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
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17         Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
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19       Log[Gamma(x)], x not a negative integer Uses real Lanczos method.
20       Determines the sign of Gamma[x] as well as Log[⎪Gamma[x]⎪] for x < 0.
21       So Gamma[x] = sgn * Exp[result_lg].
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23       gsl_sf_gamma
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25         Signature: (double x(); double [o]y(); double [o]e())
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27       Gamma(x), x not a negative integer
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29       gsl_sf_gammastar
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31         Signature: (double x(); double [o]y(); double [o]e())
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33       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi]
34       x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf
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36       gsl_sf_gammainv
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38         Signature: (double x(); double [o]y(); double [o]e())
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40       1/Gamma(x)
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42       gsl_sf_lngamma_complex
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44         Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
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46       Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr
47       = log⎪Gamma(z)⎪, arg = arg(Gamma(z))  in (-Pi, Pi]
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49       gsl_sf_taylorcoeff
50
51         Signature: (double x(); double [o]y(); double [o]e(); int n)
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53       x^n / n!
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55       gsl_sf_fact
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57         Signature: (x(); double [o]y(); double [o]e())
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59       n!
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61       gsl_sf_doublefact
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63         Signature: (x(); double [o]y(); double [o]e())
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65       n!! = n(n-2)(n-4)
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67       gsl_sf_lnfact
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69         Signature: (x(); double [o]y(); double [o]e())
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71       ln n!
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73       gsl_sf_lndoublefact
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75         Signature: (x(); double [o]y(); double [o]e())
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77       ln n!!
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79       gsl_sf_lnchoose
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81         Signature: (n(); m(); double [o]y(); double [o]e())
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83       log(n choose m)
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85       gsl_sf_choose
86
87         Signature: (n(); m(); double [o]y(); double [o]e())
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89       n choose m
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91       gsl_sf_lnpoch
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93         Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
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95       Logarithm of Pochammer (Apell) symbol, with sign information. result =
96       log( ⎪(a)_x⎪ ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a +
97       x]/Gamma[a]
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99       gsl_sf_poch
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101         Signature: (double x(); double [o]y(); double [o]e(); double a)
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103       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
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105       gsl_sf_pochrel
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107         Signature: (double x(); double [o]y(); double [o]e(); double a)
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109       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x :=
110       Gamma[a + x]/Gamma[a]
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112       gsl_sf_gamma_inc_Q
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114         Signature: (double x(); double [o]y(); double [o]e(); double a)
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116       Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[
117       t^(a-1) e^(-t), {t,x,Infinity} ]
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119       gsl_sf_gamma_inc_P
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121         Signature: (double x(); double [o]y(); double [o]e(); double a)
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123       Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a)
124       Integral[ t^(a-1) e^(-t), {t,0,x} ]
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126       gsl_sf_lnbeta
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128         Signature: (double a(); double b(); double [o]y(); double [o]e())
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130       Logarithm of Beta Function Log[B(a,b)]
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132       gsl_sf_beta
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134         Signature: (double a(); double b();double [o]y(); double [o]e())
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136       Beta Function B(a,b)
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AUTHOR

139       This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.tri‐
140       este.it> All rights reserved. There is no warranty. You are allowed to
141       redistribute this software / documentation under certain conditions.
142       For details, see the file COPYING in the PDL distribution. If this file
143       is separated from the PDL distribution, the copyright notice should be
144       included in the file.
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146       The GSL SF modules were written by G. Jungman.
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150perl v5.8.8                       2006-12-02                          GAMMA(3)