PDL::GSLSF::GAMMA(3pm)

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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FUNCTIONS

13   gsl_sf_lngamma
14         Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
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16       Log[Gamma(x)], x not a negative integer Uses real Lanczos method.
17       Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0.
18       So Gamma[x] = sgn * Exp[result_lg].
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20       gsl_sf_lngamma does not process bad values.  It will set the bad-value
21       flag of all output ndarrays if the flag is set for any of the input
22       ndarrays.
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24   gsl_sf_gamma
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_gamma does not process bad values.  It will set the bad-value
30       flag of all output ndarrays if the flag is set for any of the input
31       ndarrays.
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33   gsl_sf_gammastar
34         Signature: (double x(); double [o]y(); double [o]e())
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36       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi]
37       x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf
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39       gsl_sf_gammastar does not process bad values.  It will set the bad-
40       value flag of all output ndarrays if the flag is set for any of the
41       input ndarrays.
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43   gsl_sf_gammainv
44         Signature: (double x(); double [o]y(); double [o]e())
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46       1/Gamma(x)
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48       gsl_sf_gammainv does not process bad values.  It will set the bad-value
49       flag of all output ndarrays if the flag is set for any of the input
50       ndarrays.
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52   gsl_sf_lngamma_complex
53         Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
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55       Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr
56       = log|Gamma(z)|, arg = arg(Gamma(z))  in (-Pi, Pi]
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58       gsl_sf_lngamma_complex does not process bad values.  It will set the
59       bad-value flag of all output ndarrays if the flag is set for any of the
60       input ndarrays.
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62   gsl_sf_taylorcoeff
63         Signature: (double x(); double [o]y(); double [o]e(); int n)
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65       x^n / n!
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67       gsl_sf_taylorcoeff does not process bad values.  It will set the bad-
68       value flag of all output ndarrays if the flag is set for any of the
69       input ndarrays.
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71   gsl_sf_fact
72         Signature: (x(); double [o]y(); double [o]e())
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74       n!
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76       gsl_sf_fact does not process bad values.  It will set the bad-value
77       flag of all output ndarrays if the flag is set for any of the input
78       ndarrays.
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80   gsl_sf_doublefact
81         Signature: (x(); double [o]y(); double [o]e())
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83       n!! = n(n-2)(n-4)
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85       gsl_sf_doublefact does not process bad values.  It will set the bad-
86       value flag of all output ndarrays if the flag is set for any of the
87       input ndarrays.
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89   gsl_sf_lnfact
90         Signature: (x(); double [o]y(); double [o]e())
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92       ln n!
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94       gsl_sf_lnfact does not process bad values.  It will set the bad-value
95       flag of all output ndarrays if the flag is set for any of the input
96       ndarrays.
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98   gsl_sf_lndoublefact
99         Signature: (x(); double [o]y(); double [o]e())
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101       ln n!!
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103       gsl_sf_lndoublefact does not process bad values.  It will set the bad-
104       value flag of all output ndarrays if the flag is set for any of the
105       input ndarrays.
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107   gsl_sf_lnchoose
108         Signature: (n(); m(); double [o]y(); double [o]e())
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110       log(n choose m)
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112       gsl_sf_lnchoose does not process bad values.  It will set the bad-value
113       flag of all output ndarrays if the flag is set for any of the input
114       ndarrays.
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116   gsl_sf_choose
117         Signature: (n(); m(); double [o]y(); double [o]e())
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119       n choose m
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121       gsl_sf_choose does not process bad values.  It will set the bad-value
122       flag of all output ndarrays if the flag is set for any of the input
123       ndarrays.
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125   gsl_sf_lnpoch
126         Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
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128       Logarithm of Pochammer (Apell) symbol, with sign information. result =
129       log( |(a)_x| ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a +
130       x]/Gamma[a]
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132       gsl_sf_lnpoch does not process bad values.  It will set the bad-value
133       flag of all output ndarrays if the flag is set for any of the input
134       ndarrays.
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136   gsl_sf_poch
137         Signature: (double x(); double [o]y(); double [o]e(); double a)
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139       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
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141       gsl_sf_poch does not process bad values.  It will set the bad-value
142       flag of all output ndarrays if the flag is set for any of the input
143       ndarrays.
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145   gsl_sf_pochrel
146         Signature: (double x(); double [o]y(); double [o]e(); double a)
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148       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x :=
149       Gamma[a + x]/Gamma[a]
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151       gsl_sf_pochrel does not process bad values.  It will set the bad-value
152       flag of all output ndarrays if the flag is set for any of the input
153       ndarrays.
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155   gsl_sf_gamma_inc_Q
156         Signature: (double x(); double [o]y(); double [o]e(); double a)
157
158       Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[
159       t^(a-1) e^(-t), {t,x,Infinity} ]
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161       gsl_sf_gamma_inc_Q does not process bad values.  It will set the bad-
162       value flag of all output ndarrays if the flag is set for any of the
163       input ndarrays.
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165   gsl_sf_gamma_inc_P
166         Signature: (double x(); double [o]y(); double [o]e(); double a)
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168       Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a)
169       Integral[ t^(a-1) e^(-t), {t,0,x} ]
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171       gsl_sf_gamma_inc_P does not process bad values.  It will set the bad-
172       value flag of all output ndarrays if the flag is set for any of the
173       input ndarrays.
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175   gsl_sf_lnbeta
176         Signature: (double a(); double b(); double [o]y(); double [o]e())
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178       Logarithm of Beta Function Log[B(a,b)]
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180       gsl_sf_lnbeta does not process bad values.  It will set the bad-value
181       flag of all output ndarrays if the flag is set for any of the input
182       ndarrays.
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184   gsl_sf_beta
185         Signature: (double a(); double b();double [o]y(); double [o]e())
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187       Beta Function B(a,b)
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189       gsl_sf_beta does not process bad values.  It will set the bad-value
190       flag of all output ndarrays if the flag is set for any of the input
191       ndarrays.
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AUTHOR

194       This file copyright (C) 1999 Christian Pellegrin
195       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
196       You are allowed to redistribute this software / documentation under
197       certain conditions. For details, see the file COPYING in the PDL
198       distribution. If this file is separated from the PDL distribution, the
199       copyright notice should be included in the file.
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201       The GSL SF modules were written by G. Jungman.
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205perl v5.38.0                      2023-07-21                          GAMMA(3)