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pdl::gslsf::hyperg(3) [redhat man page]

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

NAME
PDL::GSLSF::HYPERG - PDL interface to GSL Special Functions DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library. SYNOPSIS
Functions FUNCTIONS
gsl_sf_hyperg_0F1 Signature: (double x(); double [o]y(); double [o]e(); double c) /* 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]) gsl_sf_hyperg_1F1 Signature: (double x(); double [o]y(); double [o]e(); double a; double b) Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x) gsl_sf_hyperg_U Signature: (double x(); double [o]y(); double [o]e(); double a; double b) Confluent hypergeometric function for integer parameters. U(a,b,x) gsl_sf_hyperg_2F1 Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x] gsl_sf_hyperg_2F1_conj Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] gsl_sf_hyperg_2F1_renorm Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c] gsl_sf_hyperg_2F1_conj_renorm Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c) Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c] gsl_sf_hyperg_2F0 Signature: (double x(); double [o]y(); double [o]e(); double a; double b) 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) AUTHOR
This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. The GSL SF modules were written by G. Jungman. perl v5.8.0 2003-01-29 HYPERG(3)

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GAMMA(3)						User Contributed Perl Documentation						  GAMMA(3)

NAME
PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library. SYNOPSIS
Functions FUNCTIONS
gsl_sf_lngamma Signature: (double x(); double [o]y(); double [o]s(); double [o]e()) Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0. So Gamma[x] = sgn * Exp[result_lg]. gsl_sf_gamma Signature: (double x(); double [o]y(); double [o]e()) Gamma(x), x not a negative integer gsl_sf_gammastar Signature: (double x(); double [o]y(); double [o]e()) Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf gsl_sf_gammainv Signature: (double x(); double [o]y(); double [o]e()) 1/Gamma(x) gsl_sf_lngamma_complex Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye()) Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z)) in (-Pi, Pi] gsl_sf_taylorcoeff Signature: (double x(); double [o]y(); double [o]e(); int n) x^n / n! gsl_sf_fact Signature: (x(); double [o]y(); double [o]e()) n! gsl_sf_doublefact Signature: (x(); double [o]y(); double [o]e()) n!! = n(n-2)(n-4) gsl_sf_lnfact Signature: (x(); double [o]y(); double [o]e()) ln n! gsl_sf_lndoublefact Signature: (x(); double [o]y(); double [o]e()) ln n!! gsl_sf_lnchoose Signature: (n(); m(); double [o]y(); double [o]e()) log(n choose m) gsl_sf_choose Signature: (n(); m(); double [o]y(); double [o]e()) n choose m gsl_sf_lnpoch Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a) Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn = sgn( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a] gsl_sf_poch Signature: (double x(); double [o]y(); double [o]e(); double a) Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x] gsl_sf_pochrel Signature: (double x(); double [o]y(); double [o]e(); double a) Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a] gsl_sf_gamma_inc_Q Signature: (double x(); double [o]y(); double [o]e(); double a) Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ] gsl_sf_gamma_inc_P Signature: (double x(); double [o]y(); double [o]e(); double a) Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ] gsl_sf_lnbeta Signature: (double a(); double b(); double [o]y(); double [o]e()) Logarithm of Beta Function Log[B(a,b)] gsl_sf_beta Signature: (double a(); double b();double [o]y(); double [o]e()) Beta Function B(a,b) AUTHOR
This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. The GSL SF modules were written by G. Jungman. perl v5.8.0 2003-01-29 GAMMA(3)

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