real Zeros of a Function / 1085 \\
                 Appendix 2: Gaussian Quadrature / 1089",
}


bibtype: book
filename: elefunt.bib
label: Askey:2001:SFG
editor: R. A. Askey and Tom H. Koornwinder and Walter J. Schempp
title: Special Functions: Group Theoretical Aspects and Applications
publisher: pub-SV
address: pub-SV:adr
pages: xxxiv + 311
year: 2001
ISBN: 90-277-1822-9 OR 9027718229
ISBN13: 978-90-277-1822-8 OR 9789027718228
LCCN: QA1 M428 v. 18 c.2
bibdate: Sat Oct 30 17:58:21 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 17:58:21 ???
series: Mathematics and Its Applications
acknowledgement: ack-nhfb
raweditor: R. A. Askey and Tom H. Koornwinder and Walter J. Schempp
rawtitle: Special Functions: Group Theoretical Aspects and Applications
TOC:
Editor's Preface / M. Hazewinkel / vii Preface / R. Askey / xi Jacobi functions and analysis on noncompact semisimple Lie groups / Tom H. Koornwinder / 1 Orthogonal polynomials and Chevalley groups / Dennis Stanton /87 Special functions and group theory in theoretical physics / L. C. Biedenharn, R. A. Gustafson, M. A. Lohe, J. D. Louck, S. C. Milne / 129 Lattice gauge theory, orthogonal polynomials and q-Hypergeometric functions / George E. Andrews, Enrico Onofri / 163 The Laguerre calculus on the Heisenberg group / R. W. Beals, P. C. Greiner, J. Vauthier / 189 Radar ambiguity functions, nilpotent harmonic analysis, and holomorphic theta series / Walter Schempp / 217 A factorization theorem for the Fourier transform of a separable locally compact Abelian group / Louis Auslander / 261 Band and time limiting, recursion relations and some nonlinear evolution equations / F. Alberto Grunbaum / 271 Harmonics and combinatorics / J. J. Seidel / 287 Subject Index / / 305

rawTOC:
Editor's Preface / M. Hazewinkel / vii \\ Preface / R. Askey / xi \\ Jacobi functions and analysis on noncompact semisimple Lie groups / Tom H. Koornwinder / 1 \\ Orthogonal polynomials and Chevalley groups / Dennis Stanton /87 \\ Special functions and group theory in theoretical physics / L. C. Biedenharn, R. A. Gustafson, M. A. Lohe, J. D. Louck, S. C. Milne / 129 \\ Lattice gauge theory, orthogonal polynomials and q-Hypergeometric functions / George E. Andrews, Enrico Onofri / 163 \\ The Laguerre calculus on the Heisenberg group / R. W. Beals, P. C. Greiner, J. Vauthier / 189 \\ Radar ambiguity functions, nilpotent harmonic analysis, and holomorphic theta series / Walter Schempp / 217 \\ A factorization theorem for the Fourier transform of a separable locally compact Abelian group / Louis Auslander / 261 \\ Band and time limiting, recursion relations and some nonlinear evolution equations / F. Alberto Gr{\"u}nbaum / 271 \\ Harmonics and combinatorics / J. J. Seidel / 287 \\ Subject Index / / 305

entry:
@Book{Askey:2001:SFG,
  editor =       "R. A. Askey and Tom H. Koornwinder and Walter J.
                 Schempp",
  title =        "Special Functions: Group Theoretical Aspects and
                 Applications",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxiv + 311",
  year =         "2001",
  ISBN =         "90-277-1822-9",
  ISBN-13 =      "978-90-277-1822-8",
  LCCN =         "QA1 M428 v. 18 c.2",
  bibdate =      "Sat Oct 30 17:58:21 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics and Its Applications",
  acknowledgement = ack-nhfb,
  tableofcontents = "Editor's Preface / M. Hazewinkel / vii \\
                 Preface / R. Askey / xi \\
                 Jacobi functions and analysis on noncompact semisimple
                 Lie groups / Tom H. Koornwinder / 1 \\
                 Orthogonal polynomials and Chevalley groups / Dennis
                 Stanton /87 \\
                 Special functions and group theory in theoretical
                 physics / L. C. Biedenharn, R. A. Gustafson, M. A.
                 Lohe, J. D. Louck, S. C. Milne / 129 \\
                 Lattice gauge theory, orthogonal polynomials and
                 q-Hypergeometric functions / George E. Andrews, Enrico
                 Onofri / 163 \\
                 The Laguerre calculus on the Heisenberg group / R. W.
                 Beals, P. C. Greiner, J. Vauthier / 189 \\
                 Radar ambiguity functions, nilpotent harmonic analysis,
                 and holomorphic theta series / Walter Schempp / 217 \\
                 A factorization theorem for the Fourier transform of a
                 separable locally compact Abelian group / Louis
                 Auslander / 261 \\
                 Band and time limiting, recursion relations and some
                 nonlinear evolution equations / F. Alberto Gr{\"u}nbaum
                 / 271 \\
                 Harmonics and combinatorics / J. J. Seidel / 287 \\
                 Subject Index / / 305",
}


bibtype: article
filename: elefunt.bib
label: Bashagha:2001:NRS
author: A. E. Bashagha
title: Novel radix-$2$ $k$ square root module
volume: 148
number: 4
pages: 190--196
month: aug
monthnumber: 8
year: 2001
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: A. E. Bashagha
rawtitle: Novel radix-$2$ $k$ square root module
journal:
Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G-Circuits, Devices and Systems]

entry:
@Article{Bashagha:2001:NRS,
  author =       "A. E. Bashagha",
  title =        "Novel radix-$2$ $k$ square root module",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G-Circuits, Devices and Systems]",
  volume =       "148",
  number =       "4",
  pages =        "190--196",
  month =        aug,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The conventional two's complement radix-$2$ $k$ square
                 root algorithm requires a set of $2^k$ full precision
                 comparisons to generate all the $2^k$ possible values
                 of the partial remainder. The correct remainder is the
                 minimum \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Berg:2001:CMF
author: Christian Berg and Henrik L. Pedersen
title: A completely monotone function related to the Gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 219--230
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006440
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Christian Berg and Henrik L. Pedersen
rawtitle: A completely monotone function related to the Gamma function
entry:
@Article{Berg:2001:CMF,
  author =       "Christian Berg and Henrik L. Pedersen",
  title =        "A completely monotone function related to the Gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "219--230",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006440",
  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: Berry:2001:WSF
author: Michael Berry
title: Why are special functions special?
journal: j-PHYS-TODAY
volume: 54
number: 4
pages: 11--12
month: apr
monthnumber: 4
year: 2001
CODEN: PHTOAD
DOI: https://doi.org/10.1063/1.1372098
ISSN: 0031-9228 (print), 1945-0699 (electronic) OR 00319228 (print), 19450699 (electronic)
ISSNL: 0031-9228 OR 00319228
bibdate: Sat Feb 19 13:23:33 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.02.19 13:23:33 ???
URL: http://www.physicstoday.org/resource/1/phtoad/v54/i4/p11_s1
fjournal: Physics Today
acknowledgement: ack-nhfb
journalURL: http://www.physicstoday.org/
rawauthor: Michael Berry
rawtitle: Why are special functions special?
entry:
@Article{Berry:2001:WSF,
  author =       "Michael Berry",
  title =        "Why are special functions special?",
  journal =      j-PHYS-TODAY,
  volume =       "54",
  number =       "4",
  pages =        "11--12",
  month =        apr,
  year =         "2001",
  CODEN =        "PHTOAD",
  DOI =          "https://doi.org/10.1063/1.1372098",
  ISSN =         "0031-9228 (print), 1945-0699 (electronic)",
  ISSN-L =       "0031-9228",
  bibdate =      "Sat Feb 19 13:23:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.physicstoday.org/resource/1/phtoad/v54/i4/p11_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Today",
  journal-URL =  "http://www.physicstoday.org/",
}


bibtype: article
filename: elefunt.bib
label: Boisvert:2001:MM
author: Ronald F. Boisvert and M. J. Donahue and Daniel W. Lozier and R. McMichael and B. W. Rust
title: Mathematics and Measurement
journal: NIST Journal of Research
volume: 106
number: 1
pages: 293--313
month: jan
monthnumber: 1
year: 2001
bibdate: Fri Jul 09 06:26:11 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:26:11 ???
acknowledgement: ack-nhfb
rawauthor: Ronald F. Boisvert and M. J. Donahue and Daniel W. Lozier and R. McMichael and B. W. Rust
rawtitle: Mathematics and Measurement
entry:
@Article{Boisvert:2001:MM,
  author =       "Ronald F. Boisvert and M. J. Donahue and Daniel W.
                 Lozier and R. McMichael and B. W. Rust",
  title =        "Mathematics and Measurement",
  journal =      "NIST Journal of Research",
  volume =       "106",
  number =       "1",
  pages =        "293--313",
  month =        jan # "\slash " # feb,
  year =         "2001",
  bibdate =      "Fri Jul 09 06:26:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Boyd:2001:CFS
author: John Philip Boyd
title: Chebyshev and Fourier spectral methods
publisher: pub-DOVER
address: pub-DOVER:adr
edition: Second (revised).
pages: 1375
year: 2001
ISBN: 0-486-41183-4 (paperback), 0-486-14192-6 (e-book) OR 0486411834 (paperback), 0486141926 (ebook)
LCCN: QA404.5 .B69 2001
bibdate: Sat Feb 17 14:05:46 MST 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.17 14:05:46 MST
series: Dover Books on Mathematics
URL: http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjE0MTkyMzpl
acknowledgement: ack-nhfb
authordates: 1951--
rawauthor: John Philip Boyd
rawtitle: {Chebyshev} and {Fourier} spectral methods
ISBN13:
978-0-486-41183-5 (paperback), 978-0-486-14192-3 (e-book) OR 9780486411835 (paperback), 9780486141923 (ebook)

abstract:
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more. Includes 7 appendices and over 160 text figures.

subject:
Chebyshev polynomials; Fourier analysis; Spectral theory (Mathematics); Polynyomes de Tchebychev; Analyse de Fourier; Spectre (Mathyematiques); MATHEMATICS; General.; Chebyshev polynomials; Fourier analysis; Spectral theory (Mathematics)

TOC:
1. Introduction 2. Chebyshev and Fourier Series 3. Galerkin and Weighted Residual Methods 4. Interpolation, Collocation and All That 5. Cardinal Functions 6. Pseudospectral Methods for BVPs 7. Linear Eigenvalue Problems 8. Symmetry and Parity 9. Explicit Time-Integration Methods 10. Partial Summation, the FFT and MMT 11. Aliasing, Spectral Blocking, and Blow-Up 12. Implicit Schemes and the Slow Manifold 13. Splitting and its Cousins 14. Semi-Lagrangian Advection 15. Matrix-Solving Methods 16. Coordinate Transformations 17. Methods for Unbounded Intervals 18. Spherical and Cylindrical Geometry 19. Special Tricks 20. Symbolic Calculations 21. The Tau Method 22. Domain Decomposition Methods 23. Books and Reviews

rawabstract:
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more. Includes 7 appendices and over 160 text figures.

rawTOC:
1. Introduction \\ 2. Chebyshev and Fourier Series \\ 3. Galerkin and Weighted Residual Methods \\ 4. Interpolation, Collocation and All That \\ 5. Cardinal Functions \\ 6. Pseudospectral Methods for BVPs \\ 7. Linear Eigenvalue Problems \\ 8. Symmetry and Parity \\ 9. Explicit Time-Integration Methods \\ 10. Partial Summation, the FFT and MMT \\ 11. Aliasing, Spectral Blocking, and Blow-Up \\ 12. Implicit Schemes and the Slow Manifold \\ 13. Splitting and its Cousins \\ 14. Semi-Lagrangian Advection \\ 15. Matrix-Solving Methods \\ 16. Coordinate Transformations \\ 17. Methods for Unbounded Intervals \\ 18. Spherical and Cylindrical Geometry \\ 19. Special Tricks \\ 20. Symbolic Calculations \\ 21. The Tau Method \\ 22. Domain Decomposition Methods \\ 23. Books and Reviews

entry:
@Book{Boyd:2001:CFS,
  author =       "John Philip Boyd",
  title =        "{Chebyshev} and {Fourier} spectral methods",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second (revised).",
  pages =        "1375",
  year =         "2001",
  ISBN =         "0-486-41183-4 (paperback), 0-486-14192-6 (e-book)",
  ISBN-13 =      "978-0-486-41183-5 (paperback), 978-0-486-14192-3
                 (e-book)",
  LCCN =         "QA404.5 .B69 2001",
  bibdate =      "Sat Feb 17 14:05:46 MST 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover Books on Mathematics",
  URL =          "http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjE0MTkyMzpl",
  abstract =     "Completely revised text focuses on use of spectral
                 methods to solve boundary value, eigenvalue, and
                 time-dependent problems, but also covers Hermite,
                 Laguerre, rational Chebyshev, sinc, and spherical
                 harmonic functions, as well as cardinal functions,
                 linear eigenvalue problems, matrix-solving methods,
                 coordinate transformations, spherical and cylindrical
                 geometry, and more. Includes 7 appendices and over 160
                 text figures.",
  acknowledgement = ack-nhfb,
  author-dates = "1951--",
  subject =      "Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics); Polyn{\'y}omes de Tchebychev;
                 Analyse de Fourier; Spectre (Math{\'y}ematiques);
                 MATHEMATICS; General.; Chebyshev polynomials; Fourier
                 analysis; Spectral theory (Mathematics)",
  tableofcontents = "1. Introduction \\
                 2. Chebyshev and Fourier Series \\
                 3. Galerkin and Weighted Residual Methods \\
                 4. Interpolation, Collocation and All That \\
                 5. Cardinal Functions \\
                 6. Pseudospectral Methods for BVPs \\
                 7. Linear Eigenvalue Problems \\
                 8. Symmetry and Parity \\
                 9. Explicit Time-Integration Methods \\
                 10. Partial Summation, the FFT and MMT \\
                 11. Aliasing, Spectral Blocking, and Blow-Up \\
                 12. Implicit Schemes and the Slow Manifold \\
                 13. Splitting and its Cousins \\
                 14. Semi-Lagrangian Advection \\
                 15. Matrix-Solving Methods \\
                 16. Coordinate Transformations \\
                 17. Methods for Unbounded Intervals \\
                 18. Spherical and Cylindrical Geometry \\
                 19. Special Tricks \\
                 20. Symbolic Calculations \\
                 21. The Tau Method \\
                 22. Domain Decomposition Methods \\
                 23. Books and Reviews",
}


bibtype: inproceedings
filename: elefunt.bib
label: Burgess:2001:DIR
author: N. Burgess and C. Hinds
booktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
title: Design issues in radix-$4$ SRT square root & divide unit
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1646--1650
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: N. Burgess and C. Hinds
rawbooktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
rawtitle: Design issues in radix-$4$ {SRT} square root {\&} divide unit
entry:
@InProceedings{Burgess:2001:DIR,
  author =       "N. Burgess and C. Hinds",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Design issues in radix-$4$ {SRT} square root {\&}
                 divide unit",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1646--1650",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper introduces a number of design issues not
                 covered in the open literature that arose during the
                 design of a radix-$4$ SRT divide/square root unit for a
                 vector processing chip. These include compression of
                 the partial remainder's m.s.b.'s, \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Bustoz:2001:SFC
editor: Joaquin Bustoz and Mourad Ismail and S. K. (Sergei Konstantinovich) Suslov
title: Special functions 2000: current perspective and future directions
volume: 30
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: xi + 520
year: 2001
ISBN: 0-7923-7119-4, 0-7923-7120-8 OR 0792371194, 0792371208
ISBN13: 978-0-7923-7119-9, 978-0-7923-7120-5 OR 9780792371199, 9780792371205
LCCN: QA351 .S694 2001
bibdate: Sat Oct 30 17:31:39 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:31:39 MDT
series: NATO science series. Series II, Mathematics, physics, and chemistry
subject: functions, special; congresses
acknowledgement: ack-nhfb
raweditor: Joaquin Bustoz and Mourad Ismail and S. K. (Sergei Konstantinovich) Suslov
rawtitle: Special functions 2000: current perspective and future directions
TOC:
Preface Foreword Bailey's transform, lemma, chains and tree / George E. Andrews 1 Riemann--Hilbert problems for multiple orthogonal polynomials / Walter Van Assche, Jeffrey S. Geronimo, Arno B. J. Kuijlaars 23 Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions and $q$'s / Bruce C. Berndt 61 Orthogonal rational functions and continued fractions [et al.] 87 Orthogonal polynomials and reflection groups / Charles F. Dunkl 111 The bispectral problem: an overview / F. Alberto Grunbaum 129 The Bochner--Krall problem: some new perspectives / Luc Haine 141 Lectures on $q$-orthogonal polynomials / Mourad E. H. Ismail 179 The Askey--Wilson function transform scheme / Erik Koelink, Jasper V. Stokman 221 Arithmetic of the partition function / Ken Ono 243 The associated classical orthogonal polynomials / Mizan Rahman 255 Special functions defined by analytic difference equations / S. N. M. Ruijsenaars 281 The factorization method, self-similar potentials and quantum algebras / V. P. Spiridonov 335 Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids / V. P. Spiridonov, A. S. Zhedanov 365 Orthogonal polynomials and combinatorics / Dennis Stanton 389 Basic exponential functions on a $q$-quadratic grid / Sergei K. Suslov 411 Projection operator method for quantum groups / V. N. Tolstoy 457 Uniform asymptotic expansions / R. Wong 489 Exponential asymptotics / R. Wong 505 Index 519

rawTOC:
Preface \\ Foreword \\ Bailey's transform, lemma, chains and tree / George E. Andrews 1 \\ Riemann--Hilbert problems for multiple orthogonal polynomials / Walter Van Assche, Jeffrey S. Geronimo, Arno B. J. Kuijlaars 23 \\ Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions and $q$'s / Bruce C. Berndt 61 \\ Orthogonal rational functions and continued fractions [et al.] 87 \\ Orthogonal polynomials and reflection groups / Charles F. Dunkl 111 \\ The bispectral problem: an overview / F. Alberto Grunbaum 129 \\ The Bochner--Krall problem: some new perspectives / Luc Haine 141 \\ Lectures on $q$-orthogonal polynomials / Mourad E. H. Ismail 179 \\ The Askey--Wilson function transform scheme / Erik Koelink, Jasper V. Stokman 221 \\ Arithmetic of the partition function / Ken Ono 243 \\ The associated classical orthogonal polynomials / Mizan Rahman 255 \\ Special functions defined by analytic difference equations / S. N. M. Ruijsenaars 281 \\ The factorization method, self-similar potentials and quantum algebras / V. P. Spiridonov 335 \\ Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids / V. P. Spiridonov, A. S. Zhedanov 365 \\ Orthogonal polynomials and combinatorics / Dennis Stanton 389 \\ Basic exponential functions on a $q$-quadratic grid / Sergei K. Suslov 411 \\ Projection operator method for quantum groups / V. N. Tolstoy 457 \\ Uniform asymptotic expansions / R. Wong 489 \\ Exponential asymptotics / R. Wong 505 \\ Index 519

entry:
@Book{Bustoz:2001:SFC,
  editor =       "Joaquin Bustoz and Mourad Ismail and S. K. (Sergei
                 Konstantinovich) Suslov",
  title =        "Special functions 2000: current perspective and future
                 directions",
  volume =       "30",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xi + 520",
  year =         "2001",
  ISBN =         "0-7923-7119-4, 0-7923-7120-8",
  ISBN-13 =      "978-0-7923-7119-9, 978-0-7923-7120-5",
  LCCN =         "QA351 .S694 2001",
  bibdate =      "Sat Oct 30 17:31:39 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "NATO science series. Series II, Mathematics, physics,
                 and chemistry",
  acknowledgement = ack-nhfb,
  subject =      "functions, special; congresses",
  tableofcontents = "Preface \\
                 Foreword \\
                 Bailey's transform, lemma, chains and tree / George E.
                 Andrews 1 \\
                 Riemann--Hilbert problems for multiple orthogonal
                 polynomials / Walter Van Assche, Jeffrey S. Geronimo,
                 Arno B. J. Kuijlaars 23 \\
                 Flowers which we cannot yet see growing in Ramanujan's
                 garden of hypergeometric series, elliptic functions and
                 $q$'s / Bruce C. Berndt 61 \\
                 Orthogonal rational functions and continued fractions
                 [et al.] 87 \\
                 Orthogonal polynomials and reflection groups / Charles
                 F. Dunkl 111 \\
                 The bispectral problem: an overview / F. Alberto
                 Grunbaum 129 \\
                 The Bochner--Krall problem: some new perspectives / Luc
                 Haine 141 \\
                 Lectures on $q$-orthogonal polynomials / Mourad E. H.
                 Ismail 179 \\
                 The Askey--Wilson function transform scheme / Erik
                 Koelink, Jasper V. Stokman 221 \\
                 Arithmetic of the partition function / Ken Ono 243 \\
                 The associated classical orthogonal polynomials / Mizan
                 Rahman 255 \\
                 Special functions defined by analytic difference
                 equations / S. N. M. Ruijsenaars 281 \\
                 The factorization method, self-similar potentials and
                 quantum algebras / V. P. Spiridonov 335 \\
                 Generalized eigenvalue problem and a new family of
                 rational functions biorthogonal on elliptic grids / V.
                 P. Spiridonov, A. S. Zhedanov 365 \\
                 Orthogonal polynomials and combinatorics / Dennis
                 Stanton 389 \\
                 Basic exponential functions on a $q$-quadratic grid /
                 Sergei K. Suslov 411 \\
                 Projection operator method for quantum groups / V. N.
                 Tolstoy 457 \\
                 Uniform asymptotic expansions / R. Wong 489 \\
                 Exponential asymptotics / R. Wong 505 \\
                 Index 519",
}


bibtype: incollection
filename: elefunt.bib
label: Corless:2001:RAE
author: Robert M. Corless and James H. Davenport and David J. Jeffrey and Gurjeet Litt and Stephen M. Watt
booktitle: Artificial intelligence and symbolic computation (Madrid, 2000)
title: Reasoning about the elementary functions of complex analysis
volume: 1930
publisher: pub-SV
address: pub-SV:adr
pages: 115--126
year: 2001
MRclass: 68W30 (30C35)
MRnumber: MR1882755 (2002m:68126)
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 ???
series: Lecture Notes in Comput. Sci.
acknowledgement: ack-nhfb
rawauthor: Robert M. Corless and James H. Davenport and David J. Jeffrey and Gurjeet Litt and Stephen M. Watt
rawbooktitle: Artificial intelligence and symbolic computation (Madrid, 2000)
rawtitle: Reasoning about the elementary functions of complex analysis
entry:
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  author =       "Robert M. Corless and James H. Davenport and David J.
                 Jeffrey and Gurjeet Litt and Stephen M. Watt",
  booktitle =    "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  volume =       "1930",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "115--126",
  year =         "2001",
  MRclass =      "68W30 (30C35)",
  MRnumber =     "MR1882755 (2002m:68126)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Comput. Sci.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Dunkl:2001:OPS
author: Charles F. Dunkl and Yuan Xu
title: Orthogonal Polynomials of Several Variables
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xv + 390
year: 2001
DOI: https://doi.org/10.1017/CBO9780511565717
LCCN: QA404.5 .D86 2001
bibdate: Sat Nov 11 07:30:57 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.11 07:30:57 ???
remark: See also second edition cite Dunkl:2014:OPS
acknowledgement: ack-nhfb
rawauthor: Charles F. Dunkl and Yuan Xu
rawtitle: Orthogonal Polynomials of Several Variables
ISBN:
0-511-56571-2 (e-book), 0-521-80043-9 (hardcover), 1-107-09582-4 OR 0511565712 (ebook), 0521800439 (hardcover), 1107095824

ISBN13:
978-0-511-56571-7 (e-book), 978-0-521-80043-3 (hardcover), 978-1-107-09582-3 OR 9780511565717 (ebook), 9780521800433 (hardcover), 9781107095823

abstract:
This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball. It also focuses on those of Gaussian type, for which fairly explicit formulae exist. The authors' approach blends classical analysis and symmetry-group-theoretic methods.

TOC:
1. Background 2. Examples of Orthogonal Polynomials in Several Variables 3. General Properties of Orthogonal Polynomials in Several Variables 4. Root Systems and Coxeter groups 5. Spherical Harmonics Associated with Reflection Groups 6. Classical and Generalized Classical Orthogonal Polynomials 7. Summability of Orthogonal Expansions 8. Orthogonal Polynomials Associated with Symmetric Groups 9. Orthogonal Polynomials Associated with Octahedral Groups and Applications

rawabstract:
This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball. It also focuses on those of Gaussian type, for which fairly explicit formulae exist. The authors' approach blends classical analysis and symmetry-group-theoretic methods.

rawTOC:
1. Background \\ 2. Examples of Orthogonal Polynomials in Several Variables \\ 3. General Properties of Orthogonal Polynomials in Several Variables \\ 4. Root Systems and Coxeter groups \\ 5. Spherical Harmonics Associated with Reflection Groups \\ 6. Classical and Generalized Classical Orthogonal Polynomials \\ 7. Summability of Orthogonal Expansions \\ 8. Orthogonal Polynomials Associated with Symmetric Groups \\ 9. Orthogonal Polynomials Associated with Octahedral Groups and Applications

entry:
@Book{Dunkl:2001:OPS,
  author =       "Charles F. Dunkl and Yuan Xu",
  title =        "Orthogonal Polynomials of Several Variables",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xv + 390",
  year =         "2001",
  DOI =          "https://doi.org/10.1017/CBO9780511565717",
  ISBN =         "0-511-56571-2 (e-book), 0-521-80043-9 (hardcover),
                 1-107-09582-4",
  ISBN-13 =      "978-0-511-56571-7 (e-book), 978-0-521-80043-3
                 (hardcover), 978-1-107-09582-3",
  LCCN =         "QA404.5 .D86 2001",
  bibdate =      "Sat Nov 11 07:30:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This is the first modern book on orthogonal
                 polynomials of several variables, which are valuable
                 tools used in multivariate analysis, including
                 approximations and numerical integration. The book
                 presents the theory in elegant form and with modern
                 concepts and notation. It introduces the general theory
                 and emphasizes the classical types of orthogonal
                 polynomials whose weight functions are supported on
                 standard domains such as the cube, the simplex, the
                 sphere and the ball. It also focuses on those of
                 Gaussian type, for which fairly explicit formulae
                 exist. The authors' approach blends classical analysis
                 and symmetry-group-theoretic methods.",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition \cite{Dunkl:2014:OPS}",
  tableofcontents = "1. Background \\
                 2. Examples of Orthogonal Polynomials in Several
                 Variables \\
                 3. General Properties of Orthogonal Polynomials in
                 Several Variables \\
                 4. Root Systems and Coxeter groups \\
                 5. Spherical Harmonics Associated with Reflection
                 Groups \\
                 6. Classical and Generalized Classical Orthogonal
                 Polynomials \\
                 7. Summability of Orthogonal Expansions \\
                 8. Orthogonal Polynomials Associated with Symmetric
                 Groups \\
                 9. Orthogonal Polynomials Associated with Octahedral
                 Groups and Applications",
}


bibtype: article
filename: elefunt.bib
label: Eklund:2001:CEF
author: Neil Eklund
title: CORDIC: Elementary Function Computation Using Recursive Sequences
journal: j-COLLEGE-MATH-J
volume: 32
number: 5
pages: 330--333
month: nov
monthnumber: 11
year: 2001
DOI: https://doi.org/10.1080/07468342.2001.11921899
ISSN: 0746-8342 (print), 1931-1346 (electronic) OR 07468342 (print), 19311346 (electronic)
ISSNL: 0746-8342 OR 07468342
bibdate: Thu Feb 14 09:53:12 MST 2019
bibtimestamp: 2019.02.14 09:53:12 MST
URL: http://www.tandfonline.com/doi/abs/10.1080/07468342.2001.11921899
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: Neil Eklund
rawtitle: {CORDIC}: Elementary Function Computation Using Recursive Sequences
entry:
@Article{Eklund:2001:CEF,
  author =       "Neil Eklund",
  title =        "{CORDIC}: Elementary Function Computation Using
                 Recursive Sequences",
  journal =      j-COLLEGE-MATH-J,
  volume =       "32",
  number =       "5",
  pages =        "330--333",
  month =        nov,
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.2001.11921899",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:53:12 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/10.1080/07468342.2001.11921899",
  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: Elbert:2001:CZB
author: Arpad Elbert and Andrea Laforgia
title: A conjecture on the zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 683--683
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700007172
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: {\'A}rp{\'a}d Elbert and Andrea Laforgia
rawtitle: A conjecture on the zeros of {Bessel} functions
entry:
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  author =       "{\'A}rp{\'a}d Elbert and Andrea Laforgia",
  title =        "A conjecture on the zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "683--683",
  day =          "1",
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  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700007172",
  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: Elbert:2001:SRR
author: A. Elbert
title: Some recent results on the zeros of Bessel functions and orthogonal polynomials
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 65--83
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270000635X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: {\'A}. Elbert
rawtitle: Some recent results on the zeros of {Bessel} functions and orthogonal polynomials
entry:
@Article{Elbert:2001:SRR,
  author =       "{\'A}. Elbert",
  title =        "Some recent results on the zeros of {Bessel} functions
                 and orthogonal polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "65--83",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
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  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270000635X",
  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: Giordano:2001:IMP
author: C. Giordano and A. Laforgia
title: Inequalities and monotonicity properties for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 387--396
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006592
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: C. Giordano and A. Laforgia
rawtitle: Inequalities and monotonicity properties for the gamma function
entry:
@Article{Giordano:2001:IMP,
  author =       "C. Giordano and A. Laforgia",
  title =        "Inequalities and monotonicity properties for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "387--396",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006592",
  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: Godfrey:2001:NCC
author: P. Godfrey
title: A Note on the Computation of the Convergent Lanczos Complex Gamma Approximation
pages: 387--396
year: 2001
bibdate: Mon Nov 24 21:04:40 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.11.24 21:04:40 ???
note: Unpublished Web file.
URL: http://my.fit.edu/~gabdo/gamma.txt
acknowledgement: ack-nhfb
rawauthor: P. Godfrey
rawnote: Unpublished Web file.
rawtitle: A Note on the Computation of the Convergent {Lanczos} Complex Gamma Approximation
entry:
@Unpublished{Godfrey:2001:NCC,
  author =       "P. Godfrey",
  title =        "A Note on the Computation of the Convergent {Lanczos}
                 Complex Gamma Approximation",
  year =         "2001",
  bibdate =      "Mon Nov 24 21:04:40 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Unpublished Web file.",
  URL =          "http://my.fit.edu/~gabdo/gamma.txt",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Harris:2001:KFL
author: Frank E. Harris
title: On Kryachko's formula for the leaky aquifer function
journal: j-IJQC
volume: 81
number: 5
pages: 332--334
year: 2001
CODEN: IJQCB2
DOI: https://doi.org/10.1002/1097-461X(2001)81:5<332::AID-QUA1002>3.0.CO%3B2-W
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Wed Apr 4 11:48:33 MDT 2001
bibtimestamp: 2001.04.04 11:48:33 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: Frank E. Harris
rawtitle: On {Kryachko}'s formula for the leaky aquifer function
bibsource:
http://www.interscience.wiley.com/jpages/0020-7608; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract/76507286/START; http://www3.interscience.wiley.com/cgi-bin/fulltext/76507286/FILE?TPL=ftx_start; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=76507286&PLACEBO=IE.pdf

entry:
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  author =       "Frank E. Harris",
  title =        "On {Kryachko}'s formula for the leaky aquifer
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  journal =      j-IJQC,
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  number =       "5",
  pages =        "332--334",
  month =        "????",
  year =         "2001",
  CODEN =        "IJQCB2",
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  bibsource =    "http://www.interscience.wiley.com/jpages/0020-7608;
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  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
}


bibtype: article
filename: elefunt.bib
label: Karatsuba:2001:ARE
author: Ekatherina A. Karatsuba
title: On the asymptotic representation of the Euler gamma function by Ramanujan
journal: j-J-COMPUT-APPL-MATH
volume: 135
number: 2
pages: 225--240
day: 15
month: oct
monthnumber: 10
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:20 MST 2017
bibtimestamp: 2017.02.25 12:45:20 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700005860
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Ekatherina A. Karatsuba
rawtitle: On the asymptotic representation of the {Euler} gamma function by {Ramanujan}
entry:
@Article{Karatsuba:2001:ARE,
  author =       "Ekatherina A. Karatsuba",
  title =        "On the asymptotic representation of the {Euler} gamma
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  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "135",
  number =       "2",
  pages =        "225--240",
  day =          "15",
  month =        oct,
  year =         "2001",
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  ISSN-L =       "0377-0427",
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  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lang:2001:CRR
author: Tomas Lang and Elisardo Antelo
booktitle: Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001
title: Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation
crossref: Burgess:2001:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 83--93
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawbooktitle: Proceedings of the 15th {IEEE} Symposium on Computer Arithmetic, 11--13 June 2001
rawtitle: Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation
entry:
@InProceedings{Lang:2001:CRR,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "Correctly Rounded Reciprocal Square-Root by Digit
                 Recurrence and Radix-$4$ Implementation",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "83--93",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "We present a reciprocal square-root algorithm by digit
                 recurrence and selection by a staircase function, and
                 the radix-$4$ implementation. As similar algorithms for
                 division and square-root, the results are obtained
                 correctly rounded in a \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lether:2001:VPA
author: F. G. Lether
journal: j-J-SCI-COMPUT
volume: 16
number: 1
pages: 69--79
month: mar
monthnumber: 3
year: 2001
CODEN: JSCOEB
DOI: https://doi.org/10.1023/A:1011150530703
ISSN: 0885-7474 (print), 1573-7691 (electronic) OR 08857474 (print), 15737691 (electronic)
ISSNL: 0885-7474 OR 08857474
bibdate: Sat Dec 22 13:05:47 MST 2012
bibtimestamp: 2012.12.22 13:05:47 MST
fjournal: Journal of Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10915
rawauthor: F. G. Lether
title:
Variable Precision Algorithm for the Numerical Computation of the Fermi--Dirac Function $ F_j(x) $ of Order $ j = - 3 / 2 $

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=16&issue=1; https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jscicomput.bib

URL:
http://link.springer.com/content/pdf/10.1023/A%3A1011150530703; http://www.springerlink.com/openurl.asp?genre=article&issn=0885-7474&volume=16&issue=1&spage=69-79

rawtitle:
Variable Precision Algorithm for the Numerical Computation of the {Fermi--Dirac} Function {$ F_j(x) $} of Order $ j = - 3 / 2 $

entry:
@Article{Lether:2001:VPA,
  author =       "F. G. Lether",
  title =        "Variable Precision Algorithm for the Numerical
                 Computation of the {Fermi--Dirac} Function {$ F_j(x) $}
                 of Order $ j = - 3 / 2 $",
  journal =      j-J-SCI-COMPUT,
  volume =       "16",
  number =       "1",
  pages =        "69--79",
  month =        mar,
  year =         "2001",
  CODEN =        "JSCOEB",
  DOI =          "https://doi.org/10.1023/A:1011150530703",
  ISSN =         "0885-7474 (print), 1573-7691 (electronic)",
  ISSN-L =       "0885-7474",
  bibdate =      "Sat Dec 22 13:05:47 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=16&issue=1;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
  URL =          "http://link.springer.com/content/pdf/10.1023/A%3A1011150530703;
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  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/10915",
}


bibtype: techreport
filename: elefunt.bib
label: Li:2001:LLF
author: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
title: The tt libm library and floating-point arithmetic for HP-UX on Itanium
type: Technical report
institution: pub-HP
address: pub-HP:adr
month: apr
monthnumber: 4
year: 2001
bibdate: Fri Jun 24 20:12:09 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.24 20:12:09 ???
acknowledgement: ack-nhfb
rawauthor: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
rawtitle: The {\tt libm} library and floating-point arithmetic for {HP-UX} on {Itanium}
URL:
http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf; http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html

entry:
@TechReport{Li:2001:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium}",
  type =         "Technical report",
  institution =  pub-HP,
  address =      pub-HP:adr,
  pages =        "??",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
                 http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Loenko:2001:CEF
author: M. Yu. Loenko
title: Computation of elementary functions with guaranteed accuracy
journal: j-PROGRAMMIROVANIE
volume: 2
pages: 68--80
year: 2001
CODEN: PROGD3
ISSN: 0132-3474, 0361-7688 OR 01323474, 03617688
MRclass: 65D15 (65G20)
MRnumber: MR1867584
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: Rossiui skaya Akademiya Nauk. Programmirovanie
acknowledgement: ack-nhfb
rawauthor: M. Yu. Loenko
rawtitle: Computation of elementary functions with guaranteed accuracy
entry:
@Article{Loenko:2001:CEF,
  author =       "M. Yu. Loenko",
  title =        "Computation of elementary functions with guaranteed
                 accuracy",
  journal =      j-PROGRAMMIROVANIE,
  volume =       "2",
  pages =        "68--80",
  year =         "2001",
  CODEN =        "PROGD3",
  ISSN =         "0132-3474, 0361-7688",
  MRclass =      "65D15 (65G20)",
  MRnumber =     "MR1867584",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi\u\i skaya Akademiya Nauk. Programmirovanie",
}


bibtype: article
filename: elefunt.bib
label: Meyer:2001:JEF
author: Kenneth R. Meyer
title: Jacobi Elliptic Functions from a Dynamical Systems Point of View
journal: j-AMER-MATH-MONTHLY
volume: 108
number: 8
pages: 729--737
month: oct
monthnumber: 10
year: 2001
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jan 30 12:00:14 MST 2012
bibtimestamp: 2012.01.30 12:00:14 MST
URL: http://www.jstor.org/stable/2695616
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Kenneth R. Meyer
rawtitle: {Jacobi} Elliptic Functions from a Dynamical Systems Point of View
bibsource:
http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i346008; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Meyer:2001:JEF,
  author =       "Kenneth R. Meyer",
  title =        "{Jacobi} Elliptic Functions from a Dynamical Systems
                 Point of View",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "108",
  number =       "8",
  pages =        "729--737",
  month =        oct,
  year =         "2001",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 12:00:14 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i346008;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2695616",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Muller:2001:CCH
author: Keith E. Muller
title: Computing the confluent hypergeometric function, $ M(a, b, x) $
journal: j-NUM-MATH
volume: 90
number: 1
pages: 179--196
month: nov
monthnumber: 11
year: 2001
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s002110100285
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Feb 3 10:07:57 MST 2002
bibtimestamp: 2002.02.03 10:07:57 MST
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Keith E. Muller
rawtitle: Computing the confluent hypergeometric function, {$ M(a, b, x) $}
bibsource:
http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath2000.bib

URL:
http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm; http://link.springer-ny.com/link/service/journals/00211/papers/1090001/10900179.pdf

entry:
@Article{Muller:2001:CCH,
  author =       "Keith E. Muller",
  title =        "Computing the confluent hypergeometric function, {$
                 M(a, b, x) $}",
  journal =      j-NUM-MATH,
  volume =       "90",
  number =       "1",
  pages =        "179--196",
  month =        nov,
  year =         "2001",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s002110100285",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Feb 3 10:07:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X;
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  URL =          "http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm;
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  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Nagel:2001:EHF
author: Bengt Nagel
title: An expansion of the hypergeometric function in Bessel functions
journal: j-J-MATH-PHYS
volume: 42
number: 12
pages: 5910--5914
month: dec
monthnumber: 12
year: 2001
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Thu Mar 28 19:47:21 MST 2002
bibtimestamp: 2002.03.28 19:47:21 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Bengt Nagel
rawtitle: An expansion of the hypergeometric function in {Bessel} functions
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Nagel:2001:EHF,
  author =       "Bengt Nagel",
  title =        "An expansion of the hypergeometric function in
                 {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "12",
  pages =        "5910--5914",
  month =        dec,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Thu Mar 28 19:47:21 MST 2002",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Plagianakos:2001:LCP
author: V. P. Plagianakos and N. K. Nousis and M. N. Vrahatis
title: Locating and computing in parallel all the simple roots of special functions using PVM
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 545--554
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00675-0
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006750
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: V. P. Plagianakos and N. K. Nousis and M. N. Vrahatis
rawtitle: Locating and computing in parallel all the simple roots of special functions using {PVM}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib

entry:
@Article{Plagianakos:2001:LCP,
  author =       "V. P. Plagianakos and N. K. Nousis and M. N.
                 Vrahatis",
  title =        "Locating and computing in parallel all the simple
                 roots of special functions using {PVM}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "545--554",
  day =          "1",
  month =        aug,
  year =         "2001",
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  DOI =          "https://doi.org/10.1016/S0377-0427(00)00675-0",
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  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  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: Plofker:2001:EIT
author: Kim Plofker
title: The ``Error'' in the Indian ``Taylor Series Approximation'' to the Sine
journal: j-HIST-MATH
volume: 28
number: 4
pages: 283--295
month: nov
monthnumber: 11
year: 2001
CODEN: HIMADS
DOI: https://doi.org/10.1006/hmat.2001.2331
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:20:02 MDT 2013
bibtimestamp: 2013.06.26 06:20:02 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086001923316
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: Kim Plofker
rawtitle: The {``Error''} in the {Indian} ``{Taylor} Series Approximation'' to the Sine
entry:
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  author =       "Kim Plofker",
  title =        "The {``Error''} in the {Indian} ``{Taylor} Series
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  journal =      j-HIST-MATH,
  volume =       "28",
  number =       "4",
  pages =        "283--295",
  month =        nov,
  year =         "2001",
  CODEN =        "HIMADS",
  DOI =          "https://doi.org/10.1006/hmat.2001.2331",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:20:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086001923316",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
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bibtype: article
filename: elefunt.bib
label: Rabi:2001:OCA
author: J. A. Rabi and M. J. S. de Lemos
journal: j-APPL-MATH-COMP
volume: 124
number: 2
pages: 215--226
day: 25
month: oct
monthnumber: 10
year: 2001
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Sun Nov 18 09:58:00 MST 2001
bibsource: http://www.elsevier.com/locate/issn/00963003; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.11.18 09:58:00 MST
URL: http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html
fjournal: Applied Mathematics and Computation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: J. A. Rabi and M. J. S. de Lemos
title:
Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

rawtitle:
Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

entry:
@Article{Rabi:2001:OCA,
  author =       "J. A. Rabi and M. J. S. de Lemos",
  title =        "Optimization of convergence acceleration in multigrid
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  journal =      j-APPL-MATH-COMP,
  volume =       "124",
  number =       "2",
  pages =        "215--226",
  day =          "25",
  month =        oct,
  year =         "2001",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sun Nov 18 09:58:00 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Rahavachary:2001:LSS
author: Saty Rahavachary
title: Letters: Setting the tt sqrt() record straight
journal: j-DDJ
volume: 26
number: 4
pages: 12--12
month: apr
monthnumber: 4
year: 2001
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Mar 13 15:22:36 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.03.13 15:22:36 MST
URL: http://www.ddj.com/
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Saty Rahavachary
rawtitle: Letters: Setting the {\tt sqrt()} record straight
entry:
@Article{Rahavachary:2001:LSS,
  author =       "Saty Rahavachary",
  title =        "Letters: Setting the {\tt sqrt()} record straight",
  journal =      j-DDJ,
  volume =       "26",
  number =       "4",
  pages =        "12--12",
  month =        apr,
  year =         "2001",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Mar 13 15:22:36 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ddj.com/",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: elefunt.bib
label: Rappoport:2001:CVP
author: J. M. Rappoport
journal: j-COMPUT-MATH-APPL
volume: 41
number: 3--4
pages: 399--406
month: feb
monthnumber: 2
year: 2001
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:14 MST 2017
bibtimestamp: 2017.03.01 21:49:14 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122100002820
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. M. Rappoport
title:
Canonical vector polynomials for the computation of complex order Bessel functions with the tau method

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Canonical vector polynomials for the computation of complex order {Bessel} functions with the tau method

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  author =       "J. M. Rappoport",
  title =        "Canonical vector polynomials for the computation of
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  journal =      j-COMPUT-MATH-APPL,
  volume =       "41",
  number =       "3--4",
  pages =        "399--406",
  month =        feb,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:14 MST 2017",
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  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122100002820",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Rump:2001:RPS
author: Siegfried M. Rump
title: Rigorous and Portable Standard Functions
journal: j-BIT-NUM-MATH
volume: 41
number: 3
pages: 540--562
month: jun
monthnumber: 6
year: 2001
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1023/A:1021971313412
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 15:06:04 MST 2006
bibtimestamp: 2006.01.04 15:06:04 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540
keywords: elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Siegfried M. Rump
rawtitle: Rigorous and Portable Standard Functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html; 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

abstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

rawabstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

entry:
@Article{Rump:2001:RPS,
  author =       "Siegfried M. Rump",
  title =        "Rigorous and Portable Standard Functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "540--562",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021971313412",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 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=41&issue=3&spage=540",
  abstract =     "Today's floating point implementations of elementary
                 transcendental functions are usually very accurate.
                 However, with few exceptions, the actual accuracy is
                 not known. In the present paper we describe a rigorous,
                 accurate, fast and portable implementation of the
                 elementary standard functions based on some existing
                 approximate standard functions. The scheme is outlined
                 for IEEE 754, but not difficult to adapt to other
                 floating point formats. A Matlab implementation is
                 available on the net. Accuracy of the proposed
                 algorithms can be rigorously estimated. As an example
                 we prove that the relative accuracy of the exponential
                 function is better than 2.07 eps in a slightly reduced
                 argument range (eps denoting the relative rounding
                 error unit). Otherwise, extensive computational tests
                 suggest for all elementary functions and all suitable
                 arguments an accuracy better than about 3 eps.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions; floating-point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Smith:2001:AFS
author: David M. Smith
journal: j-TOMS
volume: 27
number: 4
pages: 377--387
month: dec
monthnumber: 12
year: 2001
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Mar 13 08:49:29 MST 2002
bibtimestamp: 2002.03.13 08:49:29 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David M. Smith
title:
Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions

rawtitle:
{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions

entry:
@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: book
filename: elefunt.bib
label: Srivastava:2001:SAZ
author: H. M. Srivastava and Choi Junesang
title: Series Associated with the Zeta and Related Functions
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: ix + 388
year: 2001
DOI: https://doi.org/10.1007/978-94-015-9672-5
ISBN: 0-7923-7054-6 OR 0792370546
ISBN13: 978-0-7923-7054-3 OR 9780792370543
LCCN: QA351 .S74 2001
bibdate: Wed Jun 10 16:22:26 MDT 2015
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2015.06.10 16:22:26 MDT
subject: Functions, Zeta; Series
acknowledgement: ack-nhfb
rawauthor: H. M. Srivastava and Choi Junesang
rawtitle: Series Associated with the Zeta and Related Functions
URL:
http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html; http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html

TOC:
Acknowledgements / ix 1. Introduction and Preliminaries 1.1. Gamma and Beta functions / 1 1.2. Polygamma functions / 13 1.3. The multiple Gamma functions / 24 1.4. The Gaussian hypergeometric function and its generalization / 44 1.5. Stirling numbers of the first and second kind / 56 1.6. Bernoulli and Euler polynomials and numbers / 59 Problems / 67 2. The Zeta and Related Functions 2.1. Multiple Hurwitz Zeta functions / 77 2.2. The Hurwitz (or generalized) Zeta function / 88 2.3. The Riemann Zeta function / 96 2.4. Polylogarithm functions / 106 2.5. Hurwitz--Lerch Zeta functions / 121 Problems / 128 3. Series Involving Zeta Functions 3.1. Historical introduction / 142 3.2. Use of the Binomial theorem / 143 3.3. Use of generating functions / 152 3.4. Use of multiple Gamma functions / 159 3.5. Use of hypergeometric identities / 250 3.6. Other methods and their applications / 260 Problems / 269 4. Evaluations and Series Representations 4.1. Evaluation of $zeta (2n)$ / 275 4.2. Rapidly convergent series for $zeta (2n + 1)$ / 280 4.3. Further series representations / 289 4.4. Computational results / 295 Problems / 304 5. Determinants of the Laplacians 5.1. The $n$-dimensional problem / 315 5.2. Computations using the simple and multiple Gamma functions / 318 5.3. Computations using series of Zeta functions / 325 5.4. Remarks and observations / 328 Problems / 329 6. Miscellaneous Results 6.1. Bernoulli and Euler polynomials at rational arguments / 335 6.2. Closed-form summation of trigonometric series / 341 6.3. Integrals associated with the use of the Euler--Maclaurin summation formula / 344 Problems / 350 Bibliography / 353 Author Index / 379 Subject Index / 383

rawTOC:
Acknowledgements / ix \\ 1. Introduction and Preliminaries \\ 1.1. Gamma and Beta functions / 1 \\ 1.2. Polygamma functions / 13 \\ 1.3. The multiple Gamma functions / 24 \\ 1.4. The Gaussian hypergeometric function and its generalization / 44 \\ 1.5. Stirling numbers of the first and second kind / 56 \\ 1.6. Bernoulli and Euler polynomials and numbers / 59 \\ Problems / 67 \\ 2. The Zeta and Related Functions \\ 2.1. Multiple Hurwitz Zeta functions / 77 \\ 2.2. The Hurwitz (or generalized) Zeta function / 88 \\ 2.3. The Riemann Zeta function / 96 \\ 2.4. Polylogarithm functions / 106 \\ 2.5. Hurwitz--Lerch Zeta functions / 121 \\ Problems / 128 \\ 3. Series Involving Zeta Functions \\ 3.1. Historical introduction / 142 \\ 3.2. Use of the Binomial theorem / 143 \\ 3.3. Use of generating functions / 152 \\ 3.4. Use of multiple Gamma functions / 159 \\ 3.5. Use of hypergeometric identities / 250 \\ 3.6. Other methods and their applications / 260 \\ Problems / 269 \\ 4. Evaluations and Series Representations \\ 4.1. Evaluation of $\zeta(2n)$ / 275 \\ 4.2. Rapidly convergent series for $\zeta(2n + 1)$ / 280 \\ 4.3. Further series representations / 289 \\ 4.4. Computational results / 295 \\ Problems / 304 \\ 5. Determinants of the Laplacians \\ 5.1. The $n$-dimensional problem / 315 \\ 5.2. Computations using the simple and multiple Gamma functions / 318 \\ 5.3. Computations using series of Zeta functions / 325 \\ 5.4. Remarks and observations / 328 \\ Problems / 329 \\ 6. Miscellaneous Results \\ 6.1. Bernoulli and Euler polynomials at rational arguments / 335 \\ 6.2. Closed-form summation of trigonometric series / 341 \\ 6.3. Integrals associated with the use of the Euler--Maclaurin summation formula / 344 \\ Problems / 350 \\ Bibliography / 353 \\ Author Index / 379 \\ Subject Index / 383

entry:
@Book{Srivastava:2001:SAZ,
  author =       "H. M. Srivastava and Choi Junesang",
  title =        "Series Associated with the Zeta and Related
                 Functions",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "ix + 388",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/978-94-015-9672-5",
  ISBN =         "0-7923-7054-6",
  ISBN-13 =      "978-0-7923-7054-3",
  LCCN =         "QA351 .S74 2001",
  bibdate =      "Wed Jun 10 16:22:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Zeta; Series",
  tableofcontents = "Acknowledgements / ix \\
                 1. Introduction and Preliminaries \\
                 1.1. Gamma and Beta functions / 1 \\
                 1.2. Polygamma functions / 13 \\
                 1.3. The multiple Gamma functions / 24 \\
                 1.4. The Gaussian hypergeometric function and its
                 generalization / 44 \\
                 1.5. Stirling numbers of the first and second kind / 56
                 \\
                 1.6. Bernoulli and Euler polynomials and numbers / 59
                 \\
                 Problems / 67 \\
                 2. The Zeta and Related Functions \\
                 2.1. Multiple Hurwitz Zeta functions / 77 \\
                 2.2. The Hurwitz (or generalized) Zeta function / 88
                 \\
                 2.3. The Riemann Zeta function / 96 \\
                 2.4. Polylogarithm functions / 106 \\
                 2.5. Hurwitz--Lerch Zeta functions / 121 \\
                 Problems / 128 \\
                 3. Series Involving Zeta Functions \\
                 3.1. Historical introduction / 142 \\
                 3.2. Use of the Binomial theorem / 143 \\
                 3.3. Use of generating functions / 152 \\
                 3.4. Use of multiple Gamma functions / 159 \\
                 3.5. Use of hypergeometric identities / 250 \\
                 3.6. Other methods and their applications / 260 \\
                 Problems / 269 \\
                 4. Evaluations and Series Representations \\
                 4.1. Evaluation of $\zeta(2n)$ / 275 \\
                 4.2. Rapidly convergent series for $\zeta(2n + 1)$ /
                 280 \\
                 4.3. Further series representations / 289 \\
                 4.4. Computational results / 295 \\
                 Problems / 304 \\
                 5. Determinants of the Laplacians \\
                 5.1. The $n$-dimensional problem / 315 \\
                 5.2. Computations using the simple and multiple Gamma
                 functions / 318 \\
                 5.3. Computations using series of Zeta functions / 325
                 \\
                 5.4. Remarks and observations / 328 \\
                 Problems / 329 \\
                 6. Miscellaneous Results \\
                 6.1. Bernoulli and Euler polynomials at rational
                 arguments / 335 \\
                 6.2. Closed-form summation of trigonometric series /
                 341 \\
                 6.3. Integrals associated with the use of the
                 Euler--Maclaurin summation formula / 344 \\
                 Problems / 350 \\
                 Bibliography / 353 \\
                 Author Index / 379 \\
                 Subject Index / 383",
}


bibtype: inproceedings
filename: elefunt.bib
label: Takagi:2001:HAC
author: N. Takagi
booktitle: Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001
title: A Hardware Algorithm for Computing Reciprocal Square Root
crossref: Burgess:2001:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 94--100
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: N. Takagi
rawbooktitle: Proceedings of the 15th {IEEE} Symposium on Computer Arithmetic, 11--13 June 2001
rawtitle: A Hardware Algorithm for Computing Reciprocal Square Root
entry:
@InProceedings{Takagi:2001:HAC,
  author =       "N. Takagi",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--100",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Thorsley:2001:AEH
author: Michael D. Thorsley and Marita C. Chidichimo
title: An asymptotic expansion for the hypergeometric function $_2 F_1 (a, b; c; x)$
journal: j-J-MATH-PHYS
volume: 42
number: 4
pages: 1921--1930
month: apr
monthnumber: 4
year: 2001
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Wed Apr 18 05:33:53 MDT 2001
bibtimestamp: 2001.04.18 05:33:53 MDT
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Michael D. Thorsley and Marita C. Chidichimo
rawtitle: An asymptotic expansion for the hypergeometric function {$_2 F_1 (a, b; c; x)$}
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Thorsley:2001:AEH,
  author =       "Michael D. Thorsley and Marita C. Chidichimo",
  title =        "An asymptotic expansion for the hypergeometric
                 function {$_2 F_1 (a, b; c; x)$}",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "4",
  pages =        "1921--1930",
  month =        apr,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Apr 18 05:33:53 MDT 2001",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Verdonk:2001:PRIa
author: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
journal: j-TOMS
volume: 27
number: 1
pages: 92--118
month: mar
monthnumber: 3
year: 2001
CODEN: ACMSCU
DOI: https://doi.org/10.1145/382043.382404
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
URL: http://doi.acm.org/10.1145/382043.382404; http://www.win.ua.ac.be/~cant/ieeecc754.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
title:
A precision- and range-independent tool for testing floating-point arithmetic I: Basic operations, square root, and remainder

bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

keywords:
arithmetic; floating-point; floating-point testing; IEEE floating-point standard; multiprecision; validation; Verification

subject:
Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.0 General Subjects: Standards

rawabstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50\% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

rawtitle:
A precision- and range-independent tool for testing floating-point arithmetic {I}: {Basic} operations, square root, and remainder

entry:
@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: {Basic} operations,
                 square root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/382043.382404;
                 http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point; floating-point testing;
                 IEEE floating-point standard; multiprecision;
                 validation; Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}


bibtype: article
filename: elefunt.bib
label: Weniger:2001:IID
author: Ernst Joachim Weniger
journal: j-COMP-PHYS-COMM
volume: 133
number: 2--3
pages: 202--228
day: 15
month: jan
monthnumber: 1
year: 2001
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(00)00175-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 01 09:12:48 2011
bibtimestamp: 2011.12.01 09:12:48 ???
fjournal: Computer Physics Communications
keywords: convergence acceleration
remark: This paper concentrates on $_2 F_1 (a, b; c; z)$.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Ernst Joachim Weniger
title:
Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems

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

rawtitle:
Irregular input data in convergence acceleration and summation processes: {General} considerations and some special {Gaussian} hypergeometric series as model problems

entry:
@Article{Weniger:2001:IID,
  author =       "Ernst Joachim Weniger",
  title =        "Irregular input data in convergence acceleration and
                 summation processes: {General} considerations and some
                 special {Gaussian} hypergeometric series as model
                 problems",
  journal =      j-COMP-PHYS-COMM,
  volume =       "133",
  number =       "2--3",
  pages =        "202--228",
  day =          "15",
  month =        jan,
  year =         "2001",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(00)00175-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:12:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
  remark =       "This paper concentrates on $_2 F_1 (a, b; c; z)$.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Zheng:2001:ARE
author: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
booktitle: Proceedings of the 4th International Conference on ASIC
title: The application of redundant encoding in iterative implementation of division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 603--606
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
rawbooktitle: Proceedings of the 4th International Conference on {ASIC}
rawtitle: The application of redundant encoding in iterative implementation of division and square root
entry:
@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  booktitle =    "Proceedings of the 4th International Conference on
                 {ASIC}",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton--Raphson
                 algorithm are generally used in modern \ldots{}",
}


bibtype: misc
filename: elefunt.bib
label: Ziv:2001:APM
author: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
title: Accurate Portable Mathematical Library (IBM APMathLib)
publisher: pub-IBM
address: pub-IBM:adr
pages: 603--606
day: 20
month: dec
monthnumber: 12
year: 2001
bibdate: Wed Nov 24 08:06:54 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.24 08:06:54 ???
URL: ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz; http://oss.software.ibm.com/mathlib/
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
rawtitle: Accurate Portable Mathematical Library ({IBM APMathLib})
entry:
@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
                 http://oss.software.ibm.com/mathlib/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Al-Jarrah:2002:GSB
author: A. Al-Jarrah and K. M. Dempsey and M. L. Glasser
title: Generalized series of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 143
number: 1
pages: 1--8
day: 1
month: jun
monthnumber: 6
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:28 MST 2017
bibtimestamp: 2017.02.25 12:52:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042701005052
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. Al-Jarrah and K. M. Dempsey and M. L. Glasser
rawtitle: Generalized series of {Bessel} functions
entry:
@Article{Al-Jarrah:2002:GSB,
  author =       "A. Al-Jarrah and K. M. Dempsey and M. L. Glasser",
  title =        "Generalized series of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "143",
  number =       "1",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042701005052",
  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: Bertot:2002:PGS
author: Yves Bertot and Nicolas Magaud and Paul Zimmermann
title: A Proof of GMP Square Root
journal: j-J-AUTOM-REASON
volume: 29
number: 3--4
pages: 225--252
month: sep
monthnumber: 9
year: 2002
CODEN: JAREEW
DOI: https://doi.org/10.1023/A:1021987403425
ISSN: 0168-7433 (print), 1573-0670 (electronic) OR 01687433 (print), 15730670 (electronic)
ISSNL: 0168-7433 OR 01687433
bibdate: Sat Feb 08 08:59:09 2020
bibtimestamp: 2020.02.08 08:59:09 ???
URL: https://link.springer.com/article/10.1023/A:1021987403425
fjournal: Journal of Automated Reasoning
keywords: GNU Multiple Precision library
acknowledgement: ack-nhfb
ajournal: J. Autom. Reason.
journalURL: http://link.springer.com/journal/10817
rawauthor: Yves Bertot and Nicolas Magaud and Paul Zimmermann
rawtitle: A Proof of {GMP} Square Root
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/gnu.bib; https://www.math.utah.edu/pub/tex/bib/jautomreason.bib

entry:
@Article{Bertot:2002:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A Proof of {GMP} Square Root",
  journal =      j-J-AUTOM-REASON,
  volume =       "29",
  number =       "3--4",
  pages =        "225--252",
  month =        sep,
  year =         "2002",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1023/A:1021987403425",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Feb 08 08:59:09 2020",
  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/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1023/A:1021987403425",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "GNU Multiple Precision library",
}


bibtype: incollection
filename: elefunt.bib
label: Boisvert:2002:HMF
author: Ronald F. Boisvert and Daniel W. Lozier
title: Handbook of Mathematical Functions
crossref: Lide:2002:CEM
pages: 135--139
year: 2002
bibdate: Fri Jul 09 06:28:13 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:28:13 ???
note: Also printed as NIST Special Publication 958, Jan. 2001.
acknowledgement: ack-nhfb
rawauthor: Ronald F. Boisvert and Daniel W. Lozier
rawnote: Also printed as NIST Special Publication 958, Jan. 2001.
rawtitle: Handbook of Mathematical Functions
URL:
https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf; https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html

remark:
This article describes the history of the creation of the famous 1964 book by Milton Abramowitz and Irene Stegun named in the title.

entry:
@InCollection{Boisvert:2002:HMF,
  author =       "Ronald F. Boisvert and Daniel W. Lozier",
  title =        "Handbook of Mathematical Functions",
  crossref =     "Lide:2002:CEM",
  pages =        "135--139",
  year =         "2002",
  bibdate =      "Fri Jul 09 06:28:13 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Also printed as NIST Special Publication 958, Jan.
                 2001.",
  URL =          "https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf;
                 https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html",
  acknowledgement = ack-nhfb,
  remark =       "This article describes the history of the creation of
                 the famous 1964 book by Milton Abramowitz and Irene
                 Stegun named in the title.",
}


bibtype: article
filename: elefunt.bib
label: Bradford:2002:RAE
title: Reasoning about the elementary functions of complex analysis
journal: j-ANN-MATH-ARTIF-INTELL
volume: 36
number: 3
pages: 303--318
year: 2002
CODEN: AMAIEC
ISSN: 1012-2443 (print), 1573-7470 (electronic) OR 10122443 (print), 15737470 (electronic)
ISSNL: 1012-2443 OR 10122443
MRclass: 30-01 (03B35 68W30)
MRnumber: MR1950025 (2003m:30001)
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 ???
note: Artificial intelligence and symbolic computation (Madrid, 2000)
fjournal: Annals of Mathematics and Artificial Intelligence
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10472
rawnote: Artificial intelligence and symbolic computation (Madrid, 2000)
rawtitle: Reasoning about the elementary functions of complex analysis
author:
Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt

rawauthor:
Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt

entry:
@Article{Bradford:2002:RAE,
  author =       "Russell Bradford and Robert M. Corless and James H.
                 Davenport and David J. Jeffrey and Stephen M. Watt",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "36",
  number =       "3",
  pages =        "303--318",
  year =         "2002",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  MRclass =      "30-01 (03B35 68W30)",
  MRnumber =     "MR1950025 (2003m:30001)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}


