1GAMMA(3)              User Contributed Perl Documentation             GAMMA(3)
2
3
4

NAME

6       PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions
7

DESCRIPTION

9       This is an interface to the Special Function package present in the GNU
10       Scientific Library.
11

SYNOPSIS

FUNCTIONS

14   gsl_sf_lngamma
15         Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
16
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].
20
21       gsl_sf_lngamma does not process bad values.  It will set the bad-value
22       flag of all output piddles if the flag is set for any of the input
23       piddles.
24
25   gsl_sf_gamma
26         Signature: (double x(); double [o]y(); double [o]e())
27
28       Gamma(x), x not a negative integer
29
30       gsl_sf_gamma does not process bad values.  It will set the bad-value
31       flag of all output piddles if the flag is set for any of the input
32       piddles.
33
34   gsl_sf_gammastar
35         Signature: (double x(); double [o]y(); double [o]e())
36
37       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi]
38       x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf
39
40       gsl_sf_gammastar does not process bad values.  It will set the bad-
41       value flag of all output piddles if the flag is set for any of the
42       input piddles.
43
44   gsl_sf_gammainv
45         Signature: (double x(); double [o]y(); double [o]e())
46
47       1/Gamma(x)
48
49       gsl_sf_gammainv does not process bad values.  It will set the bad-value
50       flag of all output piddles if the flag is set for any of the input
51       piddles.
52
53   gsl_sf_lngamma_complex
54         Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
55
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]
58
59       gsl_sf_lngamma_complex does not process bad values.  It will set the
60       bad-value flag of all output piddles if the flag is set for any of the
61       input piddles.
62
63   gsl_sf_taylorcoeff
64         Signature: (double x(); double [o]y(); double [o]e(); int n)
65
66       x^n / n!
67
68       gsl_sf_taylorcoeff does not process bad values.  It will set the bad-
69       value flag of all output piddles if the flag is set for any of the
70       input piddles.
71
72   gsl_sf_fact
73         Signature: (x(); double [o]y(); double [o]e())
74
75       n!
76
77       gsl_sf_fact does not process bad values.  It will set the bad-value
78       flag of all output piddles if the flag is set for any of the input
79       piddles.
80
81   gsl_sf_doublefact
82         Signature: (x(); double [o]y(); double [o]e())
83
84       n!! = n(n-2)(n-4)
85
86       gsl_sf_doublefact does not process bad values.  It will set the bad-
87       value flag of all output piddles if the flag is set for any of the
88       input piddles.
89
90   gsl_sf_lnfact
91         Signature: (x(); double [o]y(); double [o]e())
92
93       ln n!
94
95       gsl_sf_lnfact does not process bad values.  It will set the bad-value
96       flag of all output piddles if the flag is set for any of the input
97       piddles.
98
99   gsl_sf_lndoublefact
100         Signature: (x(); double [o]y(); double [o]e())
101
102       ln n!!
103
104       gsl_sf_lndoublefact does not process bad values.  It will set the bad-
105       value flag of all output piddles if the flag is set for any of the
106       input piddles.
107
108   gsl_sf_lnchoose
109         Signature: (n(); m(); double [o]y(); double [o]e())
110
111       log(n choose m)
112
113       gsl_sf_lnchoose does not process bad values.  It will set the bad-value
114       flag of all output piddles if the flag is set for any of the input
115       piddles.
116
117   gsl_sf_choose
118         Signature: (n(); m(); double [o]y(); double [o]e())
119
120       n choose m
121
122       gsl_sf_choose does not process bad values.  It will set the bad-value
123       flag of all output piddles if the flag is set for any of the input
124       piddles.
125
126   gsl_sf_lnpoch
127         Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
128
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]
132
133       gsl_sf_lnpoch does not process bad values.  It will set the bad-value
134       flag of all output piddles if the flag is set for any of the input
135       piddles.
136
137   gsl_sf_poch
138         Signature: (double x(); double [o]y(); double [o]e(); double a)
139
140       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
141
142       gsl_sf_poch does not process bad values.  It will set the bad-value
143       flag of all output piddles if the flag is set for any of the input
144       piddles.
145
146   gsl_sf_pochrel
147         Signature: (double x(); double [o]y(); double [o]e(); double a)
148
149       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x :=
150       Gamma[a + x]/Gamma[a]
151
152       gsl_sf_pochrel does not process bad values.  It will set the bad-value
153       flag of all output piddles if the flag is set for any of the input
154       piddles.
155
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} ]
161
162       gsl_sf_gamma_inc_Q does not process bad values.  It will set the bad-
163       value flag of all output piddles if the flag is set for any of the
164       input piddles.
165
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} ]
171
172       gsl_sf_gamma_inc_P does not process bad values.  It will set the bad-
173       value flag of all output piddles if the flag is set for any of the
174       input piddles.
175
176   gsl_sf_lnbeta
177         Signature: (double a(); double b(); double [o]y(); double [o]e())
178
179       Logarithm of Beta Function Log[B(a,b)]
180
181       gsl_sf_lnbeta does not process bad values.  It will set the bad-value
182       flag of all output piddles if the flag is set for any of the input
183       piddles.
184
185   gsl_sf_beta
186         Signature: (double a(); double b();double [o]y(); double [o]e())
187
188       Beta Function B(a,b)
189
190       gsl_sf_beta does not process bad values.  It will set the bad-value
191       flag of all output piddles if the flag is set for any of the input
192       piddles.
193

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.
203
204
205
206perl v5.32.0                      2020-09-17                          GAMMA(3)