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 <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.