Main       Download       Commercial support       FAQ       Forum       About Us

Gamma function

Gamma function is an extension of the factorial function for real numbers. In x=0 and negative integer values gamma function has poles. For positive real x or negative non-integer x gamma function is

For positive integer x Γ(n)=(n-1)!

It should be noted that these formula is applicable for the complex argument too. But the gamma function of the complex argument is seldom used, so the algorithm in this module operates with real arguments only. Of course, the integration is not an effective way for gamma function calculation. Instead, it is used as a series of formulas to bring an argument to [2,3] interval in which the rational approximation is built. For big x (more than 33) Stirling's formula is used. This algorithm is implemented in the Gamma subroutine.

Gamma function can possess very big values, so it is often used as a logarithm of the gamma function, which can be calculated by using the LnGamma subroutine.

This article is intended for personal use only.

Download ALGLIB

C#

C# source.

Downloads page

 

C++

C++ source.

Downloads page

 

C++, multiple precision arithmetic

C++ source. MPFR/GMP is used.

GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.

Downloads page

 

FreePascal

FreePascal version.

Downloads page

 

Delphi

Delphi version.

Downloads page

 

VB.NET

VB.NET version.

Downloads page

 

VBA

VBA version.

Downloads page

 

Python

Python version (CPython and IronPython are supported).

Downloads page

 

 

ALGLIB® - numerical analysis library, 1999-2012.
ALGLIB is a registered trademark of the ALGLIB Project.