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

14   gsl_sf_lngamma
15         Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
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17       Log[Gamma(x)], x not a negative integer Uses real Lanczos method.
18       Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0.
19       So Gamma[x] = sgn * Exp[result_lg].
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21       gsl_sf_lngamma does not process bad values.  It will set the bad-value
22       flag of all output ndarrays if the flag is set for any of the input
23       ndarrays.
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25   gsl_sf_gamma
26         Signature: (double x(); double [o]y(); double [o]e())
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28       Gamma(x), x not a negative integer
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30       gsl_sf_gamma does not process bad values.  It will set the bad-value
31       flag of all output ndarrays if the flag is set for any of the input
32       ndarrays.
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34   gsl_sf_gammastar
35         Signature: (double x(); double [o]y(); double [o]e())
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37       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi]
38       x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf
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40       gsl_sf_gammastar does not process bad values.  It will set the bad-
41       value flag of all output ndarrays if the flag is set for any of the
42       input ndarrays.
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44   gsl_sf_gammainv
45         Signature: (double x(); double [o]y(); double [o]e())
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47       1/Gamma(x)
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49       gsl_sf_gammainv does not process bad values.  It will set the bad-value
50       flag of all output ndarrays if the flag is set for any of the input
51       ndarrays.
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53   gsl_sf_lngamma_complex
54         Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
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56       Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr
57       = log|Gamma(z)|, arg = arg(Gamma(z))  in (-Pi, Pi]
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59       gsl_sf_lngamma_complex does not process bad values.  It will set the
60       bad-value flag of all output ndarrays if the flag is set for any of the
61       input ndarrays.
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63   gsl_sf_taylorcoeff
64         Signature: (double x(); double [o]y(); double [o]e(); int n)
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66       x^n / n!
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68       gsl_sf_taylorcoeff does not process bad values.  It will set the bad-
69       value flag of all output ndarrays if the flag is set for any of the
70       input ndarrays.
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72   gsl_sf_fact
73         Signature: (x(); double [o]y(); double [o]e())
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75       n!
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77       gsl_sf_fact does not process bad values.  It will set the bad-value
78       flag of all output ndarrays if the flag is set for any of the input
79       ndarrays.
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81   gsl_sf_doublefact
82         Signature: (x(); double [o]y(); double [o]e())
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84       n!! = n(n-2)(n-4)
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86       gsl_sf_doublefact does not process bad values.  It will set the bad-
87       value flag of all output ndarrays if the flag is set for any of the
88       input ndarrays.
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90   gsl_sf_lnfact
91         Signature: (x(); double [o]y(); double [o]e())
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93       ln n!
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95       gsl_sf_lnfact does not process bad values.  It will set the bad-value
96       flag of all output ndarrays if the flag is set for any of the input
97       ndarrays.
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99   gsl_sf_lndoublefact
100         Signature: (x(); double [o]y(); double [o]e())
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102       ln n!!
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104       gsl_sf_lndoublefact does not process bad values.  It will set the bad-
105       value flag of all output ndarrays if the flag is set for any of the
106       input ndarrays.
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108   gsl_sf_lnchoose
109         Signature: (n(); m(); double [o]y(); double [o]e())
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111       log(n choose m)
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113       gsl_sf_lnchoose does not process bad values.  It will set the bad-value
114       flag of all output ndarrays if the flag is set for any of the input
115       ndarrays.
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117   gsl_sf_choose
118         Signature: (n(); m(); double [o]y(); double [o]e())
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120       n choose m
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122       gsl_sf_choose does not process bad values.  It will set the bad-value
123       flag of all output ndarrays if the flag is set for any of the input
124       ndarrays.
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126   gsl_sf_lnpoch
127         Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
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129       Logarithm of Pochammer (Apell) symbol, with sign information. result =
130       log( |(a)_x| ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a +
131       x]/Gamma[a]
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133       gsl_sf_lnpoch does not process bad values.  It will set the bad-value
134       flag of all output ndarrays if the flag is set for any of the input
135       ndarrays.
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137   gsl_sf_poch
138         Signature: (double x(); double [o]y(); double [o]e(); double a)
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140       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
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142       gsl_sf_poch does not process bad values.  It will set the bad-value
143       flag of all output ndarrays if the flag is set for any of the input
144       ndarrays.
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146   gsl_sf_pochrel
147         Signature: (double x(); double [o]y(); double [o]e(); double a)
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149       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x :=
150       Gamma[a + x]/Gamma[a]
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152       gsl_sf_pochrel does not process bad values.  It will set the bad-value
153       flag of all output ndarrays if the flag is set for any of the input
154       ndarrays.
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156   gsl_sf_gamma_inc_Q
157         Signature: (double x(); double [o]y(); double [o]e(); double a)
158
159       Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[
160       t^(a-1) e^(-t), {t,x,Infinity} ]
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162       gsl_sf_gamma_inc_Q does not process bad values.  It will set the bad-
163       value flag of all output ndarrays if the flag is set for any of the
164       input ndarrays.
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166   gsl_sf_gamma_inc_P
167         Signature: (double x(); double [o]y(); double [o]e(); double a)
168
169       Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a)
170       Integral[ t^(a-1) e^(-t), {t,0,x} ]
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172       gsl_sf_gamma_inc_P does not process bad values.  It will set the bad-
173       value flag of all output ndarrays if the flag is set for any of the
174       input ndarrays.
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176   gsl_sf_lnbeta
177         Signature: (double a(); double b(); double [o]y(); double [o]e())
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179       Logarithm of Beta Function Log[B(a,b)]
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181       gsl_sf_lnbeta does not process bad values.  It will set the bad-value
182       flag of all output ndarrays if the flag is set for any of the input
183       ndarrays.
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185   gsl_sf_beta
186         Signature: (double a(); double b();double [o]y(); double [o]e())
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188       Beta Function B(a,b)
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190       gsl_sf_beta does not process bad values.  It will set the bad-value
191       flag of all output ndarrays if the flag is set for any of the input
192       ndarrays.
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AUTHOR

195       This file copyright (C) 1999 Christian Pellegrin
196       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
197       You are allowed to redistribute this software / documentation under
198       certain conditions. For details, see the file COPYING in the PDL
199       distribution. If this file is separated from the PDL distribution, the
200       copyright notice should be included in the file.
201
202       The GSL SF modules were written by G. Jungman.
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206perl v5.34.0                      2021-08-16                          GAMMA(3)