view main/gsl/doc/gsl.ps @ 11838:b9f4ede9342a octave-forge

data-smoothing: moved to a separate mercurial repo
author carandraug
date Wed, 19 Jun 2013 02:15:35 +0000
parents 90c67cca7455
children
line wrap: on
line source

%!PS-Adobe-2.0
%%Creator: dvips(k) 5.96.1 Copyright 2007 Radical Eye Software
%%Title: gsl.dvi
%%CreationDate: Wed Apr 28 11:59:06 2010
%%Pages: 26
%%PageOrder: Ascend
%%BoundingBox: 0 0 596 842
%%DocumentFonts: CMR10 CMTT10 CMSS10 CMSLTT10 CMSL10 CMMI10 CMEX10 CMMI7
%%+ CMR7 CMSY10
%%DocumentPaperSizes: a4
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips -o gsl.ps gsl.dvi
%DVIPSParameters: dpi=600
%DVIPSSource:  TeX output 2010.04.28:1159
%%BeginProcSet: tex.pro 0 0
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S
/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy
setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask
restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: texps.pro 0 0
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A
27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF
5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09
0ABF1D42C5DDD0C384C7E22F8F8047BE1D4C1CC8E33368FB1AC82B4E96146730
DE3302B2E6B819CB6AE455B1AF3187FFE8071AA57EF8A6616B9CB7941D44EC7A
71A7BB3DF755178D7D2E4BB69859EFA4BBC30BD6BB1531133FD4D9438FF99F09
4ECC068A324D75B5F696B8688EEB2F17E5ED34CCD6D047A4E3806D000C199D7C
515DB70A8D4F6146FE068DC1E5DE8BC5703711DA090312BA3FC00A08C453C609
C627A8B1550654AD5E22C5F3F3CC8C1C0A6C7ADDAB55016A76EC46213FD9BAAF
03F7A5FD261BF647FCA5049118033F809370A84AC3ADA3D5BE032CBB494D7851
A6242E785CCC20D81FC5EE7871F1E588DA3E31BD321C67142C5D76BC6AC708DF
C21616B4CC92F0F8B92BD37A4AB83E066D1245FAD89B480CB0AC192D4CAFA6AD
241BD8DF7AD566A2022FBC67364AB89F33608554113D210FE5D27F8FB1B2B78A
F22EC999DBAAFC9C60017101D5FB2A3B6E2BF4BE47B8E5E4662B8C41AB471DFC
A31EE1
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 50 /two put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 25 /pi put
dup 61 /slash put
readonly def
/FontBBox{0 -250 1171 750}readonly def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F
C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B
B078D20B4B8A6D7F0300CF694E6956FF9C29C84FCC5C9E8890AA56B1BC60E868
DA8488AC4435E6B5CE34EA88E904D5C978514D7E476BF8971D419363125D4811
4D886EDDDCDDA8A6B0FDA5CF0603EA9FA5D4393BEBB26E1AB11C2D74FFA6FEE3
FAFBC6F05B801C1C3276B11080F5023902B56593F3F6B1F37997038F36B9E3AB
76C2E97E1F492D27A8E99F3E947A47166D0D0D063E4E6A9B535DC9F1BED129C5
123775D5D68787A58C93009FD5DA55B19511B95168C83429BD2D878207C39770
012318EA7AA39900C97B9D3859E3D0B04750B8390BF1F1BC29DC22BCAD50ECC6
A3C633D0937A59E859E5185AF9F56704708D5F1C50F78F43DFAC43C4E7DC9413
44CEFE43279AFD3C167C942889A352F2FF806C2FF8B3EB4908D50778AA58CFFC
4D1B14597A06A994ED8414BBE8B26E74D49F6CF54176B7297CDA112A69518050
01337CBA5478EB984CDD22020DAED9CA8311C33FBCC84177F5CE870E709FC608
D28B3A7208EFF72988C136142CE79B4E9C7B3FE588E9824ABC6F04D141E589B3
914A73A42801305439862414F893D5B6C327A7EE2730DEDE6A1597B09C258F05
261BC634F64C9F8477CD51634BA648FC70F659C90DC042C0D6B68CD1DF36D615
24F362B85A58D65A8E6DFD583EF9A79A428F2390A0B5398EEB78F4B5A89D9AD2
A517E0361749554ABD6547072398FFDD863E40501C316F28FDDF8B550FF8D663
9843D0BEA42289F85BD844891DB42EC7C51229D33EE7E83B1290404C799B8E8C
889787CDC0C51802EA1E0C63E6DE20980D3DD206F05379696B768B2C655CE94E
6A6D6306580B4DECD1252BDFA07285C11C1567BB487439E569DD239BA889D0AB
FFA5F5AECB67967203EAF3394E1E0D4EC6386B7155E4D111564403E3B470609F
24729C915CAFF1E2EEA1E6688F1499448DE4697BA5DA2316898BEC974C63D86F
CE081928A2258155027B5AC5DFB37D0ACEA6157CED0902BB285594299E9A6000
AA7F63919E08E6D3922A35BAE79D583ADEC857FE5E92BEF822C703066C025E85
6E025532213C9E59EEA72D1CDBB0175C7B862366A131A97EAB3AA7BED007896A
823C5A593838ADA44C8565200845106B9B23CDBC90BDD9E05C320050F25DE26E
DE1F4CDA0DFE07AD3735ED9A5FFB2669EBFD5588FA90F894F0D39947CDA3E1A9
F0DDE8F5E8C69A79B8A5679C5167661BC417AE15D1787D0258C103D391E6DFC4
0905BD77B6BEAD93E1372335F36BABBF2B65060020F5FD69AEF9BE7A85AC210E
FD60768552EE6F66E2DBB48C71D1EB15F2332FB03C68D91E384DB1E405F0AAEE
01D4B0E4691F888D7AA3DEF390B65ACE85F6D8D1371476A7BB290AAADB2DF402
27EA126AD8DE09ABB01EA67F2579B1F7E6E98D
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 90 /integraldisplay put
dup 113 /radicalBig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 69 /E put
dup 75 /K put
dup 100 /d put
dup 107 /k put
dup 109 /m put
dup 116 /t put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTT10
%!PS-AdobeFont-1.1: CMTT10 1.00B
%%CreationDate: 1992 Apr 26 10:42:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 42 /asterisk put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 58 /colon put
dup 60 /less put
dup 61 /equal put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 80 /P put
dup 81 /Q put
dup 83 /S put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 94 /asciicircum put
dup 95 /underscore put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /braceleft put
dup 124 /bar put
dup 125 /braceright put
readonly def
/FontBBox{-4 -235 731 800}readonly def
currentdict end
currentfile eexec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%%EndFont 
%%BeginFont: CMSL10
%!PS-AdobeFont-1.1: CMSL10 1.0
%%CreationDate: 1991 Aug 20 16:40:20
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSL10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -9.46 def
/isFixedPitch false def
end readonly def
/FontName /CMSL10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 46 /period put
dup 77 /M put
dup 78 /N put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 109 /m put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-62 -250 1123 750}readonly def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958
9429B9D40924DC059325D9D4CC0344F3F997A99E6CC0676735EBCD685AAC9142
08DAFEC78BB41AFC2F1C219910BDF41D6279284EF600B69776CA15BC8A34347C
30783C52AFA60FBE3E353E2AE354CF87B558776A22C776C7A0B5AB5CE1F941EF
C2D9CAC37294BF407A671F10E4743BF842143F4F7DFEE643BA3BBD8BB9E3F24A
BCCF7F0ADF8BA500620C81033EAE8C4EF2C1DEF13AC575F1B3BBB66F093D3B78
5412B82B67FFA087AF57182B2230F9F2137180CA58A7D9B2C822FF04BE6CD01D
43B2CA7058C7B953F6D9B5D6E91ECBAA5CDE1159B0E59C83DBAD96D6C8C8BAB1
374EF652D10C0F3EE7104472C98DD3572AAF2D45A70BF7061447E21EE3C3BF23
DF39C2D1B35B42CD5297BEBE6BC94F7C9DC6E61EC67E4F677256FED9064BD3E4
B51A71B1D27CA4E5AA9E1D8080E6DAB5310711EEF87C40859FA935B19524AE83
63B163FA8397BDFF443227FEDF7DB27DC35D89FB1C5E435DA0619A5C88AFC73B
89A2DF5E767C5B536BC7167A840A0C32BD57A14DE69A7D0D819AC36FF32F908A
5070F32983BB007437E3500799DF5E0AD3710A4C0000F0098D5BE99F2EB9C1C2
C444FD9552D0DCA098A94B3BF176F511CEE13DB7EFFAED7C47B5ADCF8D4700F5
7B6DF50EE617C00966B9A2828882804DB7477F4A8CF5345B7F3568B4F72BCE73
2E2AA5BC4B4C70E21F3AD9AFC3B8605A00D67EF9ED1F4D13DDAA920D45B43CE0
0941BF17CF05D2B777C11D4D844AB20C0693D1DDF00B27D9E1AA2D98A4A06CC6
D342AD8F644F4787B66CA7D861E7CE13FCDA85C1B0C9F94009768EA89838EBA2
7818F40BEAA214E36C3E9F0BC27AF8B0F2A96D2782A4FB2C3596EC2A77516B4A
80C1DBAF5572DC53CFC56E36C75357A46CEAF5517DEAE1A386B45A1515361D30
EF5783B833B623CF2397E24180D82045F6C14EDA0BF81EA839F8122AFA6EE1F1
F4BB4841EEBBE7DBCB7964D9675BC6199AFB3590F8444B252872F924DFD059ED
7811965E072C20A10C776795C64E14DBDD98B515E474CED3012CAFB178202D84
E460DBC83338E4467152739187932907A90CA61B781B54A61F3C9A8D689090BA
19B29D8F010E3CE22791137DC0F0ACF16CC84BEF88026AF8F53EA96F8A99D308
D95059F0D56204464384FFDA9BEF4E9949E73642967B40D795C0A9E6C496BED8
8ED8FA78B442653997684091D61FD89C2B850B65D6A3C9CF139D25E5067C866E
2D699ACE4404542A920C12C09A1A8BC568D339BB0A27FF6FA6AB9CA1E09FA4AE
D6974A93412E83FC9C011B97B899FFCDBAF73FD15D8E43019F4D68254F72DAD7
AB85E6C467CF0A016F2231C72900EE81323B00399B2C2ACEA6C7690159C5527E
3C45C6919D7D1020F1C3928ECE8BBB621F6882AD793403F828E165EB20F05721
497AB3B206C8024AF20E7ADF4D8F859BE4D74866FCA703A10664ABFCA396DBF3
FFE580F3AE3F3B69C9CE477E54C3FCC397D3F9140DBF63D31CD369D80B4529E9
952EBE44CE55697CF7730132C7097799E1FFE8EA104487983F095D7BD17E12A8
A1C6C620BD0FAAA46C2FF4AD0795EFCD62F861CC004B2953DC3FDDDC342E4389
802B1B403F3A5E239025F18FDAD620D4205D700E8AFA2E37E8E49061693340FB
1AA42C0A84A4517D1E2BB1E1827FEB6CEC037ACE850FD9188624FB787CF94E57
59854C6335CEA6C144DBDE5619784D917CE9E5794F6C4D2602024C596B38D657
9EF45FAE0AB64E67BBC95E1566900D72A2D8C42772759D7AA5CB9DEEB5371F4B
BF4EF8D05A48BA2A5F4AC2F9BD782FD16FB48028654C4F076B5AB617B91EB4A7
327DE28777972717A0175AEB0A70AD757C6FFFC680E8F1E6D23B661E804C2BDB
D0EB0A4CB5DB1CCAF51B9662D5F9225BB5EF820C7A96CA45E21A5F6A37DAFE7D
17803F6B7CF4137EC7A1153530646C579E56CE9B1F376BF45F01E22EB165E2C2
247418E39863C71D0001BE9B65B35171E2B50C42B48725EE7FD0B903BE3AE09C
47C12186B1AC53F70ADA65147866FD3970469131BC4B28DED6CB8D12A6A473F2
5836797A80C8ACC11A1582B04A957E2AD25274B8DA4B47E8741B20751E381B5F
D07FFEFDE2A98A0D444BB38F142A0AF18EDE6A77A47B60FDFAC38181A5099438
620F7B2B5E766299BB340D5A23DF8A7D63AD507FD0DB8FBA2772F03F3BF3A912
9F9F2641E4A3F015A825C10C0BDC530E5F060A4841C5B70D83830CC770C811E7
88A90006528DFD6450D5ED261C091ED8080D0C5C97B4E85A3483E31692F3524B
3EE13756C64AA6217A5338A4D0108FBA187BC11EDBC1E8533F566C987BC8FF76
76FF09FE88AE38C761C70F4B0D28D6E19048208AE757408E201F91A71B6316F9
CEC022179F66E8793D7C271F45D9BA51C92C5696259EA1C636A7E9F8B8367C63
982285D584A1EFF78ECA5BDA2AFE4219CC9FC85CCED5D4B207B47D96B2DF2567
5D195A0D618253D0E5CE2FA8C5368908EB47CACEC3FC7F17DD0B5136B9A20100
53933589A7EB88C01EE1F990CF30B3BDFC81F0516780C060D483496931D6B100
EFFEAFF5C219B88448E6BA99A99FA4D4C5EAA78EF3548AECDCAA855996CE0E10
18F60B0F8391495EE6B6DF826CDF8DAA22E6219A90468F871D506EA16B9877DC
2C0223978745585641DE610D550A60929177D71E11BBF70EA498309BB1B417AA
40AB117D3EC42424E9A60882D3F07AB840B52326CA647152FA3AF149F2D18635
30803D2890F258A5FE8589F72DE38C500BB1262E18B724818DA822749B95678B
780E7FC1276FD79831C81EEBA716F9C57635A1D6CE05D41D4C007ECE54F4E69C
B55D42A4758BA4B45043466EFE761ECB732F9DEA94ACBC516425BDF4B40C3953
65A7F501816A3D8CD676B49526E579FDD042C52A491AED75F7317D99C56F1D3B
ADEBF6F3D31A19E00B2131D0ABEBD5E66DAE43BA5AD388B029F137E4849D7414
53FED49EF39A4E94C48C098F107360BB26EDA18FB3DF6A1F47565627F650F441
98D590891F1C57A73D547E6823B47411DEC9FDBF84A10C454878E378966F28B3
FE8F39E24F6FB9CDFD20297C485B551CE7F2E72B884FC4335A27B3E92081D0CC
A975E33E7A0289CF2D9D37A4FB63903AB4A3DA33F7F8EA622877D3F2C629E05B
BF52144F885E2A84CBA97973A83897EB847D4866B180A71D04002CDFC2FE2D2A
23C6D20B5C05426F1200FA86889BF34A686F0CCAD753C5E1756AF52BC8BE4826
673FA7544B6C3D4ADD50EF8575628D82BA8A712777F87A5772BCF7D30EBD31C0
DB4F7B805522A0558F0E4ABEB009B823AFCF9936F83629FE5098AC0070C3D5FB
3962B0B90E779CFCB771A8BFB76A1500D9113D5BFD4F391B8ABD0060F8F08018
DCFC8A94D98DAE2A61C7A78A586264EEE55022CCD5F4E6580D39E6968A1C2713
1EB2679D614693A630F28218D479396B7D84CDF297483471B4B5A94756B1E70E
2A7412EEB07C2CFC62F9EA5AADCB2938E21C30CF0AD2EC78E407492882B30034
8B1B72D0A2B6568A810F08FF77269B2D3862DF8BE1B3BA6FCE3BAC197FFD4B8D
364FE83258BA34ECCF21FD76DE97A8A18B8C7028C038A4234950598B69338925
9852866F0CFD39BBA4FAC966FB86862F011765239CD2BB3E81B7BE2C76FDD905
286AD41F05402294E8D9055DBA014E4F4D82DB525DAE2ED35CAFE5B71A268595
656E326BE34626370B4D014AC4E94B95E6C50C46A447C42E95A55E225F5E8F85
359E2308E870C9B5E932CFF0C819BFF9B929B4DAD09E8480B08E4FBF0985A2BF
5708541F39135AA1334C442859D946B07281EF812193C4EF637641CC480EE7C2
AAF2ABB466A30F62425009E3264D560F132AA70F5212CFF57A9D537B69574D1E
8A20BE6D8452C4A29114CCF99AE53F16B9572CD5A5ECAA36FBB378DE6EAC68C1
CDE8A7BB65335A5C02077FB9A6E19960FC91A02985553855D5C93F1F845FBE75
D11A2ABF19AEB61A4A2997182DB0E30D5416251BB3179A3355A859D8E9694223
7EE27C0994DB3758111D2E86266460D9141BB86662C61C29FF182AA696A4B121
00134C0B16E41E60F81055DD33B046F9D0B3CF53E2155D01369717FC6AE44B3A
8CB2EBF87D70F48E5DBB6B917B395EC0222EBAA96FB43516B7B9FF83ACF9FDB1
405DD92FB459CD9BC9CBD325D04F47BCCDD6EC4938D4CE0C2D4E80FFDF92D0F2
E25280B4E6855C0BE51BE7EFDA8A11DCE9AAD43F86E277F99D5A2911F3867978
A2BA4B6FEFFBA17BC570DEB719BEDDD1BF3A803D6A55FEA6119B9774045B3C7E
1DEF925A5DE00A37501FD0023B27D3E6AAE446666B604BBE6ADCB4C83B49F585
43918FAAA3E1B65A628F33B725A7A720ED68C2735AD8E8D1F6D204B7A3C0E034
7D0ACC4727F6CC6A4D9EC7653CDC5B90A22C4F43F88041E6D19DFA32B697E636
E2B551EEC39EC3E25A0A932593251A6B505AFCE1F63113235519CCC5C1201FAF
FA3B6AFFDDD9C906B8AC41E50ACE5B83D68DBD91315E6EF411D0FD8A8AF2C343
4D54DD66D5B3769EC714BFB263776A4109A42FC78A5812081A48C790BEB35756
F5DCCB15AD75D38D4C1C7E651AE25F4124E6D8C73FD1BD32799EAFEEE783D798
3CE8758DEFD3F2931D4FDB841A8B89093BE3F5EC969C5D4383E193DF613099B8
3ECDF485A0A293207B0B45DB71A429E5DB6A2A80DEE9DD4A521CD3DE376F429D
9045C1AFB8D8E98BE6D4F17BE69931C5A2E09176DC1BF949C57926ED5709206D
B35F65A5E15EFE8AD3D095FEE3C338DD1031BDD9C79DCE340E374C846AEE6B8F
1E2323D51A68151A753E1840F927A32A0BC026863ABECA52BE31EF59487F59A6
FC53D1E1AB8FCC75F5D66C2434AE412BE85651089AC7C8127D2147198F515425
9EBD15B006B75E05474DA502E58BAEC055197E8298AAFC5C29BE1B420CDC5197
B3B0B9F170C41A6F5B057E35A7E1F947B15B575090D3C86DE4DD501B6A75468D
252EABEF52A347F5C18BF57EBD37D36907C5119E006AAE838126A78FA52127E9
FE6615B2396C3D2E59496F58309096FB4B3ADC3155CE586CBA573D280CC4EA10
4415FAD06C9B34407DB046D93CFA74D65BD12FDB2F4CE5AE03DF452FEE66D3B3
592B5A2201FF506CCD565396850F3EF9AFB78B5408E0B2B82231FF5CDFB982EF
0B5F5B806EAC5A1DDF7648D9B80B90F67C1F66563D639A646ABA64D40CE92572
3D7F5B3B6F025145E84D5E3A456A2CBFACF701590D8132CC9AB8740C59F93398
7631F004E459AE969591995910102691599001020B9BC0F30515F0CFA57F8880
A82E1713F54F633067DF80ADDF7B26006F22762573DE6A937AFCF4137A8FC198
B2BBBE1ADFE5A19C5244AF1694B81AEC0518B0C004E4803CDC6EB86539E7863A
0CE62E8272771B567F6D7BE3C6E422E4477EB023A5D50054E456681D7963F7AA
CA5811DBA63A80CE69AC8530ECAE2E8E6064533F7D51532A58F57901E1CB77EA
069750DE094186E79B77AB3C277EB6DF81D137F79C1C50026C1F697134140FC3
AD5544C0B1AFBFAA7100F5455B2B17F2CD7847C773C926865879E33A5346BEE9
3B81497ECD98187F40AADD311F7E1D8BFB9867428A7B51B2A3F96BECD16A2864
0F27C79BD847994D82113B13BD6377F7FF90D3CB13AFAC4F7D42627D67B0D20B
BB64321589F64638E26E04737827A931DA27EE823636052782616EF8208814A7
EDBEFA2CB0E6B65E3753D2271E4A91ABECB20F1552E2CD4A7986AEB2510CB824
B006F1D93B739F76FDC6356115B2DC3B6E5CAC92342BC7E5A5889CE941E0D298
C028DD5CD81327D75ABBC71C8386EE8E314F7782618C3AF4A40981A183E4465D
9025F8FD4B5B04BD6E
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSLTT10
%!PS-AdobeFont-1.1: CMSLTT10 1.0
%%CreationDate: 1991 Aug 20 16:41:43
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSLTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -9.46 def
/isFixedPitch true def
end readonly def
/FontName /CMSLTT10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 100 /d put
dup 101 /e put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 116 /t put
dup 117 /u put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-20 -233 617 696}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSS10
%!PS-AdobeFont-1.1: CMSS10 1.0
%%CreationDate: 1991 Aug 20 17:33:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSS10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
readonly def
/FontBBox{-61 -250 999 759}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 31 /Oslash put
dup 33 /exclam put
dup 36 /dollar put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 55 /seven put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 95 /dotaccent put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
TeXDict begin 39158280 55380996 1000 600 600 (gsl.dvi)
@start /Fa 255[71{}1 90.9091 /CMSY10 rf /Fb 205[33 1[33
48[{}2 58.1154 /CMR7 rf /Fc 194[34 35[39 25[{}2 58.1154
/CMMI7 rf /Fd 142[83 22[46 90[{}2 83.022 /CMEX10 rf /Fe
139[33 6[80 1[47 6[47 24[77 5[67 69[{}6 90.9091 /CMMI10
rf /Ff 130[48 48 48 3[48 1[48 48 48 48 1[48 48 48 1[48
3[48 48 48 48 3[48 2[48 31[48 1[48 1[48 2[48 48 48 48
1[48 48 48 48 48 48 2[48 42[{}32 90.9091 /CMTT10 rf /Fg
133[40 48 3[51 35 36 36 2[45 1[76 1[48 1[25 51 2[40 51
40 1[45 18[68 83 30[25 1[25 44[{}19 90.9091 /CMSL10 rf
/Fh 133[52 52 52 2[52 52 1[52 2[52 52 52 7[52 52 49[52
52 52 48[{}14 99.6264 /CMSLTT10 rf /Fi 214[35 35 40[{}2
90.9091 /CMSS10 rf /Fj 133[52 52 52 52 52 52 52 52 52
1[52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 1[52
1[52 1[52 52 52 1[52 1[52 1[52 1[52 52 4[52 52 52 2[52
52 1[52 52 52 3[52 7[52 52 52 52 52 52 3[52 44[{}51 99.6264
/CMTT10 rf /Fk 133[40 48 48 66 48 51 35 36 36 48 51 45
51 76 25 48 28 25 51 45 28 40 51 40 51 45 1[25 1[25 1[25
56 68 68 93 68 68 66 51 67 71 62 71 68 83 57 71 47 33
68 71 59 62 69 66 64 68 3[71 1[25 25 45 1[45 1[45 45
45 45 45 45 45 25 30 25 71 45 35 35 25 71 1[45 2[25 1[71
16[76 51 51 53 11[{}83 90.9091 /CMR10 rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%BeginPaperSize: a4
/setpagedevice where
{ pop << /PageSize [595 842] >> setpagedevice }
{ /a4 where { pop a4 } if }
ifelse
%%EndPaperSize
 end
%%EndSetup
%%Page: 1 1
TeXDict begin 1 0 bop 275 299 a Fk(\037gsl_sf)30 b(-*-)h(texinfo)g(-*-)
2960 473 y([Loadable)g(F)-8 b(unction])-3599 b Fj(gsl_sf)47
b Fi(\(\))390 582 y Fk(Octa)m(v)m(e)30 b(bindings)d(to)h(the)g(GNU)h
(Scien)m(ti\014c)f(Library)-8 b(.)40 b(All)28 b(GSL)g(functions)f(can)h
(b)s(e)f(called)i(with)390 692 y(b)m(y)h(the)h(GSL)f(names)g(within)g
(o)s(cta)m(v)m(e.)275 866 y(\037clausen)g(-*-)h(texinfo)g(-*-)2960
1039 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(clausen)47 b Fi(\()p Fh(x)12 b Fi(\))2960 1149
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(clausen)47 b Fi(\()6
b Fg(.)23 b(.)f(.)11 b Fi(\))390 1258 y Fk(The)30 b(Clausen)g(function)
g(is)g(de\014ned)f(b)m(y)i(the)f(follo)m(wing)i(in)m(tegral,)390
1389 y(Cl_2\(x\))g(=)e(-)g(in)m(t_0)p Ff(^)p Fk(x)i(dt)e(log\(2)i
(sin\(t/2\)\))390 1520 y(It)e(is)h(related)g(to)g(the)g(dilogarithm)g
(b)m(y)f(Cl_2\(theta\))j(=)d(Im)g(Li_2\(exp\(i)i(theta\)\).)390
1651 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
1782 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1803 42 84 v 390 1892 a Fk(for)30 b(do)s(cumen)m(tation.)275
2066 y(\037da)m(wson)f(-*-)j(texinfo)f(-*-)2960 2239
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(dawson)47 b Fi(\()p Fh(x)12 b Fi(\))2960 2349 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(dawson)47 b Fi(\()6 b Fg(.)22 b(.)h(.)11
b Fi(\))390 2459 y Fk(The)29 b(Da)m(wson)i(in)m(tegral)h(is)e
(de\014ned)f(b)m(y)h(exp\(-x)p Ff(^)p Fk(2\))h(in)m(t_0)p
Ff(^)p Fk(x)g(dt)e(exp\(t)p Ff(^)p Fk(2\).)42 b(A)30
b(table)h(of)f(Da)m(wson)390 2568 y(in)m(tegral)i(can)f(b)s(e)e(found)h
(in)g(Abramo)m(witz)h(&)f(Stegun,)g(T)-8 b(able)31 b(7.5.)390
2699 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2830 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2850 V 390 2940 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3113 y(\037deb)m(y)m(e_1)h(-*-)g(texinfo)g(-*-)2960
3287 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(debye_1)47 b Fi(\()p Fh(x)12 b Fi(\))2960 3397
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(debye_1)47 b Fi(\()6
b Fg(.)23 b(.)f(.)11 b Fi(\))390 3506 y Fk(The)30 b(Deb)m(y)m(e)i
(functions)e(are)h(de\014ned)e(b)m(y)h(the)h(in)m(tegral)390
3637 y(D_n\(x\))g(=)f(n/x)p Ff(^)p Fk(n)g(in)m(t_0)p
Ff(^)p Fk(x)h(dt)f(\(t)p Ff(^)p Fk(n/\(e)p Ff(^)p Fk(t)i(-)e(1\)\).)390
3768 y(F)-8 b(or)31 b(further)e(information)i(see)g(Abramo)m(witz)g(&)f
(Stegun,)h(Section)g(27.1.)390 3899 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 4030 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4050
V 390 4140 a Fk(for)30 b(do)s(cumen)m(tation.)275 4314
y(\037deb)m(y)m(e_2)h(-*-)g(texinfo)g(-*-)2960 4487 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(debye_2)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 4597 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(debye_2)47
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 4706 y Fk(The)30
b(Deb)m(y)m(e)i(functions)e(are)h(de\014ned)e(b)m(y)h(the)h(in)m
(tegral)390 4837 y(D_n\(x\))g(=)f(n/x)p Ff(^)p Fk(n)g(in)m(t_0)p
Ff(^)p Fk(x)h(dt)f(\(t)p Ff(^)p Fk(n/\(e)p Ff(^)p Fk(t)i(-)e(1\)\).)390
4968 y(F)-8 b(or)31 b(further)e(information)i(see)g(Abramo)m(witz)g(&)f
(Stegun,)h(Section)g(27.1.)390 5099 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251
V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end
%%Page: 2 2
TeXDict begin 2 1 bop 275 299 a Fk(\037deb)m(y)m(e_3)31
b(-*-)g(texinfo)g(-*-)2960 484 y([Loadable)g(F)-8 b(unction])-3599
b Fh(y)64 b Fj(=)53 b(debye_3)47 b Fi(\()p Fh(x)12 b
Fi(\))2960 594 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(debye_3)47
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 703 y Fk(The)30
b(Deb)m(y)m(e)i(functions)e(are)h(de\014ned)e(b)m(y)h(the)h(in)m
(tegral)390 838 y(D_n\(x\))g(=)f(n/x)p Ff(^)p Fk(n)g(in)m(t_0)p
Ff(^)p Fk(x)h(dt)f(\(t)p Ff(^)p Fk(n/\(e)p Ff(^)p Fk(t)i(-)e(1\)\).)390
973 y(F)-8 b(or)31 b(further)e(information)i(see)g(Abramo)m(witz)g(&)f
(Stegun,)h(Section)g(27.1.)390 1108 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 1243 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1264
42 84 v 390 1353 a Fk(for)30 b(do)s(cumen)m(tation.)275
1538 y(\037deb)m(y)m(e_4)h(-*-)g(texinfo)g(-*-)2960 1724
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(debye_4)47 b Fi(\()p Fh(x)12 b Fi(\))2960 1833 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(debye_4)47 b Fi(\()6 b Fg(.)23 b(.)f(.)11
b Fi(\))390 1943 y Fk(The)30 b(Deb)m(y)m(e)i(functions)e(are)h
(de\014ned)e(b)m(y)h(the)h(in)m(tegral)390 2078 y(D_n\(x\))g(=)f(n/x)p
Ff(^)p Fk(n)g(in)m(t_0)p Ff(^)p Fk(x)h(dt)f(\(t)p Ff(^)p
Fk(n/\(e)p Ff(^)p Fk(t)i(-)e(1\)\).)390 2213 y(F)-8 b(or)31
b(further)e(information)i(see)g(Abramo)m(witz)g(&)f(Stegun,)h(Section)g
(27.1.)390 2348 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f
(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b
Fg(y)p Fk(.)390 2483 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2503 V
390 2592 a Fk(for)30 b(do)s(cumen)m(tation.)275 2778
y(\037erf_gsl)g(-*-)i(texinfo)f(-*-)2960 2963 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(erf_gsl)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 3072 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(erf_gsl)47
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3182 y Fk(These)28
b(routines)h(compute)g(the)g(error)f(function)g(erf\(x\))h(=)g
(\(2/sqrt\(pi\)\))h(in)m(t_0)p Ff(^)p Fk(x)g(dt)e(exp\(-t)p
Ff(^)p Fk(2\).)390 3317 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 3452 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3472 V
390 3562 a Fk(for)30 b(do)s(cumen)m(tation.)275 3747
y(\037erfc_gsl)h(-*-)g(texinfo)g(-*-)2960 3932 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(erfc_gsl)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 4042 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(erfc_gsl)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 4151 y Fk(These)43 b(routines)g(compute)g(the)h(complemen)m
(tary)g(error)f(function)f(erfc\(x\))i(=)f(1)g(-)h(erf\(x\))f(=)390
4261 y(\(2/sqrt\(pi\)\))32 b(in)m(t_x)p Ff(^)p Fk(inft)m(y)f(exp\(-t)p
Ff(^)p Fk(2\).)390 4396 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 4531 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4551 V
390 4641 a Fk(for)30 b(do)s(cumen)m(tation.)275 4826
y(\037log_erfc)h(-*-)h(texinfo)f(-*-)2960 5011 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(log_erfc)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 5121 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(log_erfc)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 5230 y Fk(These)70 b(routines)h(compute)g(the)g(logarithm)g
(of)g(the)g(complemen)m(tary)h(error)e(function)390 5340
y(log\(erfc\(x\)\).)p eop end
%%Page: 3 3
TeXDict begin 3 2 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 437 y(This)19 b(function)h(is)h(from)f(the)
g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 457 42
84 v 390 546 a Fk(for)30 b(do)s(cumen)m(tation.)275 737
y(\037erf_Z)f(-*-)j(texinfo)f(-*-)2960 928 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(erf_Z)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 1038 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(erf_Z)47
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 1147 y Fk(These)42
b(routines)g(compute)g(the)g(Gaussian)h(probabilit)m(y)f(function)g
(Z\(x\))g(=)g(\(1/\(2pi\)\))i(exp\(-)390 1257 y(x)p Ff(^)p
Fk(2/2\).)390 1395 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f
(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b
Fg(y)p Fk(.)390 1533 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1553 V
390 1642 a Fk(for)30 b(do)s(cumen)m(tation.)275 1833
y(\037erf_Q)f(-*-)j(texinfo)f(-*-)2960 2024 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(erf_Q)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 2134 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(erf_Q)47
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2243 y Fk(These)33
b(routines)h(compute)g(the)f(upp)s(er)f(tail)j(of)f(the)f(Gaussian)h
(probabilit)m(y)g(function)f(Q\(x\))h(=)390 2353 y(\(1/\(2pi\)\))f(in)m
(t_x)p Ff(^)p Fk(inft)m(y)e(dt)f(exp\(-t)p Ff(^)p Fk(2/2\).)390
2491 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2628 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2649 V 390 2738 a Fk(for)30 b(do)s(cumen)m(tation.)
275 2929 y(\037hazard)f(-*-)j(texinfo)f(-*-)2960 3120
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(hazard)47 b Fi(\()p Fh(x)12 b Fi(\))2960 3230 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(hazard)47 b Fi(\()6 b Fg(.)22 b(.)h(.)11
b Fi(\))390 3339 y Fk(The)43 b(hazard)g(function)g(for)g(the)h(normal)f
(distrbution,)j(also)e(kno)m(wn)f(as)h(the)g(in)m(v)m(erse)g(Mill's)390
3449 y(ratio,)32 b(is)e(de\014ned)g(as)g(h\(x\))h(=)f(Z\(x\)/Q\(x\))h
(=)g(sqrt)p Ff({)p Fk(2/pi)f(exp\(-x)p Ff(^)p Fk(2)h(/)g(2\))g(/)g
(erfc\(x/sqrt)g(2\))p Ff(})p Fk(.)42 b(It)390 3558 y(decreases)25
b(rapidly)f(as)g(x)g(approac)m(hes)h(-inft)m(y)f(and)g(asymptotes)h(to)
g(h\(x\))f(sim)g(x)g(as)g(x)g(approac)m(hes)390 3668
y(+inft)m(y)-8 b(.)390 3806 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 3944 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3964
V 390 4053 a Fk(for)30 b(do)s(cumen)m(tation.)275 4244
y(\037expm1)g(-*-)h(texinfo)g(-*-)2960 4435 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(expm1)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 4545 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(expm1)47
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4654 y Fk(These)26
b(routines)h(compute)g(the)g(quan)m(tit)m(y)h(exp\(x\)-1)g(using)e(an)g
(algorithm)i(that)f(is)g(accurate)h(for)390 4764 y(small)j(x.)390
4902 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 5039 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 5060 V 390 5149 a Fk(for)30 b(do)s(cumen)m(tation.)
275 5340 y(\037exprel)g(-*-)h(texinfo)g(-*-)p eop end
%%Page: 4 4
TeXDict begin 4 3 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(exprel)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(exprel)47
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 518 y Fk(These)24
b(routines)g(compute)g(the)g(quan)m(tit)m(y)i(\(exp\(x\)-1\)/x)g(using)
e(an)g(algorithm)h(that)f(is)g(accurate)390 628 y(for)30
b(small)g(x.)41 b(F)-8 b(or)31 b(small)f(x)g(the)g(algorithm)h(is)f
(based)g(on)g(the)g(expansion)g(\(exp\(x\)-1\)/x)i(=)e(1)g(+)390
737 y(x/2)h(+)f(x)p Ff(^)p Fk(2/\(2*3\))j(+)d(x)p Ff(^)p
Fk(3/\(2*3*4\))k(+)c(dots.)390 871 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 1005 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1025
42 84 v 390 1115 a Fk(for)30 b(do)s(cumen)m(tation.)275
1297 y(\037exprel_2)g(-*-)i(texinfo)f(-*-)2960 1480 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(exprel_2)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 1590 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(exprel_2)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 1699 y Fk(These)38 b(routines)g(compute)g(the)h(quan)m(tit)
m(y)g(2\(exp\(x\)-1-x\)/x)p Ff(^)p Fk(2)i(using)d(an)g(algorithm)h
(that)g(is)390 1809 y(accurate)34 b(for)f(small)g(x.)47
b(F)-8 b(or)34 b(small)f(x)g(the)g(algorithm)g(is)g(based)f(on)h(the)g
(expansion)f(2\(exp\(x\)-)390 1918 y(1-x\)/x)p Ff(^)p
Fk(2)g(=)e(1)h(+)f(x/3)h(+)f(x)p Ff(^)p Fk(2/\(3*4\))j(+)d(x)p
Ff(^)p Fk(3/\(3*4*5\))k(+)c(dots.)390 2052 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2186 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2206 V 390 2296 a Fk(for)30 b(do)s(cumen)m(tation.)275
2478 y(\037expin)m(t_E1)h(-*-)g(texinfo)g(-*-)2960 2661
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(expint_E1)48 b Fi(\()p Fh(x)12 b Fi(\))2960 2771 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(expint_E1)48 b Fi(\()6
b Fg(.)22 b(.)g(.)12 b Fi(\))390 2880 y Fk(These)30 b(routines)g
(compute)h(the)g(exp)s(onen)m(tial)g(in)m(tegral)h(E_1\(x\),)390
3014 y(E_1\(x\))g(:=)e(Re)g(in)m(t_1)p Ff(^)p Fk(inft)m(y)i(dt)e
(exp\(-xt\)/t.)390 3148 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 3282 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3302 V
390 3392 a Fk(for)30 b(do)s(cumen)m(tation.)275 3574
y(\037expin)m(t_E2)h(-*-)g(texinfo)g(-*-)2960 3757 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(expint_E2)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 3867 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(expint_E2)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 3976 y Fk(These)30 b(routines)g(compute)h(the)g
(second-order)f(exp)s(onen)m(tial)h(in)m(tegral)h(E_2\(x\),)390
4110 y(E_2\(x\))g(:=)e(Re)g(in)m(t_1)p Ff(^)p Fk(inft)m(y)i(dt)e
(exp\(-xt\)/t)p Ff(^)p Fk(2.)390 4244 y Fg(err)36 b Fk(con)m(tains)c
(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 4378 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4398
V 390 4488 a Fk(for)30 b(do)s(cumen)m(tation.)275 4670
y(\037expin)m(t_Ei)g(-*-)i(texinfo)f(-*-)2960 4853 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(expint_Ei)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 4963 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(expint_Ei)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 5072 y Fk(These)30 b(routines)g(compute)h(the)g(exp)s(onen)
m(tial)g(in)m(tegral)h(E_i\(x\),)390 5206 y(Ei\(x\))f(:=)f(-)h(PV\(in)m
(t_)p Ff({)p Fk(-x)p Ff(}^)p Fk(inft)m(y)g(dt)f(exp\(-t\)/t\))390
5340 y(where)g(PV)g(denotes)h(the)g(principal)f(v)-5
b(alue)30 b(of)h(the)g(in)m(tegral.)p eop end
%%Page: 5 5
TeXDict begin 5 4 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 446 y(This)19 b(function)h(is)h(from)f(the)
g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 466 42
84 v 390 556 a Fk(for)30 b(do)s(cumen)m(tation.)275 765
y(\037Shi)f(-*-)i(texinfo)g(-*-)2960 975 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(Shi)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 1085 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(Shi)46
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1194 y Fk(These)30
b(routines)g(compute)h(the)g(in)m(tegral)h(Shi\(x\))e(=)g(in)m(t_0)p
Ff(^)p Fk(x)h(dt)f(sinh\(t\)/t.)390 1342 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1489 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1509 V 390 1598 a Fk(for)30 b(do)s(cumen)m(tation.)275
1808 y(\037Chi)f(-*-)i(texinfo)g(-*-)2960 2018 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(Chi)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 2127 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(Chi)46
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 2237 y Fk(These)30
b(routines)g(compute)h(the)g(in)m(tegral)390 2384 y(Chi\(x\))f(:=)h
(Re[)g(gamma_E)g(+)f(log\(x\))i(+)e(in)m(t_0)p Ff(^)p
Fk(x)h(dt)f(\(cosh[t]-1\)/t])k(,)390 2531 y(where)c(gamma_E)h(is)g(the)
f(Euler)g(constan)m(t.)390 2679 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 2826 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2846
V 390 2935 a Fk(for)30 b(do)s(cumen)m(tation.)275 3145
y(\037expin)m(t_3)h(-*-)g(texinfo)g(-*-)2960 3355 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(expint_3)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 3464 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(expint_3)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 3574 y Fk(These)29 b(routines)h(compute)f(the)h(exp)s(onen)
m(tial)g(in)m(tegral)h(Ei_3\(x\))g(=)e(in)m(t_0)p Ff(^)p
Fk(x)i(dt)e(exp\(-t)p Ff(^)p Fk(3\))i(for)e(x)390 3684
y Ff(>)p Fk(=)h(0.)390 3831 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 3978 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3998
V 390 4088 a Fk(for)30 b(do)s(cumen)m(tation.)275 4297
y(\037Si)f(-*-)j(texinfo)f(-*-)2960 4507 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(Si)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 4617 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(Si)46
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4726 y Fk(These)30
b(routines)g(compute)h(the)g(Sine)f(in)m(tegral)i(Si\(x\))e(=)g(in)m
(t_0)p Ff(^)p Fk(x)i(dt)e(sin\(t\)/t.)390 4873 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5021 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 5041 V 390 5130 a Fk(for)30 b(do)s(cumen)m(tation.)275
5340 y(\037Ci)f(-*-)j(texinfo)f(-*-)p eop end
%%Page: 6 6
TeXDict begin 6 5 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(Ci)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(Ci)46
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 518 y Fk(These)27
b(routines)h(compute)g(the)g(Cosine)f(in)m(tegral)j(Ci\(x\))e(=)f(-in)m
(t_x)p Ff(^)p Fk(inft)m(y)i(dt)e(cos\(t\)/t)j(for)e(x)f
Ff(>)g Fk(0.)390 667 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)
f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 815 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 835 42
84 v 390 925 a Fk(for)30 b(do)s(cumen)m(tation.)275 1137
y(\037atanin)m(t)h(-*-)g(texinfo)g(-*-)2960 1350 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(atanint)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 1459 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(atanint)47
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 1569 y Fk(These)27
b(routines)g(compute)g(the)g(Arctangen)m(t)i(in)m(tegral)g(A)m(tanIn)m
(t\(x\))g(=)d(in)m(t_0)p Ff(^)p Fk(x)i(dt)f(arctan\(t\)/t.)390
1717 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 1866 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 1886 V 390 1975 a Fk(for)30 b(do)s(cumen)m(tation.)
275 2188 y(\037fermi_dirac_mhalf)g(-*-)h(texinfo)g(-*-)2960
2400 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(fermi_dirac_mhalf)d Fi(\()p Fh(x)12 b Fi(\))2960
2510 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(fermi_dirac_mhalf)d
Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 2619 y Fk(These)30
b(routines)g(compute)h(the)g(complete)g(F)-8 b(ermi-Dirac)33
b(in)m(tegral)f(F_)p Ff({)p Fk(-1/2)p Ff(})p Fk(\(x\).)390
2768 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
2917 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2937 V 390 3026 a Fk(for)30 b(do)s(cumen)m(tation.)275
3239 y(\037fermi_dirac_half)g(-*-)h(texinfo)g(-*-)2960
3451 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(fermi_dirac_half)d Fi(\()p Fh(x)12 b Fi(\))2960
3561 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(fermi_dirac_half)d
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 3670 y Fk(These)30
b(routines)g(compute)h(the)g(complete)g(F)-8 b(ermi-Dirac)33
b(in)m(tegral)f(F_)p Ff({)p Fk(1/2)p Ff(})p Fk(\(x\).)390
3819 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
3967 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 3987 V 390 4077 a Fk(for)30 b(do)s(cumen)m(tation.)275
4289 y(\037fermi_dirac_3half)h(-*-)g(texinfo)g(-*-)2960
4502 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(fermi_dirac_3half)d Fi(\()p Fh(x)12 b Fi(\))2960
4611 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(fermi_dirac_3half)d
Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 4721 y Fk(These)30
b(routines)g(compute)h(the)g(complete)g(F)-8 b(ermi-Dirac)33
b(in)m(tegral)f(F_)p Ff({)p Fk(3/2)p Ff(})p Fk(\(x\).)390
4869 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
5018 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 5038 V 390 5128 a Fk(for)30 b(do)s(cumen)m(tation.)275
5340 y(\037gamma_gsl)h(-*-)h(texinfo)f(-*-)p eop end
%%Page: 7 7
TeXDict begin 7 6 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(gamma_gsl)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(gamma_gsl)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 518 y Fk(These)36 b(routines)h(compute)g(the)g(Gamma)g
(function)f(Gamma\(x\),)k(sub)5 b(ject)37 b(to)g(x)f(not)h(b)s(eing)g
(a)390 628 y(negativ)m(e)44 b(in)m(teger.)77 b(The)41
b(function)h(is)f(computed)h(using)g(the)g(real)g(Lanczos)h(metho)s(d.)
74 b(The)390 737 y(maxim)m(um)34 b(v)-5 b(alue)34 b(of)h(x)f(suc)m(h)f
(that)i(Gamma\(x\))g(is)f(not)h(considered)f(an)f(o)m(v)m(er\015o)m(w)j
(is)e(giv)m(en)h(b)m(y)390 847 y(the)c(macro)g(GSL_SF_GAMMA_XMAX)h(and)
e(is)h(171.0.)390 986 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 1125 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1145 42
84 v 390 1234 a Fk(for)30 b(do)s(cumen)m(tation.)275
1427 y(\037lngamma_gsl)h(-*-)g(texinfo)g(-*-)2960 1620
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(lngamma_gsl)c Fi(\()p Fh(x)12 b Fi(\))2960 1730 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(lngamma_gsl)c Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 1839 y Fk(These)28 b(routines)g(compute)h(the)f(logarithm)i
(of)e(the)h(Gamma)g(function,)g(log\(Gamma\(x\)\),)j(sub-)390
1949 y(ject)39 b(to)h(x)e(not)h(a)g(b)s(eing)f(negativ)m(e)j(in)m
(teger.)67 b(F)-8 b(or)39 b(x)p Ff(<)p Fk(0)g(the)g(real)g(part)f(of)h
(log\(Gamma\(x\)\))j(is)390 2059 y(returned,)32 b(whic)m(h)h(is)g
(equiv)-5 b(alen)m(t)34 b(to)g(log\()p Ff(|)p Fk(Gamma\(x\))p
Ff(|)p Fk(\).)50 b(The)33 b(function)f(is)h(computed)f(using)390
2168 y(the)f(real)g(Lanczos)g(metho)s(d.)390 2307 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2446 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2466 V 390 2555 a Fk(for)30 b(do)s(cumen)m(tation.)275
2748 y(\037gammastar)h(-*-)g(texinfo)g(-*-)2960 2941
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(gammastar)48 b Fi(\()p Fh(x)12 b Fi(\))2960 3051 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(gammastar)48 b Fi(\()6
b Fg(.)22 b(.)g(.)12 b Fi(\))390 3161 y Fk(These)28 b(routines)h
(compute)g(the)g(regulated)g(Gamma)g(F)-8 b(unction)30
b(Gamma)p Ff(^)p Fk(*\(x\))g(for)e(x)h Ff(>)f Fk(0.)40
b(The)390 3270 y(regulated)31 b(gamma)g(function)f(is)h(giv)m(en)g(b)m
(y)-8 b(,)390 3409 y(Gamma)p Ff(^)p Fk(*\(x\))39 b(=)e
(Gamma\(x\)/\(sqrt)p Ff({)p Fk(2pi)p Ff(})i Fk(x)p Ff(^{)p
Fk(\(x-1/2\))p Ff(})g Fk(exp\(-x\)\))g(=)e(\(1)i(+)e(\(1/12x\))j(+)d
(...\))390 3519 y(for)30 b(x)g(to)i(inft)m(y)390 3658
y(and)e(is)g(a)h(useful)f(suggestion)h(of)f(T)-8 b(emme.)390
3796 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3935 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3955 V 390 4045 a Fk(for)30 b(do)s(cumen)m(tation.)
275 4238 y(\037gammain)m(v_gsl)h(-*-)h(texinfo)f(-*-)2960
4431 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(gammainv_gsl)c Fi(\()p Fh(x)12 b Fi(\))2960
4540 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(gammainv_gsl)c
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4650 y Fk(These)38
b(routines)h(compute)g(the)g(recipro)s(cal)g(of)g(the)g(gamma)g
(function,)i(1/Gamma\(x\))f(using)390 4760 y(the)31 b(real)g(Lanczos)g
(metho)s(d.)390 4899 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)
f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 5037 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5058 V
390 5147 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340
y(\037lam)m(b)s(ert_W0)h(-*-)g(texinfo)g(-*-)p eop end
%%Page: 8 8
TeXDict begin 8 7 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(lambert_W0)48
b Fi(\()p Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(lambert_W0)48 b Fi(\()6 b Fg(.)23 b(.)f(.)11
b Fi(\))390 518 y Fk(These)30 b(compute)h(the)f(principal)g(branc)m(h)g
(of)h(the)f(Lam)m(b)s(ert)g(W)h(function,)g(W_0\(x\).)390
657 y(Lam)m(b)s(ert's)46 b(W)h(functions,)i(W\(x\),)j(are)46
b(de\014ned)f(to)i(b)s(e)f(solutions)g(of)h(the)f(equation)h(W\(x\))390
767 y(exp\(W\(x\)\))f(=)f(x.)84 b(This)44 b(function)g(has)h(m)m
(ultiple)g(branc)m(hes)g(for)f(x)h Ff(<)f Fk(0;)53 b(ho)m(w)m(ev)m(er,)
d(it)45 b(has)390 876 y(only)34 b(t)m(w)m(o)i(real-v)-5
b(alued)35 b(branc)m(hes.)51 b(W)-8 b(e)35 b(de\014ne)f(W_0\(x\))i(to)e
(b)s(e)g(the)g(principal)g(branc)m(h,)g(where)390 986
y(W)29 b Ff(>)g Fk(-1)h(for)f(x)g Ff(<)f Fk(0,)i(and)f(W_)p
Ff({)p Fk(-1)p Ff(})p Fk(\(x\))h(to)g(b)s(e)e(the)i(other)f(real)h
(branc)m(h,)e(where)h(W)g Ff(<)g Fk(-1)h(for)f(x)g Ff(<)f
Fk(0.)390 1125 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)
g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 1263 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 1284 42 84 v 390 1373 a Fk(for)30
b(do)s(cumen)m(tation.)275 1566 y(\037lam)m(b)s(ert_Wm1)h(-*-)g
(texinfo)g(-*-)2960 1759 y([Loadable)g(F)-8 b(unction])-3599
b Fh(y)64 b Fj(=)53 b(lambert_Wm1)c Fi(\()p Fh(x)12 b
Fi(\))2960 1869 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(lambert_Wm1)c
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1978 y Fk(These)35
b(compute)g(the)h(secondary)f(real-v)-5 b(alued)36 b(branc)m(h)f(of)g
(the)g(Lam)m(b)s(ert)g(W)h(function,)g(W_)p Ff({)p Fk(-)390
2088 y(1)p Ff(})p Fk(\(x\).)390 2227 y(Lam)m(b)s(ert's)46
b(W)h(functions,)i(W\(x\),)j(are)46 b(de\014ned)f(to)i(b)s(e)f
(solutions)g(of)h(the)f(equation)h(W\(x\))390 2336 y(exp\(W\(x\)\))f(=)
f(x.)84 b(This)44 b(function)g(has)h(m)m(ultiple)g(branc)m(hes)g(for)f
(x)h Ff(<)f Fk(0;)53 b(ho)m(w)m(ev)m(er,)d(it)45 b(has)390
2446 y(only)34 b(t)m(w)m(o)i(real-v)-5 b(alued)35 b(branc)m(hes.)51
b(W)-8 b(e)35 b(de\014ne)f(W_0\(x\))i(to)e(b)s(e)g(the)g(principal)g
(branc)m(h,)g(where)390 2555 y(W)29 b Ff(>)g Fk(-1)h(for)f(x)g
Ff(<)f Fk(0,)i(and)f(W_)p Ff({)p Fk(-1)p Ff(})p Fk(\(x\))h(to)g(b)s(e)e
(the)i(other)f(real)h(branc)m(h,)e(where)h(W)g Ff(<)g
Fk(-1)h(for)f(x)g Ff(<)f Fk(0.)390 2694 y Fg(err)36 b
Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2833 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2853 V 390 2943 a Fk(for)30 b(do)s(cumen)m(tation.)275
3136 y(\037log_1plusx)h(-*-)g(texinfo)g(-*-)2960 3329
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(log_1plusx)48 b Fi(\()p Fh(x)12 b Fi(\))2960 3438 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(log_1plusx)48 b Fi(\()6
b Fg(.)23 b(.)f(.)11 b Fi(\))390 3548 y Fk(These)30 b(routines)g
(compute)g(log\(1)i(+)e(x\))g(for)g(x)g Ff(>)g Fk(-1)h(using)f(an)g
(algorithm)h(that)f(is)h(accurate)g(for)390 3658 y(small)g(x.)390
3796 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3935 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3955 V 390 4045 a Fk(for)30 b(do)s(cumen)m(tation.)
275 4238 y(\037log_1plusx_mx)h(-*-)g(texinfo)g(-*-)2960
4431 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(log_1plusx_mx)c Fi(\()p Fh(x)12 b Fi(\))2960
4540 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(log_1plusx_mx)c
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4650 y Fk(These)30
b(routines)g(compute)g(log\(1)i(+)e(x\))h(-)f(x)g(for)g(x)g
Ff(>)g Fk(-1)h(using)e(an)h(algorithm)h(that)g(is)f(accurate)390
4760 y(for)g(small)h(x.)390 4899 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 5037 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5058
V 390 5147 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340
y(\037psi)f(-*-)j(texinfo)f(-*-)p eop end
%%Page: 9 9
TeXDict begin 9 8 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi)46
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 518 y Fk(These)30
b(routines)g(compute)h(the)g(digamma)g(function)f(psi\(x\))g(for)g
(general)i(x,)e(x)h(e)f(0.)390 651 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 783 y(This)19 b(function)h(is)h(from)f(the)
g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 804 42
84 v 390 893 a Fk(for)30 b(do)s(cumen)m(tation.)275 1072
y(\037psi_1piy)g(-*-)h(texinfo)g(-*-)2960 1251 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(psi_1piy)48 b
Fi(\()p Fh(x)12 b Fi(\))2960 1360 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(psi_1piy)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 1470 y Fk(These)41 b(routines)f(compute)h(the)g(real)h
(part)e(of)h(the)g(digamma)h(function)e(on)h(the)g(line)g(1+i)g(y)-8
b(,)390 1579 y(Re[psi\(1)31 b(+)f(i)h(y\)].)390 1712
y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
1845 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1865 V 390 1954 a Fk(for)30 b(do)s(cumen)m(tation.)275
2133 y(\037sync)m(hrotron_1)g(-*-)h(texinfo)g(-*-)2960
2312 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(synchrotron_1)c Fi(\()p Fh(x)12 b Fi(\))2960
2421 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(synchrotron_1)c
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 2531 y Fk(These)27
b(routines)g(compute)h(the)f(\014rst)g(sync)m(hrotron)g(function)g(x)g
(in)m(t_x)p Ff(^)p Fk(inft)m(y)h(dt)f(K_)p Ff({)p Fk(5/3)p
Ff(})p Fk(\(t\))i(for)390 2641 y(x)h Ff(>)p Fk(=)g(0.)390
2773 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2906 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2926 V 390 3016 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3194 y(\037sync)m(hrotron_2)g(-*-)h(texinfo)g(-*-)2960
3373 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(synchrotron_2)c Fi(\()p Fh(x)12 b Fi(\))2960
3483 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(synchrotron_2)c
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 3592 y Fk(These)30
b(routines)g(compute)h(the)g(second)f(sync)m(hrotron)g(function)g(x)g
(K_)p Ff({)p Fk(2/3)p Ff(})p Fk(\(x\))i(for)e(x)h Ff(>)p
Fk(=)e(0.)390 3725 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f
(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b
Fg(y)p Fk(.)390 3858 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3878 V
390 3967 a Fk(for)30 b(do)s(cumen)m(tation.)275 4146
y(\037transp)s(ort_2)f(-*-)j(texinfo)f(-*-)2960 4325
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(transport_2)c Fi(\()p Fh(x)12 b Fi(\))2960 4434 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(transport_2)c Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 4544 y Fk(These)30 b(routines)g(compute)h(the)g(transp)s
(ort)e(function)h(J\(2,x\).)390 4677 y(The)j(transp)s(ort)f(functions)h
(J\(n,x\))g(are)h(de\014ned)d(b)m(y)i(the)h(in)m(tegral)h(represen)m
(tations)f(J\(n,x\))f(:=)390 4786 y(in)m(t_0)p Ff(^)p
Fk(x)e(dt)f(t)p Ff(^)p Fk(n)g(e)p Ff(^)p Fk(t)h(/\(e)p
Ff(^)p Fk(t)h(-)e(1\))p Ff(^)p Fk(2.)390 4919 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5052 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 5072 V 390 5161 a Fk(for)30 b(do)s(cumen)m(tation.)275
5340 y(\037transp)s(ort_3)f(-*-)j(texinfo)f(-*-)p eop
end
%%Page: 10 10
TeXDict begin 10 9 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(transport_3)c
Fi(\()p Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(transport_3)c Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 518 y Fk(These)30 b(routines)g(compute)h(the)g(transp)s
(ort)e(function)h(J\(3,x\).)390 648 y(The)j(transp)s(ort)f(functions)h
(J\(n,x\))g(are)h(de\014ned)d(b)m(y)i(the)h(in)m(tegral)h(represen)m
(tations)f(J\(n,x\))f(:=)390 758 y(in)m(t_0)p Ff(^)p
Fk(x)e(dt)f(t)p Ff(^)p Fk(n)g(e)p Ff(^)p Fk(t)h(/\(e)p
Ff(^)p Fk(t)h(-)e(1\))p Ff(^)p Fk(2.)390 888 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 1019 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1039 42 84 v 390 1128 a Fk(for)30 b(do)s(cumen)m(tation.)275
1300 y(\037transp)s(ort_4)f(-*-)j(texinfo)f(-*-)2960
1472 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(transport_4)c Fi(\()p Fh(x)12 b Fi(\))2960
1581 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(transport_4)c
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1691 y Fk(These)30
b(routines)g(compute)h(the)g(transp)s(ort)e(function)h(J\(4,x\).)390
1821 y(The)j(transp)s(ort)f(functions)h(J\(n,x\))g(are)h(de\014ned)d(b)
m(y)i(the)h(in)m(tegral)h(represen)m(tations)f(J\(n,x\))f(:=)390
1931 y(in)m(t_0)p Ff(^)p Fk(x)e(dt)f(t)p Ff(^)p Fk(n)g(e)p
Ff(^)p Fk(t)h(/\(e)p Ff(^)p Fk(t)h(-)e(1\))p Ff(^)p Fk(2.)390
2061 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2192 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2212 V 390 2301 a Fk(for)30 b(do)s(cumen)m(tation.)
275 2473 y(\037transp)s(ort_5)f(-*-)j(texinfo)f(-*-)2960
2645 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(transport_5)c Fi(\()p Fh(x)12 b Fi(\))2960
2754 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(transport_5)c
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 2864 y Fk(These)30
b(routines)g(compute)h(the)g(transp)s(ort)e(function)h(J\(5,x\).)390
2994 y(The)j(transp)s(ort)f(functions)h(J\(n,x\))g(are)h(de\014ned)d(b)
m(y)i(the)h(in)m(tegral)h(represen)m(tations)f(J\(n,x\))f(:=)390
3104 y(in)m(t_0)p Ff(^)p Fk(x)e(dt)f(t)p Ff(^)p Fk(n)g(e)p
Ff(^)p Fk(t)h(/\(e)p Ff(^)p Fk(t)h(-)e(1\))p Ff(^)p Fk(2.)390
3234 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3364 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3385 V 390 3474 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3646 y(\037sinc_gsl)g(-*-)i(texinfo)f(-*-)2960 3818
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(sinc_gsl)48 b Fi(\()p Fh(x)12 b Fi(\))2960 3927 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(sinc_gsl)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 4037 y Fk(These)30 b(routines)g(compute)h(sinc\(x\))g(=)f
(sin\(pi)g(x\))h(/)g(\(pi)f(x\))h(for)f(an)m(y)g(v)-5
b(alue)31 b(of)g(x.)390 4167 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 4297 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4318
V 390 4407 a Fk(for)30 b(do)s(cumen)m(tation.)275 4579
y(\037lnsinh)e(-*-)k(texinfo)f(-*-)2960 4751 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(lnsinh)47 b Fi(\()p
Fh(x)12 b Fi(\))2960 4860 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(lnsinh)47
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4970 y Fk(These)30
b(routines)g(compute)h(log\(sinh\(x\)\))h(for)e(x)g Ff(>)g
Fk(0.)390 5100 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)
g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p
eop end
%%Page: 11 11
TeXDict begin 11 10 bop 275 299 a Fk(\037lncosh)30 b(-*-)h(texinfo)g
(-*-)2960 476 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64
b Fj(=)53 b(lncosh)47 b Fi(\()p Fh(x)12 b Fi(\))2960
585 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(lncosh)47
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 695 y Fk(These)30
b(routines)g(compute)h(log\(cosh\(x\)\))i(for)d(an)m(y)h(x.)390
827 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)
g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
959 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 979 42 84 v 390 1069 a Fk(for)30 b(do)s(cumen)m(tation.)275
1246 y(\037zeta)h(-*-)h(texinfo)f(-*-)2960 1423 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(zeta)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 1532 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(zeta)47
b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1642 y Fk(These)30
b(routines)g(compute)h(the)g(Riemann)f(zeta)i(function)e(zeta\(s\))i
(for)e(arbitrary)g(s,)h(s)f(e)h(1.)390 1774 y(The)d(Riemann)g(zeta)h
(function)f(is)g(de\014ned)f(b)m(y)h(the)h(in\014nite)f(sum)f
(zeta\(s\))j(=)e(sum_)p Ff({)p Fk(k=1)p Ff(}^)p Fk(inft)m(y)390
1884 y(k)p Ff(^{)p Fk(-s)p Ff(})p Fk(.)390 2016 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 2148 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2168 V 390 2257 a Fk(for)30 b(do)s(cumen)m(tation.)275
2434 y(\037eta)h(-*-)g(texinfo)g(-*-)2960 2611 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(eta)46 b Fi(\()p
Fh(x)12 b Fi(\))2960 2721 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(eta)46
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 2831 y Fk(These)30
b(routines)g(compute)h(the)g(eta)g(function)f(eta\(s\))i(for)e
(arbitrary)h(s.)390 2963 y(The)f(eta)h(function)f(is)h(de\014ned)e(b)m
(y)h(eta\(s\))i(=)e(\(1-2)p Ff(^{)p Fk(1-s)p Ff(})p Fk(\))i(zeta\(s\).)
390 3095 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3227 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3247 V 390 3336 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3513 y(\037b)s(essel_Jn)f(-*-)i(texinfo)g(-*-)2960
3691 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(bessel_Jn)48 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12
b Fi(\))2960 3800 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Jn)48
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3910 y Fk(These)30
b(routines)g(compute)h(the)g(regular)f(cylindrical)h(Bessel)h(function)
e(of)g(order)g(n,)g(J_n\(x\).)390 4042 y Fg(err)36 b
Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4174 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 4194 V 390 4283 a Fk(for)30 b(do)s(cumen)m(tation.)275
4460 y(\037b)s(essel_Yn)f(-*-)j(texinfo)f(-*-)2960 4637
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(bessel_Yn)48 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960
4747 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Yn)48
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4857 y Fk(These)34
b(routines)h(compute)g(the)f(irregular)h(cylindrical)g(Bessel)h
(function)e(of)h(order)f(n,)h(Y_n\(x\),)390 4966 y(for)30
b(x)p Ff(>)p Fk(0.)390 5098 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251
V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end
%%Page: 12 12
TeXDict begin 12 11 bop 275 299 a Fk(\037b)s(essel_In)29
b(-*-)i(texinfo)g(-*-)2960 490 y([Loadable)g(F)-8 b(unction])-3599
b Fh(y)64 b Fj(=)53 b(bessel_In)48 b Fi(\()p Fh(n)p Fg(,)31
b Fh(x)12 b Fi(\))2960 599 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_In)48
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 709 y Fk(These)35
b(routines)g(compute)h(the)g(regular)f(mo)s(di\014ed)f(cylindrical)i
(Bessel)h(function)e(of)g(order)g(n,)390 819 y(I_n\(x\).)390
956 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
1094 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1114 42 84 v 390 1204 a Fk(for)30 b(do)s(cumen)m(tation.)275
1395 y(\037b)s(essel_In_scaled)g(-*-)h(texinfo)g(-*-)2960
1586 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(bessel_In_scaled)d Fi(\()p Fh(n)p Fg(,)31 b
Fh(x)12 b Fi(\))2960 1695 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_In_scaled)d
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1805 y Fk(These)43
b(routines)g(compute)h(the)g(scaled)g(regular)g(mo)s(di\014ed)e
(cylindrical)i(Bessel)h(function)e(of)390 1914 y(order)30
b(n,)g(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))h(I_n\(x\))390
2052 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2190 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2210 V 390 2300 a Fk(for)30 b(do)s(cumen)m(tation.)
275 2491 y(\037b)s(essel_Kn)f(-*-)i(texinfo)g(-*-)2960
2682 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(bessel_Kn)48 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12
b Fi(\))2960 2791 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Kn)48
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2901 y Fk(These)30
b(routines)f(compute)h(the)g(irregular)g(mo)s(di\014ed)f(cylindrical)i
(Bessel)f(function)g(of)g(order)f(n,)390 3010 y(K_n\(x\),)i(for)f(x)g
Ff(>)g Fk(0.)390 3148 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 3286 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3306 V
390 3396 a Fk(for)30 b(do)s(cumen)m(tation.)275 3587
y(\037b)s(essel_Kn_scaled)g(-*-)h(texinfo)g(-*-)2960
3778 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(bessel_Kn_scaled)d Fi(\()p Fh(n)p Fg(,)31 b
Fh(x)12 b Fi(\))2960 3887 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Kn_scaled)d
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 3997 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 4134 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 4155 V 390 4244 a Fk(for)30 b(do)s(cumen)m(tation.)275
4435 y(\037b)s(essel_jl)g(-*-)h(texinfo)g(-*-)2960 4626
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(bessel_jl)48 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960
4736 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_jl)48
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4845 y Fk(These)35
b(routines)g(compute)h(the)f(regular)h(spherical)f(Bessel)i(function)e
(of)g(order)g(l,)i(j_l\(x\),)h(for)d(l)390 4955 y Ff(>)p
Fk(=)30 b(0)g(and)g(x)h Ff(>)p Fk(=)e(0.)390 5093 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 5230 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p
eop end
%%Page: 13 13
TeXDict begin 13 12 bop 275 299 a Fk(\037b)s(essel_yl)30
b(-*-)h(texinfo)g(-*-)2960 514 y([Loadable)g(F)-8 b(unction])-3599
b Fh(y)64 b Fj(=)53 b(bessel_yl)48 b Fi(\()p Fh(n)p Fg(,)31
b Fh(x)12 b Fi(\))2960 623 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_yl)48
b Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 733 y Fk(These)29
b(routines)g(compute)h(the)f(irregular)g(spherical)h(Bessel)g(function)
f(of)g(order)g(l,)h(y_l\(x\),)h(for)e(l)390 843 y Ff(>)p
Fk(=)h(0.)390 992 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f
(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b
Fg(y)p Fk(.)390 1142 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1163 42
84 v 390 1252 a Fk(for)30 b(do)s(cumen)m(tation.)275
1467 y(\037b)s(essel_il_scaled)h(-*-)h(texinfo)f(-*-)2960
1682 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(bessel_il_scaled)d Fi(\()p Fh(n)p Fg(,)31 b
Fh(x)12 b Fi(\))2960 1791 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_il_scaled)d
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1901 y Fk(These)26
b(routines)g(compute)h(the)f(scaled)h(regular)g(mo)s(di\014ed)e
(spherical)i(Bessel)g(function)f(of)g(order)390 2011
y(l,)31 b(exp\(-)p Ff(|)p Fk(x)p Ff(|)p Fk(\))f(i_l\(x\))390
2160 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2310 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2331 V 390 2420 a Fk(for)30 b(do)s(cumen)m(tation.)
275 2635 y(\037b)s(essel_kl_scaled)h(-*-)g(texinfo)g(-*-)2960
2850 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(bessel_kl_scaled)d Fi(\()p Fh(n)p Fg(,)31 b
Fh(x)12 b Fi(\))2960 2960 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_kl_scaled)d
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 3069 y Fk(These)43
b(routines)h(compute)g(the)g(scaled)g(irregular)g(mo)s(di\014ed)e
(spherical)i(Bessel)g(function)g(of)390 3179 y(order)30
b(l,)h(exp\(x\))g(k_l\(x\),)g(for)f(x)p Ff(>)p Fk(0.)390
3329 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3478 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3499 V 390 3588 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3803 y(\037exprel_n)f(-*-)j(texinfo)f(-*-)2960 4018
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(exprel_n)48 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960
4128 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(exprel_n)48
b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4237 y Fk(These)33
b(routines)h(compute)f(the)h(N-relativ)m(e)i(exp)s(onen)m(tial,)g(whic)
m(h)d(is)g(the)h(n-th)f(generalization)390 4347 y(of)k(the)f(functions)
g(gsl_sf_exprel)i(and)e(gsl_sf_exprel2.)60 b(The)36 b(N-relativ)m(e)j
(exp)s(onen)m(tial)e(is)g(giv)m(en)390 4456 y(b)m(y)-8
b(,)390 4606 y(exprel_N\(x\))49 b(=)f(N!/x)p Ff(^)p Fk(N)h(\(exp\(x\))g
(-)f(sum_)p Ff({)p Fk(k=0)p Ff(}^{)p Fk(N-1)p Ff(})f
Fk(x)p Ff(^)p Fk(k/k!\))94 b(=)48 b(1)g(+)g(x/\(N+1\))h(+)390
4716 y(x)p Ff(^)p Fk(2/\(\(N+1\)\(N+2\)\))34 b(+)c(...)41
b(=)30 b(1F1)h(\(1,1+N,x\))390 4866 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 5015 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5036
V 390 5125 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340
y(\037fermi_dirac_in)m(t)h(-*-)g(texinfo)g(-*-)p eop
end
%%Page: 14 14
TeXDict begin 14 13 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(fermi_dirac_int)d
Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 408 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(fermi_dirac_int)d Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 518 y Fk(These)27 b(routines)h(compute)g(the)f(complete)i
(F)-8 b(ermi-Dirac)30 b(in)m(tegral)f(with)f(an)f(in)m(teger)i(index)e
(of)h(j,)390 628 y(F_j\(x\))j(=)f(\(1/Gamma\(j+1\)\))k(in)m(t_0)p
Ff(^)p Fk(inft)m(y)d(dt)g(\(t)p Ff(^)p Fk(j)f(/\(exp\(t-x\)+1\)\).)390
768 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)
g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
909 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 929 42 84 v 390 1019 a Fk(for)30 b(do)s(cumen)m(tation.)275
1215 y(\037ta)m(ylorco)s(e\013)i(-*-)f(texinfo)g(-*-)2960
1412 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(taylorcoeff)c Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12
b Fi(\))2960 1522 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(taylorcoeff)c
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1631 y Fk(These)30
b(routines)g(compute)h(the)g(T)-8 b(a)m(ylor)31 b(co)s(e\016cien)m(t)h
(x)p Ff(^)p Fk(n)e(/)h(n!)40 b(for)30 b(x)g Ff(>)p Fk(=)g(0,)h(n)f
Ff(>)p Fk(=)g(0.)390 1772 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)
i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 1913 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1933 V
390 2022 a Fk(for)30 b(do)s(cumen)m(tation.)275 2219
y(\037legendre_Pl)g(-*-)i(texinfo)f(-*-)2960 2416 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Pl)c
Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 2526 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Pl)c Fi(\()6
b Fg(.)22 b(.)g(.)11 b Fi(\))390 2635 y Fk(These)36 b(functions)f(ev)-5
b(aluate)38 b(the)e(Legendre)f(p)s(olynomial)i(P_l\(x\))g(for)e(a)h(sp)
s(eci\014c)g(v)-5 b(alue)36 b(of)g(l,)i(x)390 2745 y(sub)5
b(ject)30 b(to)h(l)g Ff(>)p Fk(=)f(0,)h Ff(|)p Fk(x)p
Ff(|)e(<)p Fk(=)h(1)390 2885 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 3026 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3046
V 390 3136 a Fk(for)30 b(do)s(cumen)m(tation.)275 3333
y(\037legendre_Ql)g(-*-)i(texinfo)f(-*-)2960 3529 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_Ql)c
Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960 3639 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Ql)c Fi(\()6
b Fg(.)22 b(.)g(.)11 b Fi(\))390 3748 y Fk(These)30 b(routines)g
(compute)h(the)g(Legendre)f(function)g(Q_l\(x\))h(for)f(x)h
Ff(>)f Fk(-1,)h(x)f(!=)h(1)f(and)g(l)h Ff(>)p Fk(=)e(0.)390
3889 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 4030 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 4050 V 390 4139 a Fk(for)30 b(do)s(cumen)m(tation.)
275 4336 y(\037psi_n)f(-*-)i(texinfo)g(-*-)2960 4533
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(psi_n)47 b Fi(\()p Fh(n)p Fg(,)31 b Fh(x)12 b Fi(\))2960
4643 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_n)47 b
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4752 y Fk(These)30
b(routines)g(compute)h(the)g(p)s(olygamma)g(function)f(psi)p
Ff(^{)p Fk(\(m\))p Ff(})p Fk(\(x\))g(for)g(m)g Ff(>)p
Fk(=)g(0,)h(x)f Ff(>)g Fk(0.)390 4893 y Fg(err)36 b Fk(con)m(tains)c
(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 5034 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5054
V 390 5143 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340
y(\037b)s(essel_Jn)m(u)f(-*-)i(texinfo)g(-*-)p eop end
%%Page: 15 15
TeXDict begin 15 14 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(z)64 b Fj(=)53 b(bessel_Jnu)48
b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 408 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Jnu)48 b Fi(\()6
b Fg(.)23 b(.)f(.)11 b Fi(\))390 518 y Fk(These)28 b(routines)f
(compute)h(the)g(regular)g(cylindrical)h(Bessel)f(function)g(of)g
(fractional)h(order)e(n)m(u,)390 628 y(J_u\(x\).)390
763 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)
g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390
899 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 919 42 84 v 390 1009 a Fk(for)30 b(do)s(cumen)m(tation.)275
1195 y(\037b)s(essel_Yn)m(u)f(-*-)j(texinfo)f(-*-)2960
1382 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(bessel_Ynu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12
b Fi(\))2960 1491 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Ynu)48
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 1601 y Fk(These)37
b(routines)f(compute)h(the)g(irregular)g(cylindrical)h(Bessel)g
(function)e(of)h(fractional)h(order)390 1711 y(n)m(u,)30
b(Y_u\(x\).)390 1846 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)
f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 1982 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2002 V
390 2091 a Fk(for)30 b(do)s(cumen)m(tation.)275 2278
y(\037b)s(essel_In)m(u)f(-*-)i(texinfo)g(-*-)2960 2465
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(bessel_Inu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b
Fi(\))2960 2574 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Inu)48
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 2684 y Fk(These)34
b(routines)g(compute)h(the)f(regular)g(mo)s(di\014ed)f(Bessel)j
(function)e(of)g(fractional)i(order)d(n)m(u,)390 2793
y(I_u\(x\))e(for)f(x)p Ff(>)p Fk(0,)g(u)p Ff(>)p Fk(0.)390
2929 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p
Fk(.)390 3065 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3085 V 390 3174 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3361 y(\037b)s(essel_In)m(u_scaled)g(-*-)h(texinfo)g(-*-)2960
3547 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(bessel_Inu_scaled)d Fi(\()p Fh(x)p Fg(,)32
b Fh(y)12 b Fi(\))2960 3657 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(bessel_Inu_scaled)d Fi(\()6 b Fg(.)23
b(.)f(.)11 b Fi(\))390 3767 y Fk(These)24 b(routines)f(compute)h(the)g
(scaled)h(regular)f(mo)s(di\014ed)f(Bessel)i(function)e(of)h
(fractional)h(order)390 3876 y(n)m(u,)30 b(exp\(-)p Ff(|)p
Fk(x)p Ff(|)p Fk(\)I_u\(x\))h(for)f(x)p Ff(>)p Fk(0,)h(u)p
Ff(>)p Fk(0.)390 4012 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 4148 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4168 V
390 4257 a Fk(for)30 b(do)s(cumen)m(tation.)275 4444
y(\037b)s(essel_Kn)m(u)f(-*-)i(texinfo)g(-*-)2960 4630
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(bessel_Knu)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b
Fi(\))2960 4740 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_Knu)48
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 4850 y Fk(These)28
b(routines)h(compute)g(the)g(irregular)g(mo)s(di\014ed)e(Bessel)j
(function)e(of)h(fractional)h(order)e(n)m(u,)390 4959
y(K_u\(x\))i(for)h(x)p Ff(>)p Fk(0,)f(u)p Ff(>)p Fk(0.)390
5095 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p
Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 5251 V 390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p
eop end
%%Page: 16 16
TeXDict begin 16 15 bop 275 299 a Fk(\037b)s(essel_lnKn)m(u)29
b(-*-)i(texinfo)g(-*-)2960 480 y([Loadable)g(F)-8 b(unction])-3599
b Fh(z)64 b Fj(=)53 b(bessel_lnKnu)c Fi(\()p Fh(x)p Fg(,)31
b Fh(y)12 b Fi(\))2960 589 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_lnKnu)c
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 699 y Fk(These)40
b(routines)g(compute)g(the)g(logarithm)h(of)f(the)g(irregular)g(mo)s
(di\014ed)f(Bessel)i(function)f(of)390 808 y(fractional)32
b(order)e(n)m(u,)g(ln\(K_u\(x\)\))h(for)f(x)p Ff(>)p
Fk(0,)h(u)p Ff(>)p Fk(0.)390 942 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(z)p Fk(.)390 1075 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1095
42 84 v 390 1184 a Fk(for)30 b(do)s(cumen)m(tation.)275
1365 y(\037b)s(essel_Kn)m(u_scaled)g(-*-)h(texinfo)g(-*-)2960
1546 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(bessel_Knu_scaled)d Fi(\()p Fh(x)p Fg(,)32
b Fh(y)12 b Fi(\))2960 1655 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(bessel_Knu_scaled)d Fi(\()6 b Fg(.)23
b(.)f(.)11 b Fi(\))390 1765 y Fk(These)41 b(routines)f(compute)i(the)f
(scaled)g(irregular)g(mo)s(di\014ed)f(Bessel)i(function)e(of)h
(fractional)390 1875 y(order)30 b(n)m(u,)g(exp\(+)p Ff(|)p
Fk(x)p Ff(|)p Fk(\))g(K_u\(x\))g(for)h(x)p Ff(>)p Fk(0,)f(u)p
Ff(>)p Fk(0.)390 2008 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 2141 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2161 V
390 2251 a Fk(for)30 b(do)s(cumen)m(tation.)275 2431
y(\037exp_m)m(ult)g(-*-)h(texinfo)g(-*-)2960 2612 y([Loadable)g(F)-8
b(unction])-3599 b Fh(z)64 b Fj(=)53 b(exp_mult)48 b
Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 2722 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(exp_mult)48 b Fi(\()6
b Fg(.)22 b(.)g(.)11 b Fi(\))390 2831 y Fk(These)33 b(routines)f(exp)s
(onen)m(tiate)j(x)d(and)h(m)m(ultiply)g(b)m(y)f(the)h(factor)h(y)f(to)h
(return)d(the)i(pro)s(duct)f(y)390 2941 y(exp\(x\).)390
3074 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390
3207 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 3228 V 390 3317 a Fk(for)30 b(do)s(cumen)m(tation.)275
3498 y(\037fermi_dirac_inc_0)h(-*-)g(texinfo)g(-*-)2960
3678 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(fermi_dirac_inc_0)d Fi(\()p Fh(x)p Fg(,)32
b Fh(y)12 b Fi(\))2960 3788 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(fermi_dirac_inc_0)d Fi(\()6 b Fg(.)23
b(.)f(.)11 b Fi(\))390 3898 y Fk(These)35 b(routines)h(compute)g(the)f
(incomplete)i(F)-8 b(ermi-Dirac)38 b(in)m(tegral)f(with)f(an)f(index)g
(of)h(zero,)390 4007 y(F_0\(x,b\))c(=)e(ln\(1)h(+)f(e)p
Ff(^{)p Fk(b-x)p Ff(})p Fk(\))g(-)g(\(b-x\).)390 4140
y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390
4274 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 4294 V 390 4383 a Fk(for)30 b(do)s(cumen)m(tation.)275
4564 y(\037p)s(o)s(c)m(h)f(-*-)i(texinfo)g(-*-)2960 4745
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(poch)46 b Fi(\()p Fh(x)p Fg(,)32 b Fh(y)12 b Fi(\))2960
4854 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(poch)47 b
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4964 y Fk(These)30
b(routines)g(compute)h(the)g(P)m(o)s(c)m(hhammer)f(sym)m(b)s(ol)390
5097 y(\(a\)_x)i(:=)e(Gamma\(a)i(+)e(x\)/Gamma\(a\),)390
5230 y(sub)5 b(ject)34 b(to)h(a)g(and)e(a+x)h(not)h(b)s(eing)f(negativ)
m(e)i(in)m(tegers.)54 b(The)33 b(P)m(o)s(c)m(hhammer)i(sym)m(b)s(ol)f
(is)g(also)390 5340 y(kno)m(wn)c(as)g(the)h(Ap)s(ell)f(sym)m(b)s(ol.)p
eop end
%%Page: 17 17
TeXDict begin 17 16 bop 390 299 a Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(z)p Fk(.)390 445 y(This)19 b(function)h(is)h(from)f(the)
g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 465 42
84 v 390 554 a Fk(for)30 b(do)s(cumen)m(tation.)275 762
y(\037lnp)s(o)s(c)m(h)f(-*-)i(texinfo)g(-*-)2960 969
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(lnpoch)47 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960
1078 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(lnpoch)47
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 1188 y Fk(These)48
b(routines)g(compute)h(the)g(logarithm)g(of)g(the)f(P)m(o)s(c)m
(hhammer)h(sym)m(b)s(ol,)k(log\(\(a\)_x\))e(=)390 1298
y(log\(Gamma\(a)33 b(+)d(x\)/Gamma\(a\)\))k(for)c(a)h
Ff(>)f Fk(0,)h(a+x)f Ff(>)g Fk(0.)390 1443 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390 1589 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1610 V 390 1699 a Fk(for)30 b(do)s(cumen)m(tation.)275
1906 y(\037p)s(o)s(c)m(hrel)f(-*-)j(texinfo)f(-*-)2960
2113 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(pochrel)47 b Fi(\()p Fh(x)p Fg(,)32 b Fh(y)12
b Fi(\))2960 2223 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(pochrel)47
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 2333 y Fk(These)27
b(routines)h(compute)f(the)h(relativ)m(e)h(P)m(o)s(c)m(hhammer)f(sym)m
(b)s(ol)f(\(\(a,x\))i(-)f(1\)/x)h(where)e(\(a,x\))h(=)390
2442 y(\(a\)_x)k(:=)e(Gamma\(a)i(+)e(x\)/Gamma\(a\).)390
2588 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p
Fk(.)390 2734 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2754 V 390 2844 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3051 y(\037gamma_inc_Q)h(-*-)g(texinfo)g(-*-)2960
3258 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(gamma_inc_Q)c Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12
b Fi(\))2960 3368 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(gamma_inc_Q)c
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 3477 y Fk(These)54
b(routines)g(compute)g(the)g(normalized)h(incomplete)g(Gamma)g(F)-8
b(unction)54 b(Q\(a,x\))h(=)390 3587 y(1/Gamma\(a\))33
b(in)m(t_xinft)m(y)f(dt)e(t)p Ff(^{)p Fk(a-1)p Ff(})h
Fk(exp\(-t\))g(for)g(a)f Ff(>)g Fk(0,)h(x)g Ff(>)p Fk(=)e(0.)390
3733 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p
Fk(.)390 3879 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3899 V 390 3988 a Fk(for)30 b(do)s(cumen)m(tation.)
275 4195 y(\037gamma_inc_P)h(-*-)g(texinfo)g(-*-)2960
4403 y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b
Fj(=)53 b(gamma_inc_P)c Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12
b Fi(\))2960 4512 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(gamma_inc_P)c
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4622 y Fk(These)26
b(routines)g(compute)h(the)f(complemen)m(tary)i(normalized)f
(incomplete)g(Gamma)g(F)-8 b(unction)390 4731 y(P\(a,x\))32
b(=)e(1/Gamma\(a\))j(in)m(t_0)p Ff(^)p Fk(x)e(dt)f(t)p
Ff(^{)p Fk(a-1)p Ff(})h Fk(exp\(-t\))h(for)e(a)h Ff(>)f
Fk(0,)h(x)f Ff(>)p Fk(=)g(0.)390 4877 y Fg(err)36 b Fk(con)m(tains)c
(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(z)p Fk(.)390 5023 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5043
V 390 5133 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340
y(\037gamma_inc)h(-*-)g(texinfo)g(-*-)p eop end
%%Page: 18 18
TeXDict begin 18 17 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(z)64 b Fj(=)53 b(gamma_inc)48 b
Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 408 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(gamma_inc)48 b Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 518 y Fk(These)34 b(functions)f(compute)i(the)f(incomplete)
h(Gamma)g(F)-8 b(unction)35 b(the)f(normalization)i(factor)390
628 y(included)k(in)g(the)h(previously)f(de\014ned)f(functions:)61
b(Gamma\(a,x\))42 b(=)e(in)m(t_xinft)m(y)i(dt)e(t)p Ff(^{)p
Fk(a-1)p Ff(})390 737 y Fk(exp\(-t\))32 b(for)e(a)g(real)h(and)f(x)h
Ff(>)p Fk(=)e(0.)390 873 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 1009 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1029 42
84 v 390 1118 a Fk(for)30 b(do)s(cumen)m(tation.)275
1305 y(\037b)s(eta_gsl)h(-*-)g(texinfo)g(-*-)2960 1491
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(beta_gsl)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960
1601 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(beta_gsl)48
b Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 1711 y Fk(These)20
b(routines)g(compute)h(the)f(Beta)i(F)-8 b(unction,)23
b(B\(a,b\))f(=)e(Gamma\(a\)Gamma\(b\)/Gamma\(a+b\))p
3915 1733 42 91 v 390 1820 a(for)30 b(a)h Ff(>)f Fk(0,)h(b)f
Ff(>)g Fk(0.)390 1956 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 2091 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2112 42
84 v 390 2201 a Fk(for)30 b(do)s(cumen)m(tation.)275
2388 y(\037ln)m(b)s(eta)g(-*-)h(texinfo)g(-*-)2960 2574
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(lnbeta)47 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960
2684 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(lnbeta)47
b Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 2793 y Fk(These)31
b(routines)g(compute)g(the)g(logarithm)h(of)f(the)g(Beta)i(F)-8
b(unction,)32 b(log\(B\(a,b\)\))i(for)d(a)g Ff(>)g Fk(0,)g(b)390
2903 y Ff(>)f Fk(0.)390 3039 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(z)p Fk(.)390 3174 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3194
V 390 3284 a Fk(for)30 b(do)s(cumen)m(tation.)275 3470
y(\037h)m(yp)s(erg_0F1)h(-*-)g(texinfo)g(-*-)2960 3657
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(hyperg_0F1)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b
Fi(\))2960 3767 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(hyperg_0F1)48
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 3876 y Fk(These)30
b(routines)g(compute)h(the)g(h)m(yp)s(ergeometric)g(function)f
(0F1\(c,x\).)390 4012 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 4148 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4168 V
390 4257 a Fk(for)30 b(do)s(cumen)m(tation.)275 4444
y(\037conicalP_half)h(-*-)h(texinfo)f(-*-)2960 4630 y([Loadable)g(F)-8
b(unction])-3599 b Fh(z)64 b Fj(=)53 b(conicalP_half)c
Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 4740 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(conicalP_half)c Fi(\()6
b Fg(.)22 b(.)h(.)11 b Fi(\))390 4850 y Fk(These)31 b(routines)h
(compute)g(the)g(irregular)f(Spherical)h(Conical)g(F)-8
b(unction)33 b(P)p Ff(^{)p Fk(1/2)p Ff(})p Fk(_)p Ff({)p
Fk(-1/2)g(+)f(i)390 4959 y(lam)m(b)s(da)p Ff(})p Fk(\(x\))f(for)f(x)g
Ff(>)g Fk(-1.)390 5095 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251 V
390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end
%%Page: 19 19
TeXDict begin 19 18 bop 275 299 a Fk(\037conicalP_mhalf)31
b(-*-)h(texinfo)f(-*-)2960 482 y([Loadable)g(F)-8 b(unction])-3599
b Fh(z)64 b Fj(=)53 b(conicalP_mhalf)c Fi(\()p Fh(x)p
Fg(,)32 b Fh(y)12 b Fi(\))2960 592 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(conicalP_mhalf)d Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 702 y Fk(These)34 b(routines)h(compute)g(the)g(regular)g
(Spherical)f(Conical)i(F)-8 b(unction)35 b(P)p Ff(^{)p
Fk(-1/2)p Ff(})p Fk(_)p Ff({)p Fk(-1/2)i(+)e(i)390 811
y(lam)m(b)s(da)p Ff(})p Fk(\(x\))c(for)f(x)g Ff(>)g Fk(-1.)390
945 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)
g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390
1080 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1100 42 84 v 390 1189 a Fk(for)30 b(do)s(cumen)m(tation.)275
1373 y(\037conicalP_0)i(-*-)f(texinfo)g(-*-)2960 1556
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(conicalP_0)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b
Fi(\))2960 1666 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(conicalP_0)48
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 1776 y Fk(These)30
b(routines)g(compute)h(the)g(conical)h(function)e(P)p
Ff(^)p Fk(0_)p Ff({)p Fk(-1/2)i(+)e(i)g(lam)m(b)s(da)p
Ff(})p Fk(\(x\))h(for)f(x)g Ff(>)g Fk(-1.)390 1910 y
Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390
2044 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2064 V 390 2154 a Fk(for)30 b(do)s(cumen)m(tation.)275
2337 y(\037conicalP_1)i(-*-)f(texinfo)g(-*-)2960 2521
y([Loadable)g(F)-8 b(unction])-3599 b Fh(z)64 b Fj(=)53
b(conicalP_1)48 b Fi(\()p Fh(x)p Fg(,)31 b Fh(y)12 b
Fi(\))2960 2630 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(conicalP_1)48
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 2740 y Fk(These)30
b(routines)g(compute)h(the)g(conical)h(function)e(P)p
Ff(^)p Fk(1_)p Ff({)p Fk(-1/2)i(+)e(i)g(lam)m(b)s(da)p
Ff(})p Fk(\(x\))h(for)f(x)g Ff(>)g Fk(-1.)390 2874 y
Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(z)p Fk(.)390
3008 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 3029 V 390 3118 a Fk(for)30 b(do)s(cumen)m(tation.)275
3302 y(\037hzeta)h(-*-)g(texinfo)g(-*-)2960 3485 y([Loadable)g(F)-8
b(unction])-3599 b Fh(z)64 b Fj(=)53 b(hzeta)47 b Fi(\()p
Fh(x)p Fg(,)31 b Fh(y)12 b Fi(\))2960 3595 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(z)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(hzeta)47 b Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 3704 y Fk(These)30 b(routines)g(compute)h(the)g(Hurwitz)f
(zeta)i(function)e(zeta\(s,q\))j(for)d(s)g Ff(>)g Fk(1,)h(q)f
Ff(>)g Fk(0.)390 3839 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(z)p Fk(.)390 3973 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3993 V
390 4082 a Fk(for)30 b(do)s(cumen)m(tation.)275 4266
y(\037airy_Ai)h(-*-)g(texinfo)g(-*-)2960 4450 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_Ai)47 b Fi(\()p
Fh(x)p Fg(,)32 b Fh(mode)12 b Fi(\))2960 4559 y Fk([Loadable)31
b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(airy_Ai)47 b Fi(\()6 b Fg(.)23 b(.)f(.)11
b Fi(\))390 4669 y Fk(These)28 b(routines)g(compute)h(the)f(Airy)g
(function)g(Ai\(x\))h(with)f(an)g(accuracy)i(sp)s(eci\014ed)d(b)m(y)h
(mo)s(de.)390 4803 y(The)i(second)g(argumen)m(t)h Fg(mo)s(de)k
Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390
4962 y(0)h(=)f(GSL_PREC_DOUBLE)870 5071 y(Double-precision,)i(a)e
(relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p
Fk(.)390 5230 y(1)h(=)f(GSL_PREC_SINGLE)870 5340 y(Single-precision,)h
(a)g(relativ)m(e)i(accuracy)e(of)g(appro)m(ximately)h
Ff(10^-7)p Fk(.)p eop end
%%Page: 20 20
TeXDict begin 20 19 bop 390 299 a Fk(2)31 b(=)f(GSL_PREC_APPR)m(O)m(X)
870 408 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h
(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p
Fk(.)390 589 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 737 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 757 42 84 v 390 847 a Fk(for)30 b(do)s(cumen)m
(tation.)275 1059 y(\037airy_Bi)h(-*-)g(texinfo)g(-*-)2960
1271 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(airy_Bi)47 b Fi(\()p Fh(x)p Fg(,)32 b Fh(mode)12
b Fi(\))2960 1381 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Bi)47
b Fi(\()6 b Fg(.)23 b(.)f(.)11 b Fi(\))390 1490 y Fk(These)28
b(routines)h(compute)f(the)h(Airy)g(function)f(Bi\(x\))i(with)e(an)g
(accuracy)i(sp)s(eci\014ed)e(b)m(y)g(mo)s(de.)390 1639
y(The)i(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30
b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390
1819 y(0)h(=)f(GSL_PREC_DOUBLE)870 1928 y(Double-precision,)i(a)e
(relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p
Fk(.)390 2102 y(1)h(=)f(GSL_PREC_SINGLE)870 2211 y(Single-precision,)h
(a)g(relativ)m(e)i(accuracy)e(of)g(appro)m(ximately)h
Ff(10^-7)p Fk(.)390 2385 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870
2494 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g
(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390
2674 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2823 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2843 V 390 2932 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3145 y(\037airy_Ai_scaled)i(-*-)f(texinfo)g(-*-)2960
3357 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(airy_Ai_scaled)c Fi(\()p Fh(x)p Fg(,)32 b Fh(mode)12
b Fi(\))2960 3466 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Ai_scaled)d
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 3576 y Fk(These)32
b(routines)g(compute)h(a)f(scaled)h(v)m(ersion)g(of)f(the)h(Airy)f
(function)g(S_A\(x\))h(Ai\(x\).)47 b(F)-8 b(or)33 b(x)p
Ff(>)p Fk(0)390 3686 y(the)e(scaling)g(factor)g(S_A\(x\))g(is)g
(exp\(+\(2/3\))h(x)p Ff(^)p Fk(\(3/2\)\),)h(and)d(is)g(1)h(for)f(x)p
Ff(<)p Fk(0.)390 3834 y(The)g(second)g(argumen)m(t)h
Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s
(onding)e(to)390 4014 y(0)h(=)f(GSL_PREC_DOUBLE)870 4124
y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m
(ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 4297 y(1)h(=)f
(GSL_PREC_SINGLE)870 4407 y(Single-precision,)h(a)g(relativ)m(e)i
(accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390
4580 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 4690 y(Appro)m(ximate)h(v)-5
b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i
Ff(5)e(*)g(10^-4)p Fk(.)390 4870 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 5018 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5038
V 390 5128 a Fk(for)30 b(do)s(cumen)m(tation.)275 5340
y(\037airy_Bi_scaled)i(-*-)f(texinfo)g(-*-)p eop end
%%Page: 21 21
TeXDict begin 21 20 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(airy_Bi_scaled)c
Fi(\()p Fh(x)p Fg(,)32 b Fh(mode)12 b Fi(\))2960 408
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Bi_scaled)d
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 518 y Fk(These)32
b(routines)h(compute)g(a)g(scaled)h(v)m(ersion)f(of)g(the)g(Airy)f
(function)h(S_B\(x\))g(Bi\(x\).)49 b(F)-8 b(or)34 b(x)p
Ff(>)p Fk(0)390 628 y(the)d(scaling)g(factor)g(S_B\(x\))h(is)e
(exp\(-\(2/3\))j(x)p Ff(^)p Fk(\(3/2\)\),)g(and)c(is)i(1)g(for)f(x)p
Ff(<)p Fk(0.)390 761 y(The)g(second)g(argumen)m(t)h Fg(mo)s(de)k
Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390
918 y(0)h(=)f(GSL_PREC_DOUBLE)870 1027 y(Double-precision,)i(a)e
(relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p
Fk(.)390 1184 y(1)h(=)f(GSL_PREC_SINGLE)870 1294 y(Single-precision,)h
(a)g(relativ)m(e)i(accuracy)e(of)g(appro)m(ximately)h
Ff(10^-7)p Fk(.)390 1451 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870
1561 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g
(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390
1718 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 1851 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 1871 42 84 v 390 1960 a Fk(for)30
b(do)s(cumen)m(tation.)275 2141 y(\037airy_Ai_deriv)h(-*-)g(texinfo)g
(-*-)2960 2322 y([Loadable)g(F)-8 b(unction])-3599 b
Fh(y)64 b Fj(=)53 b(airy_Ai_deriv)c Fi(\()p Fh(x)p Fg(,)31
b Fh(mode)12 b Fi(\))2960 2431 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(airy_Ai_deriv)c Fi(\()6 b Fg(.)22 b(.)h(.)11
b Fi(\))390 2541 y Fk(These)24 b(routines)f(compute)h(the)h(Airy)e
(function)h(deriv)-5 b(ativ)m(e)25 b(Ai'\(x\))g(with)f(an)g(accuracy)h
(sp)s(eci\014ed)390 2651 y(b)m(y)30 b(mo)s(de.)390 2784
y(The)g(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30
b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390
2941 y(0)h(=)f(GSL_PREC_DOUBLE)870 3050 y(Double-precision,)i(a)e
(relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p
Fk(.)390 3207 y(1)h(=)f(GSL_PREC_SINGLE)870 3317 y(Single-precision,)h
(a)g(relativ)m(e)i(accuracy)e(of)g(appro)m(ximately)h
Ff(10^-7)p Fk(.)390 3474 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870
3584 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g
(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390
3741 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3874 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3894 V 390 3983 a Fk(for)30 b(do)s(cumen)m(tation.)
275 4164 y(\037airy_Bi_deriv)h(-*-)g(texinfo)g(-*-)2960
4345 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(airy_Bi_deriv)c Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12
b Fi(\))2960 4454 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_Bi_deriv)c
Fi(\()6 b Fg(.)22 b(.)h(.)11 b Fi(\))390 4564 y Fk(These)24
b(routines)g(compute)h(the)f(Airy)g(function)g(deriv)-5
b(ativ)m(e)26 b(Bi'\(x\))f(with)f(an)g(accuracy)i(sp)s(eci\014ed)390
4674 y(b)m(y)k(mo)s(de.)390 4807 y(The)g(second)g(argumen)m(t)h
Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s
(onding)e(to)390 4964 y(0)h(=)f(GSL_PREC_DOUBLE)870 5073
y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m
(ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 5230 y(1)h(=)f
(GSL_PREC_SINGLE)870 5340 y(Single-precision,)h(a)g(relativ)m(e)i
(accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)p
eop end
%%Page: 22 22
TeXDict begin 22 21 bop 390 299 a Fk(2)31 b(=)f(GSL_PREC_APPR)m(O)m(X)
870 408 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h
(accuracy)g(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p
Fk(.)390 584 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 729 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 749 42 84 v 390 839 a Fk(for)30 b(do)s(cumen)m
(tation.)275 1045 y(\037airy_Ai_deriv_scaled)i(-*-)f(texinfo)g(-*-)2960
1251 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(airy_Ai_deriv_scaled)e Fi(\()p Fh(x)p Fg(,)31
b Fh(mode)12 b Fi(\))2960 1360 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(airy_Ai_deriv_scaled)e Fi(\()6 b Fg(.)23
b(.)f(.)11 b Fi(\))390 1470 y Fk(These)30 b(routines)g(compute)h(the)g
(deriv)-5 b(ativ)m(e)32 b(of)e(the)h(scaled)g(Airy)f(function)g
(S_A\(x\))h(Ai\(x\).)390 1615 y(The)f(second)g(argumen)m(t)h
Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s
(onding)e(to)390 1791 y(0)h(=)f(GSL_PREC_DOUBLE)870 1900
y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m
(ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 2070 y(1)h(=)f
(GSL_PREC_SINGLE)870 2180 y(Single-precision,)h(a)g(relativ)m(e)i
(accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390
2350 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 2460 y(Appro)m(ximate)h(v)-5
b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i
Ff(5)e(*)g(10^-4)p Fk(.)390 2635 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 2780 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2801
V 390 2890 a Fk(for)30 b(do)s(cumen)m(tation.)275 3096
y(\037airy_Bi_deriv_scaled)i(-*-)f(texinfo)g(-*-)2960
3302 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(airy_Bi_deriv_scaled)e Fi(\()p Fh(x)p Fg(,)31
b Fh(mode)12 b Fi(\))2960 3411 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(airy_Bi_deriv_scaled)e Fi(\()6 b Fg(.)23
b(.)f(.)11 b Fi(\))390 3521 y Fk(These)30 b(routines)g(compute)h(the)g
(deriv)-5 b(ativ)m(e)32 b(of)e(the)h(scaled)g(Airy)f(function)g
(S_B\(x\))h(Bi\(x\).)390 3666 y(The)f(second)g(argumen)m(t)h
Fg(mo)s(de)k Fk(m)m(ust)30 b(b)s(e)g(an)g(in)m(teger)i(corresp)s
(onding)e(to)390 3842 y(0)h(=)f(GSL_PREC_DOUBLE)870 3951
y(Double-precision,)i(a)e(relativ)m(e)j(accuracy)e(of)g(appro)m
(ximately)h Ff(2)e(*)g(10^-16)p Fk(.)390 4121 y(1)h(=)f
(GSL_PREC_SINGLE)870 4231 y(Single-precision,)h(a)g(relativ)m(e)i
(accuracy)e(of)g(appro)m(ximately)h Ff(10^-7)p Fk(.)390
4401 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870 4511 y(Appro)m(ximate)h(v)-5
b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g(of)e(appro)m(ximately)i
Ff(5)e(*)g(10^-4)p Fk(.)390 4686 y Fg(err)36 b Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 4832 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4852
V 390 4941 a Fk(for)30 b(do)s(cumen)m(tation.)275 5147
y(\037ellin)m(t_Kcomp)h(-*-)g(texinfo)h(-*-)2960 5353
y([Loadable)f(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(ellint_Kcomp)c Fi(\()p Fh(x)p Fg(,)31 b Fh(mode)12
b Fi(\))p eop end
%%Page: 23 23
TeXDict begin 23 22 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(ellint_Kcomp)c Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 408 y Fk(These)30 b(routines)g(compute)h(the)g(complete)g
(elliptic)h(in)m(tegral)h(K\(k\))1339 674 y Fe(K)7 b
Fk(\()p Fe(k)s Fk(\))26 b(=)1665 559 y Fd(Z)1748 580
y Fc(\031)r(=)p Fb(2)1711 748 y(0)2178 612 y Fe(dt)p
1885 653 666 4 v 1885 669 a Fd(q)p 1968 669 583 4 v 103
x Fk(\(1)21 b Fa(\000)f Fe(k)2210 746 y Fb(2)2263 772
y Fk(sin)2375 732 y Fb(2)2412 772 y Fk(\()p Fe(t)p Fk(\)\))390
1013 y(The)31 b(notation)i(used)d(here)h(is)h(based)f(on)g(Carlson,)h
Fg(Numerisc)m(he)g(Mathematik)38 b Fk(33)33 b(\(1979\))h(and)390
1123 y(di\013ers)23 b(sligh)m(tly)i(from)d(that)i(used)f(b)m(y)g
(Abramo)m(witz)h(&)f(Stegun,)i(where)e(the)g(functions)g(are)h(giv)m
(en)390 1232 y(in)30 b(terms)g(of)h(the)f(parameter)h
Fe(m)25 b Fk(=)g Fe(k)1695 1199 y Fb(2)1733 1232 y Fk(.)390
1366 y(The)30 b(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30
b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390
1525 y(0)h(=)f(GSL_PREC_DOUBLE)870 1634 y(Double-precision,)i(a)e
(relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p
Fk(.)390 1793 y(1)h(=)f(GSL_PREC_SINGLE)870 1902 y(Single-precision,)h
(a)g(relativ)m(e)i(accuracy)e(of)g(appro)m(ximately)h
Ff(10^-7)p Fk(.)390 2061 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870
2170 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g
(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390
2329 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 2463 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 2483 42 84 v 390 2573 a Fk(for)30
b(do)s(cumen)m(tation.)275 2756 y(\037ellin)m(t_Ecomp)h(-*-)h(texinfo)f
(-*-)2960 2939 y([Loadable)g(F)-8 b(unction])-3599 b
Fh(y)64 b Fj(=)53 b(ellint_Ecomp)c Fi(\()p Fh(x)p Fg(,)31
b Fh(mode)12 b Fi(\))2960 3048 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(ellint_Ecomp)c Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 3158 y Fk(These)32 b(routines)g(compute)g(the)g(complete)i
(elliptic)f(in)m(tegral)h(E\(k\))f(to)f(the)g(accuracy)i(sp)s
(eci\014ed)390 3267 y(b)m(y)c(the)h(mo)s(de)f(v)-5 b(ariable)31
b(mo)s(de.)1315 3548 y Fe(E)5 b Fk(\()p Fe(k)s Fk(\))26
b(=)1629 3434 y Fd(Z)1712 3454 y Fc(\031)r(=)p Fb(2)1675
3622 y(0)1840 3441 y Fd(q)p 1923 3441 583 4 v 108 x Fk(\(1)21
b Fa(\000)f Fe(k)2165 3522 y Fb(2)2217 3549 y Fk(sin)2329
3508 y Fb(2)2366 3549 y Fk(\()p Fe(t)p Fk(\)\))2505 3548
y Fe(dt)390 3780 y Fk(The)31 b(notation)i(used)d(here)h(is)h(based)f
(on)g(Carlson,)h Fg(Numerisc)m(he)g(Mathematik)38 b Fk(33)33
b(\(1979\))h(and)390 3890 y(di\013ers)23 b(sligh)m(tly)i(from)d(that)i
(used)f(b)m(y)g(Abramo)m(witz)h(&)f(Stegun,)i(where)e(the)g(functions)g
(are)h(giv)m(en)390 3999 y(in)30 b(terms)g(of)h(the)f(parameter)h
Fe(m)25 b Fk(=)g Fe(k)1695 3967 y Fb(2)1733 3999 y Fk(.)390
4134 y(The)30 b(second)g(argumen)m(t)h Fg(mo)s(de)k Fk(m)m(ust)30
b(b)s(e)g(an)g(in)m(teger)i(corresp)s(onding)e(to)390
4292 y(0)h(=)f(GSL_PREC_DOUBLE)870 4402 y(Double-precision,)i(a)e
(relativ)m(e)j(accuracy)e(of)g(appro)m(ximately)h Ff(2)e(*)g(10^-16)p
Fk(.)390 4560 y(1)h(=)f(GSL_PREC_SINGLE)870 4670 y(Single-precision,)h
(a)g(relativ)m(e)i(accuracy)e(of)g(appro)m(ximately)h
Ff(10^-7)p Fk(.)390 4828 y(2)f(=)f(GSL_PREC_APPR)m(O)m(X)870
4938 y(Appro)m(ximate)h(v)-5 b(alues,)31 b(a)g(relativ)m(e)h(accuracy)g
(of)e(appro)m(ximately)i Ff(5)e(*)g(10^-4)p Fk(.)390
5096 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 5251 42 84 v 390 5340 a Fk(for)30
b(do)s(cumen)m(tation.)p eop end
%%Page: 24 24
TeXDict begin 24 23 bop 275 299 a Fk(\037airy_zero_Ai)32
b(-*-)f(texinfo)g(-*-)2960 488 y([Loadable)g(F)-8 b(unction])-3599
b Fh(y)64 b Fj(=)53 b(airy_zero_Ai)c Fi(\()p Fh(n)12
b Fi(\))2960 597 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Ai)c
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 707 y Fk(These)30
b(routines)g(compute)h(the)g(lo)s(cation)h(of)e(the)h(s-th)f(zero)h(of)
g(the)f(Airy)h(function)f(Ai\(x\).)390 844 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390 981 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1001 42 84 v 390 1090 a Fk(for)30 b(do)s(cumen)m(tation.)275
1279 y(\037airy_zero_Bi)i(-*-)f(texinfo)g(-*-)2960 1468
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(airy_zero_Bi)c Fi(\()p Fh(n)12 b Fi(\))2960 1578 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Bi)c Fi(\()6
b Fg(.)22 b(.)g(.)12 b Fi(\))390 1687 y Fk(These)30 b(routines)g
(compute)h(the)g(lo)s(cation)h(of)e(the)h(s-th)f(zero)h(of)g(the)f
(Airy)h(function)f(Bi\(x\).)390 1824 y Fg(err)36 b Fk(con)m(tains)c(an)
e(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 1961 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1981
V 390 2070 a Fk(for)30 b(do)s(cumen)m(tation.)275 2259
y(\037airy_zero_Ai_deriv)i(-*-)f(texinfo)g(-*-)2960 2448
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(airy_zero_Ai_deriv)e Fi(\()p Fh(n)12 b Fi(\))2960 2558
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Ai_deriv)e
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 2667 y Fk(These)33
b(routines)f(compute)h(the)g(lo)s(cation)i(of)e(the)g(s-th)g(zero)g(of)
g(the)g(Airy)g(function)f(deriv)-5 b(ativ)m(e)390 2777
y(Ai\(x\).)390 2914 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f
(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b
Fg(y)p Fk(.)390 3051 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 3071 V
390 3160 a Fk(for)30 b(do)s(cumen)m(tation.)275 3349
y(\037airy_zero_Bi_deriv)i(-*-)f(texinfo)g(-*-)2960 3538
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(airy_zero_Bi_deriv)e Fi(\()p Fh(n)12 b Fi(\))2960 3648
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(airy_zero_Bi_deriv)e
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 3757 y Fk(These)33
b(routines)f(compute)h(the)g(lo)s(cation)i(of)e(the)g(s-th)g(zero)g(of)
g(the)g(Airy)g(function)f(deriv)-5 b(ativ)m(e)390 3867
y(Bi\(x\).)390 4004 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f
(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b
Fg(y)p Fk(.)390 4141 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 4161 V
390 4250 a Fk(for)30 b(do)s(cumen)m(tation.)275 4439
y(\037b)s(essel_zero_J0)h(-*-)g(texinfo)g(-*-)2960 4628
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(bessel_zero_J0)c Fi(\()p Fh(n)12 b Fi(\))2960 4738
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_zero_J0)d
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 4847 y Fk(These)34
b(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g(s-th)g(p)s
(ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function)390
4957 y(J_0\(x\).)390 5094 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i
(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 5230 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 5251 V
390 5340 a Fk(for)30 b(do)s(cumen)m(tation.)p eop end
%%Page: 25 25
TeXDict begin 25 24 bop 275 299 a Fk(\037b)s(essel_zero_J1)31
b(-*-)g(texinfo)g(-*-)2960 482 y([Loadable)g(F)-8 b(unction])-3599
b Fh(y)64 b Fj(=)53 b(bessel_zero_J1)c Fi(\()p Fh(n)12
b Fi(\))2960 592 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(bessel_zero_J1)d
Fi(\()6 b Fg(.)22 b(.)g(.)11 b Fi(\))390 702 y Fk(These)34
b(routines)g(compute)g(the)g(lo)s(cation)i(of)e(the)g(s-th)g(p)s
(ositiv)m(e)h(zero)g(of)f(the)g(Bessel)h(function)390
811 y(J_1\(x\).)390 945 y Fg(err)h Fk(con)m(tains)c(an)e(estimate)i(of)
f(the)g(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31
b Fg(y)p Fk(.)390 1080 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h
(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f Ff
(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 1100 42
84 v 390 1189 a Fk(for)30 b(do)s(cumen)m(tation.)275
1373 y(\037psi_1_in)m(t)h(-*-)g(texinfo)g(-*-)2960 1556
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(psi_1_int)48 b Fi(\()p Fh(n)12 b Fi(\))2960 1666 y
Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(psi_1_int)48 b Fi(\()6
b Fg(.)22 b(.)g(.)12 b Fi(\))390 1776 y Fk(These)30 b(routines)g
(compute)h(the)g(T)-8 b(rigamma)31 b(function)f(psi\(n\))g(for)g(p)s
(ositiv)m(e)h(in)m(teger)h(n.)390 1910 y Fg(err)k Fk(con)m(tains)c(an)e
(estimate)i(of)f(the)g(absolute)g(error)f(in)g(the)g(v)-5
b(alue)31 b Fg(y)p Fk(.)390 2044 y(This)19 b(function)h(is)h(from)f
(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8 b(,)22 b(see)f
Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p 3977 2064
V 390 2154 a Fk(for)30 b(do)s(cumen)m(tation.)275 2337
y(\037zeta_in)m(t)i(-*-)f(texinfo)g(-*-)2960 2521 y([Loadable)g(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(zeta_int)48 b
Fi(\()p Fh(n)12 b Fi(\))2960 2630 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12
b Fj(])53 b(=)g(zeta_int)48 b Fi(\()6 b Fg(.)22 b(.)g(.)11
b Fi(\))390 2740 y Fk(These)30 b(routines)g(compute)h(the)g(Riemann)f
(zeta)i(function)e(zeta\(n\))i(for)e(in)m(teger)i(n,)e(n)g(e)g(1.)390
2874 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 3008 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 3029 V 390 3118 a Fk(for)30 b(do)s(cumen)m(tation.)
275 3302 y(\037eta_in)m(t)i(-*-)f(texinfo)g(-*-)2960
3485 y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b
Fj(=)53 b(eta_int)47 b Fi(\()p Fh(n)12 b Fi(\))2960 3595
y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p Fh(y)p
Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(eta_int)47 b Fi(\()6
b Fg(.)23 b(.)f(.)11 b Fi(\))390 3704 y Fk(These)30 b(routines)g
(compute)h(the)g(eta)g(function)f(eta\(n\))i(for)e(in)m(teger)i(n.)390
3839 y Fg(err)k Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g
(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
3973 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 3993 V 390 4082 a Fk(for)30 b(do)s(cumen)m(tation.)275
4266 y(\037legendre_Plm)g(-*-)i(texinfo)f(-*-)2960 4450
y([Loadable)g(F)-8 b(unction])-3599 b Fh(y)64 b Fj(=)53
b(legendre_Plm)c Fi(\()p Fh(n)p Fg(,)31 b Fh(m)p Fg(,)g
Fh(x)12 b Fi(\))2960 4559 y Fk([Loadable)31 b(F)-8 b(unction])-3599
b Fj([)p Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_Plm)c
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 4669 y Fk(These)32
b(routines)g(compute)h(the)g(asso)s(ciated)g(Legendre)g(p)s(olynomial)f
(P_l)p Ff(^)p Fk(m\(x\))h(for)f(m)h Ff(>)p Fk(=)e(0,)j(l)390
4778 y Ff(>)p Fk(=)c(m,)g Ff(|)p Fk(x)p Ff(|)g(<)p Fk(=)g(1.)390
4913 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g
(absolute)g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p
Fk(.)390 5047 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m
(ti\014c)g(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o
(re/g)o(sl/)p 3977 5067 V 390 5156 a Fk(for)30 b(do)s(cumen)m(tation.)
275 5340 y(\037legendre_sphPlm)f(-*-)i(texinfo)g(-*-)p
eop end
%%Page: 26 26
TeXDict begin 26 25 bop 2960 299 a Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fh(y)64 b Fj(=)53 b(legendre_sphPlm)d
Fi(\()p Fh(n)p Fg(,)31 b Fh(m)p Fg(,)g Fh(x)12 b Fi(\))2960
408 y Fk([Loadable)31 b(F)-8 b(unction])-3599 b Fj([)p
Fh(y)p Fj(,)53 b Fh(err)12 b Fj(])53 b(=)g(legendre_sphPlm)d
Fi(\()6 b Fg(.)22 b(.)g(.)12 b Fi(\))390 518 y Fk(These)101
b(routines)g(compute)g(the)g(normalized)h(asso)s(ciated)h(Legendre)e(p)
s(olynomial)390 628 y($sqrt)p Ff({)p Fk(\(2l+1\)/\(4pi\))p
Ff(})61 b Fk(sqrt)p Ff({)p Fk(\(l-m\)!/\(l+m\)!)p Ff(})f
Fk(P_l)p Ff(^)p Fk(m\(x\)$)g(suitable)f(for)f(use)g(in)h(spherical)390
737 y(harmonics.)40 b(The)28 b(parameters)i(m)m(ust)e(satisfy)i(m)e
Ff(>)p Fk(=)g(0,)i(l)f Ff(>)p Fk(=)f(m,)i Ff(|)p Fk(x)p
Ff(|)e(<)p Fk(=)g(1.)41 b(Theses)28 b(routines)390 847
y(a)m(v)m(oid)k(the)e(o)m(v)m(er\015o)m(ws)i(that)f(o)s(ccur)f(for)g
(the)h(standard)f(normalization)i(of)e(P_l)p Ff(^)p Fk(m\(x\).)390
981 y Fg(err)36 b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)
g(error)f(in)g(the)g(v)-5 b(alue)31 b Fg(y)p Fk(.)390
1116 y(This)19 b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g
(Library)-8 b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 1136 42 84 v 390 1225 a Fk(for)30 b(do)s(cumen)m(tation.)275
1410 y(\037h)m(yp)s(erg_U)f(-*-)j(texinfo)f(-*-)2960
1594 y([Loadable)g(F)-8 b(unction])-3599 b Fh(out)65
b Fj(=)52 b(hyperg_U)c Fi(\()p Fh(x0)p Fg(,)32 b Fh(x1)p
Fg(,)f Fh(x2)12 b Fi(\))2960 1704 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(out)p Fj(,)54 b Fh(err)12
b Fj(])53 b(=)f(hyperg_U)c Fi(\()6 b Fg(.)23 b(.)f(.)11
b Fi(\))390 1813 y Fk(Secondary)28 b(Con\015uen)m(t)g(Hyp)s(ergo)s
(emetric)h(U)g(function)f(A&E)g(13.1.3)i(All)f(input)f(are)h(double)f
(as)390 1923 y(is)i(the)h(output.)390 2057 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(out)p Fk(.a.)390 2192 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 2212 V 390 2301 a Fk(for)30 b(do)s(cumen)m(tation.)275
2486 y(\037h)m(yp)s(erg_1F1)h(-*-)g(texinfo)g(-*-)2960
2670 y([Loadable)g(F)-8 b(unction])-3599 b Fh(out)65
b Fj(=)52 b(hyperg_1F1)d Fi(\()p Fh(x0)p Fg(,)31 b Fh(x1)p
Fg(,)h Fh(x2)12 b Fi(\))2960 2780 y Fk([Loadable)31 b(F)-8
b(unction])-3599 b Fj([)p Fh(out)p Fj(,)54 b Fh(err)12
b Fj(])53 b(=)f(hyperg_1F1)d Fi(\()6 b Fg(.)22 b(.)g(.)12
b Fi(\))390 2889 y Fk(Primary)32 b(Con\015uen)m(t)f(Hyp)s(ergo)s
(emetric)j(U)e(function)g(A&E)g(13.1.3)j(All)e(inputs)e(are)i(double)f
(as)390 2999 y(is)e(the)h(output.)390 3133 y Fg(err)36
b Fk(con)m(tains)c(an)e(estimate)i(of)f(the)g(absolute)g(error)f(in)g
(the)g(v)-5 b(alue)31 b Fg(out)p Fk(.a.)390 3268 y(This)19
b(function)h(is)h(from)f(the)g(GNU)h(Scien)m(ti\014c)g(Library)-8
b(,)22 b(see)f Ff(http://www.gnu.org/softwa)o(re/g)o(sl/)p
3977 3288 V 390 3377 a Fk(for)30 b(do)s(cumen)m(tation.)p
eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF