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Complex Analysis by ITL ESL

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Appendix 1: Gamma, Beta and Zeta Functions

GAMMA FUNCTION

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

images

In particular

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Now, from (A.1), we have

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Integrating this integral by parts, we obtain

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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 ...

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