# Gamma Function for Non-Negative Integer Argument

## Theorem

The Gamma function satisfies:

$\map \Gamma z = \dfrac {\map \Gamma {z + 1} } z$

for any $z$ which is not a nonpositive integer.

## Proof

$\map \Gamma {z + 1} = z \, \map \Gamma z$

which is valid for all $z \notin \Z_{\le 0}$.

The result follows by dividing by $z$.