Linux Certif

Toute la documentation sur la certification Linux LPI

PDL::GSLSF::GAMMA.3pm

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.