Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
Gamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[a,z] > Introduction to the gamma functions





Connections within the group of gamma functions and with other function groups

Representations through more general functions

The incomplete gamma functions , , , and are particular cases of the more general hypergeometric and Meijer G functions.

For example, they can be represented through hypergeometric functions and or the Tricomi confluent hypergeometric function :

These functions also have rather simple representations in terms of classical Meijer G functions:

The log‐gamma function can be expressed through polygamma and zeta functions by the following formulas:

Representations through related equivalent functions

The gamma functions , , , and can be represented using the related exponential integral by the following formulas:

Relations to inverse functions

The gamma functions , , , and are connected with the inverse of the regularized incomplete gamma function and the inverse of the generalized regularized incomplete gamma function by the following formulas:

Representations through other gamma functions

The gamma functions , , , , , and are connected with each other by the formulas: