PDL::GSLSF::GAMMA(3pm)

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

FUNCTIONS

13   gsl_sf_lngamma
14         Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
15
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].
19
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.
23
24   gsl_sf_gamma
25         Signature: (double x(); double [o]y(); double [o]e())
26
27       Gamma(x), x not a negative integer
28
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.
32
33   gsl_sf_gammastar
34         Signature: (double x(); double [o]y(); double [o]e())
35
36       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi]
37       x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf
38
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.
42
43   gsl_sf_gammainv
44         Signature: (double x(); double [o]y(); double [o]e())
45
46       1/Gamma(x)
47
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.
51
52   gsl_sf_lngamma_complex
53         Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
54
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]
57
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.
61
62   gsl_sf_taylorcoeff
63         Signature: (double x(); double [o]y(); double [o]e(); int n)
64
65       x^n / n!
66
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.
70
71   gsl_sf_fact
72         Signature: (x(); double [o]y(); double [o]e())
73
74       n!
75
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.
79
80   gsl_sf_doublefact
81         Signature: (x(); double [o]y(); double [o]e())
82
83       n!! = n(n-2)(n-4)
84
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.
88
89   gsl_sf_lnfact
90         Signature: (x(); double [o]y(); double [o]e())
91
92       ln n!
93
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.
97
98   gsl_sf_lndoublefact
99         Signature: (x(); double [o]y(); double [o]e())
100
101       ln n!!
102
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.
106
107   gsl_sf_lnchoose
108         Signature: (n(); m(); double [o]y(); double [o]e())
109
110       log(n choose m)
111
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.
115
116   gsl_sf_choose
117         Signature: (n(); m(); double [o]y(); double [o]e())
118
119       n choose m
120
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.
124
125   gsl_sf_lnpoch
126         Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
127
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]
131
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.
135
136   gsl_sf_poch
137         Signature: (double x(); double [o]y(); double [o]e(); double a)
138
139       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
140
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.
144
145   gsl_sf_pochrel
146         Signature: (double x(); double [o]y(); double [o]e(); double a)
147
148       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x :=
149       Gamma[a + x]/Gamma[a]
150
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.
154
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} ]
160
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.
164
165   gsl_sf_gamma_inc_P
166         Signature: (double x(); double [o]y(); double [o]e(); double a)
167
168       Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a)
169       Integral[ t^(a-1) e^(-t), {t,0,x} ]
170
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.
174
175   gsl_sf_lnbeta
176         Signature: (double a(); double b(); double [o]y(); double [o]e())
177
178       Logarithm of Beta Function Log[B(a,b)]
179
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.
183
184   gsl_sf_beta
185         Signature: (double a(); double b();double [o]y(); double [o]e())
186
187       Beta Function B(a,b)
188
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.
192

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.
200
201       The GSL SF modules were written by G. Jungman.
202
203
204
205perl v5.36.0                      2022-07-22                          GAMMA(3)