.\" Automatically generated by Pod::Man 4.14 (Pod::Simple 3.43) .\" .\" Standard preamble: .\" ======================================================================== .de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. .de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. .de Ve \" End verbatim text .ft R .fi .. .\" Set up some character translations and predefined strings. \*(-- will .\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left .\" double quote, and \*(R" will give a right double quote. \*(C+ will .\" give a nicer C++. Capital omega is used to do unbreakable dashes and .\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff, .\" nothing in troff, for use with C<>. .tr \(*W- .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' .ie n \{\ . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} .el\{\ . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\} .\" .\" Escape single quotes in literal strings from groff's Unicode transform. .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" .\" If the F register is >0, we'll generate index entries on stderr for .\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index .\" entries marked with X<> in POD. Of course, you'll have to process the .\" output yourself in some meaningful fashion. .\" .\" Avoid warning from groff about undefined register 'F'. .de IX .. .nr rF 0 .if \n(.g .if rF .nr rF 1 .if (\n(rF:(\n(.g==0)) \{\ . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF .\" ======================================================================== .\" .IX Title "HYPERG 3pm" .TH HYPERG 3pm "2023-06-17" "perl v5.36.0" "User Contributed Perl Documentation" .\" For nroff, turn off justification. Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .SH "NAME" PDL::GSLSF::HYPERG \- PDL interface to GSL Special Functions .SH "DESCRIPTION" .IX Header "DESCRIPTION" This is an interface to the Special Function package present in the \s-1GNU\s0 Scientific Library. .SH "FUNCTIONS" .IX Header "FUNCTIONS" .SS "gsl_sf_hyperg_0F1" .IX Subsection "gsl_sf_hyperg_0F1" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double c) .Ve .PP /* Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^(1/2(1\-c)) I_{c\-1}(2 Sqrt[x]) Gamma[c] (\-x)^(1/2(1\-c)) J_{c\-1}(2 Sqrt[\-x]) .PP gsl_sf_hyperg_0F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_1F1" .IX Subsection "gsl_sf_hyperg_1F1" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b) .Ve .PP Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x) .PP gsl_sf_hyperg_1F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_U" .IX Subsection "gsl_sf_hyperg_U" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b) .Ve .PP Confluent hypergeometric function for integer parameters. U(a,b,x) .PP gsl_sf_hyperg_U does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_2F1" .IX Subsection "gsl_sf_hyperg_2F1" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) .Ve .PP Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x] .PP gsl_sf_hyperg_2F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_2F1_conj" .IX Subsection "gsl_sf_hyperg_2F1_conj" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) .Ve .PP Gauss hypergeometric function 2F1[aR + I aI, aR \- I aI, c, x] .PP gsl_sf_hyperg_2F1_conj does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_2F1_renorm" .IX Subsection "gsl_sf_hyperg_2F1_renorm" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) .Ve .PP Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c] .PP gsl_sf_hyperg_2F1_renorm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_2F1_conj_renorm" .IX Subsection "gsl_sf_hyperg_2F1_conj_renorm" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) .Ve .PP Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR \- I aI, c, x] / Gamma[c] .PP gsl_sf_hyperg_2F1_conj_renorm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SS "gsl_sf_hyperg_2F0" .IX Subsection "gsl_sf_hyperg_2F0" .Vb 1 \& Signature: (double x(); double [o]y(); double [o]e(); double a; double b) .Ve .PP Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (\-1/x)^a U(a,1+a\-b,\-1/x) .PP gsl_sf_hyperg_2F0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. .SH "AUTHOR" .IX Header "AUTHOR" This file copyright (C) 1999 Christian Pellegrin All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file \&\s-1COPYING\s0 in the \s-1PDL\s0 distribution. If this file is separated from the \&\s-1PDL\s0 distribution, the copyright notice should be included in the file. .PP The \s-1GSL SF\s0 modules were written by G. Jungman.