1HYPERG(3)             User Contributed Perl Documentation            HYPERG(3)
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NAME

6       PDL::GSLSF::HYPERG - 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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FUNCTIONS

13   gsl_sf_hyperg_0F1
14         Signature: (double x(); double [o]y(); double [o]e(); double c)
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16       /* Hypergeometric function related to Bessel functions 0F1[c,x] =
17       Gamma[c]    x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c))
18       J_{c-1}(2 Sqrt[-x])
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20       gsl_sf_hyperg_0F1 does not process bad values.  It will set the bad-
21       value flag of all output ndarrays if the flag is set for any of the
22       input ndarrays.
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24   gsl_sf_hyperg_1F1
25         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
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27       Confluent hypergeometric function  for integer parameters. 1F1[a,b,x] =
28       M(a,b,x)
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30       gsl_sf_hyperg_1F1 does not process bad values.  It will set the bad-
31       value flag of all output ndarrays if the flag is set for any of the
32       input ndarrays.
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34   gsl_sf_hyperg_U
35         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
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37       Confluent hypergeometric function  for integer parameters. U(a,b,x)
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39       gsl_sf_hyperg_U does not process bad values.  It will set the bad-value
40       flag of all output ndarrays if the flag is set for any of the input
41       ndarrays.
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43   gsl_sf_hyperg_2F1
44         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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46       Confluent hypergeometric function  for integer parameters. 2F1[a,b,c,x]
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48       gsl_sf_hyperg_2F1 does not process bad values.  It will set the bad-
49       value flag of all output ndarrays if the flag is set for any of the
50       input ndarrays.
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52   gsl_sf_hyperg_2F1_conj
53         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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55       Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]
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57       gsl_sf_hyperg_2F1_conj does not process bad values.  It will set the
58       bad-value flag of all output ndarrays if the flag is set for any of the
59       input ndarrays.
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61   gsl_sf_hyperg_2F1_renorm
62         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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64       Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]
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66       gsl_sf_hyperg_2F1_renorm does not process bad values.  It will set the
67       bad-value flag of all output ndarrays if the flag is set for any of the
68       input ndarrays.
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70   gsl_sf_hyperg_2F1_conj_renorm
71         Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
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73       Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c,
74       x] / Gamma[c]
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76       gsl_sf_hyperg_2F1_conj_renorm does not process bad values.  It will set
77       the bad-value flag of all output ndarrays if the flag is set for any of
78       the input ndarrays.
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80   gsl_sf_hyperg_2F0
81         Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
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83       Mysterious hypergeometric function. The series representation is a
84       divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x)
85       = (-1/x)^a U(a,1+a-b,-1/x)
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87       gsl_sf_hyperg_2F0 does not process bad values.  It will set the bad-
88       value flag of all output ndarrays if the flag is set for any of the
89       input ndarrays.
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AUTHOR

92       This file copyright (C) 1999 Christian Pellegrin
93       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
94       You are allowed to redistribute this software / documentation under
95       certain conditions. For details, see the file COPYING in the PDL
96       distribution. If this file is separated from the PDL distribution, the
97       copyright notice should be included in the file.
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99       The GSL SF modules were written by G. Jungman.
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103perl v5.36.0                      2023-01-20                         HYPERG(3)