Connections within the group of gamma functions and with other function groups
Representations through more general functions
The gamma function is the main example of a group of functions collectively referred to as gamma functions. For example, it can be written in terms of the incomplete gamma function:
All four incomplete gamma functions , , , and can be represented as cases of the hypergeometric function . Further, the gamma function Γ(z) is the special degenerate case of the hypergeometric function .
Representations through related equivalent functions
The gamma function and two factorial functions are connected by the formulas: