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 Gamma

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: