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

NAME

6       PDL::GSLSF::HYPERG - 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_hyperg_0F1
15         Signature: (double x(); double [o]y(); double [o]e(); double c)
16
17       /* Hypergeometric function related to Bessel functions 0F1[c,x] =
18       Gamma[c]    x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c))
19       J_{c-1}(2 Sqrt[-x])
20
21       gsl_sf_hyperg_0F1 does not process bad values.  It will set the bad-
22       value flag of all output piddles if the flag is set for any of the
23       input piddles.
24
25   gsl_sf_hyperg_1F1
26         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
27
28       Confluent hypergeometric function  for integer parameters. 1F1[a,b,x] =
29       M(a,b,x)
30
31       gsl_sf_hyperg_1F1 does not process bad values.  It will set the bad-
32       value flag of all output piddles if the flag is set for any of the
33       input piddles.
34
35   gsl_sf_hyperg_U
36         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
37
38       Confluent hypergeometric function  for integer parameters. U(a,b,x)
39
40       gsl_sf_hyperg_U does not process bad values.  It will set the bad-value
41       flag of all output piddles if the flag is set for any of the input
42       piddles.
43
44   gsl_sf_hyperg_2F1
45         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
46
47       Confluent hypergeometric function  for integer parameters. 2F1[a,b,c,x]
48
49       gsl_sf_hyperg_2F1 does not process bad values.  It will set the bad-
50       value flag of all output piddles if the flag is set for any of the
51       input piddles.
52
53   gsl_sf_hyperg_2F1_conj
54         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
55
56       Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]
57
58       gsl_sf_hyperg_2F1_conj does not process bad values.  It will set the
59       bad-value flag of all output piddles if the flag is set for any of the
60       input piddles.
61
62   gsl_sf_hyperg_2F1_renorm
63         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
64
65       Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]
66
67       gsl_sf_hyperg_2F1_renorm does not process bad values.  It will set the
68       bad-value flag of all output piddles if the flag is set for any of the
69       input piddles.
70
71   gsl_sf_hyperg_2F1_conj_renorm
72         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
73
74       Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c,
75       x] / Gamma[c]
76
77       gsl_sf_hyperg_2F1_conj_renorm does not process bad values.  It will set
78       the bad-value flag of all output piddles if the flag is set for any of
79       the input piddles.
80
81   gsl_sf_hyperg_2F0
82         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
83
84       Mysterious hypergeometric function. The series representation is a
85       divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x)
86       = (-1/x)^a U(a,1+a-b,-1/x)
87
88       gsl_sf_hyperg_2F0 does not process bad values.  It will set the bad-
89       value flag of all output piddles if the flag is set for any of the
90       input piddles.
91

AUTHOR

93       This file copyright (C) 1999 Christian Pellegrin
94       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
95       You are allowed to redistribute this software / documentation under
96       certain conditions. For details, see the file COPYING in the PDL
97       distribution. If this file is separated from the PDL distribution, the
98       copyright notice should be included in the file.
99
100       The GSL SF modules were written by G. Jungman.
101
102
103
104perl v5.30.0                      2019-09-05                         HYPERG(3)