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:
