Complex Analysis

Appendix 1: Gamma, Beta and Zeta Functions

GAMMA FUNCTION

The gamma function Γ (z) is defined by the integral

In particular

Now, from (A.1), we have

Integrating this integral by parts, we obtain

which is known as recursion formula.

Recursion formula can also be written as

Equation (A.1) together with the equation (A.2) gives the complete ...