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RedHat 9 (Linux i386) - man page for pdl::gslsf::gamma (redhat section 3)

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

PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions
This is an interface to the Special Function package present in the GNU Scientific Library.
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)
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 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)