1GAMMA(3) User Contributed Perl Documentation GAMMA(3)
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6 PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions
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9 This is an interface to the Special Function package present in the GNU
10 Scientific Library.
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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)
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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
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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)
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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)
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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)
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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)
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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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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.
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203 The GSL SF modules were written by G. Jungman.
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207perl v5.12.3 2011-03-31 GAMMA(3)