Diagram of gamma function identities

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:

  • Conjugation
  • Addition
  • Reflection
  • Multiplication

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.

Other diagrams:

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