PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions
This is an interface to the Special Function package present in the GNU Scientific Library.
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].
Signature: (double x(); double [o]y(); double [o]e())
Gamma(x), x not a negative integer
Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf
1/Gamma(x)
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]
Signature: (double x(); double [o]y(); double [o]e(); int n)
x^n / n!
Signature: (x(); double [o]y(); double [o]e())
n!
n!! = n(n-2)(n-4)
ln n!
ln n!!
Signature: (n(); m(); double [o]y(); double [o]e())
log(n choose m)
n choose m
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]
Signature: (double x(); double [o]y(); double [o]e(); double a)
Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]
Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]
Signature: (double a(); double b(); double [o]y(); double [o]e())
Logarithm of Beta Function Log[B(a,b)]
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.
To install PDL, copy and paste the appropriate command in to your terminal.
cpanm
cpanm PDL
CPAN shell
perl -MCPAN -e shell install PDL
For more information on module installation, please visit the detailed CPAN module installation guide.