1GAMMA(3)              User Contributed Perl Documentation             GAMMA(3)
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NAME

6       PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions
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DESCRIPTION

9       This is an interface to the Special Function package present in the GNU
10       Scientific Library.
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SYNOPSIS

Functions

FUNCTIONS

15   gsl_sf_lngamma
16         Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
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18       Log[Gamma(x)], x not a negative integer Uses real Lanczos method.
19       Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0.
20       So Gamma[x] = sgn * Exp[result_lg].
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22       gsl_sf_lngamma does not process bad values.  It will set the bad-value
23       flag of all output piddles if the flag is set for any of the input
24       piddles.
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26   gsl_sf_gamma
27         Signature: (double x(); double [o]y(); double [o]e())
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29       Gamma(x), x not a negative integer
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31       gsl_sf_gamma does not process bad values.  It will set the bad-value
32       flag of all output piddles if the flag is set for any of the input
33       piddles.
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35   gsl_sf_gammastar
36         Signature: (double x(); double [o]y(); double [o]e())
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38       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi]
39       x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf
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41       gsl_sf_gammastar does not process bad values.  It will set the bad-
42       value flag of all output piddles if the flag is set for any of the
43       input piddles.
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45   gsl_sf_gammainv
46         Signature: (double x(); double [o]y(); double [o]e())
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48       1/Gamma(x)
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50       gsl_sf_gammainv does not process bad values.  It will set the bad-value
51       flag of all output piddles if the flag is set for any of the input
52       piddles.
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54   gsl_sf_lngamma_complex
55         Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
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57       Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr
58       = log|Gamma(z)|, arg = arg(Gamma(z))  in (-Pi, Pi]
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60       gsl_sf_lngamma_complex does not process bad values.  It will set the
61       bad-value flag of all output piddles if the flag is set for any of the
62       input piddles.
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64   gsl_sf_taylorcoeff
65         Signature: (double x(); double [o]y(); double [o]e(); int n)
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67       x^n / n!
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69       gsl_sf_taylorcoeff does not process bad values.  It will set the bad-
70       value flag of all output piddles if the flag is set for any of the
71       input piddles.
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73   gsl_sf_fact
74         Signature: (x(); double [o]y(); double [o]e())
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76       n!
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78       gsl_sf_fact does not process bad values.  It will set the bad-value
79       flag of all output piddles if the flag is set for any of the input
80       piddles.
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82   gsl_sf_doublefact
83         Signature: (x(); double [o]y(); double [o]e())
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85       n!! = n(n-2)(n-4)
86
87       gsl_sf_doublefact does not process bad values.  It will set the bad-
88       value flag of all output piddles if the flag is set for any of the
89       input piddles.
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91   gsl_sf_lnfact
92         Signature: (x(); double [o]y(); double [o]e())
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94       ln n!
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96       gsl_sf_lnfact does not process bad values.  It will set the bad-value
97       flag of all output piddles if the flag is set for any of the input
98       piddles.
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100   gsl_sf_lndoublefact
101         Signature: (x(); double [o]y(); double [o]e())
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103       ln n!!
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105       gsl_sf_lndoublefact does not process bad values.  It will set the bad-
106       value flag of all output piddles if the flag is set for any of the
107       input piddles.
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109   gsl_sf_lnchoose
110         Signature: (n(); m(); double [o]y(); double [o]e())
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112       log(n choose m)
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114       gsl_sf_lnchoose does not process bad values.  It will set the bad-value
115       flag of all output piddles if the flag is set for any of the input
116       piddles.
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118   gsl_sf_choose
119         Signature: (n(); m(); double [o]y(); double [o]e())
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121       n choose m
122
123       gsl_sf_choose does not process bad values.  It will set the bad-value
124       flag of all output piddles if the flag is set for any of the input
125       piddles.
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127   gsl_sf_lnpoch
128         Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
129
130       Logarithm of Pochammer (Apell) symbol, with sign information. result =
131       log( |(a)_x| ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a +
132       x]/Gamma[a]
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134       gsl_sf_lnpoch does not process bad values.  It will set the bad-value
135       flag of all output piddles if the flag is set for any of the input
136       piddles.
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138   gsl_sf_poch
139         Signature: (double x(); double [o]y(); double [o]e(); double a)
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141       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
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143       gsl_sf_poch does not process bad values.  It will set the bad-value
144       flag of all output piddles if the flag is set for any of the input
145       piddles.
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147   gsl_sf_pochrel
148         Signature: (double x(); double [o]y(); double [o]e(); double a)
149
150       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x :=
151       Gamma[a + x]/Gamma[a]
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153       gsl_sf_pochrel does not process bad values.  It will set the bad-value
154       flag of all output piddles if the flag is set for any of the input
155       piddles.
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157   gsl_sf_gamma_inc_Q
158         Signature: (double x(); double [o]y(); double [o]e(); double a)
159
160       Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[
161       t^(a-1) e^(-t), {t,x,Infinity} ]
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163       gsl_sf_gamma_inc_Q does not process bad values.  It will set the bad-
164       value flag of all output piddles if the flag is set for any of the
165       input piddles.
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167   gsl_sf_gamma_inc_P
168         Signature: (double x(); double [o]y(); double [o]e(); double a)
169
170       Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a)
171       Integral[ t^(a-1) e^(-t), {t,0,x} ]
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173       gsl_sf_gamma_inc_P does not process bad values.  It will set the bad-
174       value flag of all output piddles if the flag is set for any of the
175       input piddles.
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177   gsl_sf_lnbeta
178         Signature: (double a(); double b(); double [o]y(); double [o]e())
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180       Logarithm of Beta Function Log[B(a,b)]
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182       gsl_sf_lnbeta does not process bad values.  It will set the bad-value
183       flag of all output piddles if the flag is set for any of the input
184       piddles.
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186   gsl_sf_beta
187         Signature: (double a(); double b();double [o]y(); double [o]e())
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189       Beta Function B(a,b)
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191       gsl_sf_beta does not process bad values.  It will set the bad-value
192       flag of all output piddles if the flag is set for any of the input
193       piddles.
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AUTHOR

196       This file copyright (C) 1999 Christian Pellegrin
197       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
198       You are allowed to redistribute this software / documentation under
199       certain conditions. For details, see the file COPYING in the PDL
200       distribution. If this file is separated from the PDL distribution, the
201       copyright notice should be included in the file.
202
203       The GSL SF modules were written by G. Jungman.
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207perl v5.12.3                      2011-03-31                          GAMMA(3)