The gamma function has a large number of identities relating its values at one point to values at other points. By focusing on just the function arguments and not the details of the relationships, a simple pattern emerges. Most of the identities can be derived from just four fundamental identities:
The same holds for functions derived from the gamma function: log gamma, digamma, trigramma, etc.
For the details of the relationships, see Identities for gamma and related functions.