Gamma Function for Non-Negative Integer Argument

Theorem
The Gamma function satisfies:


 * $\Gamma \left({z}\right) = \dfrac {\Gamma \left({z+1}\right)} z$

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

Proof
From Gamma Difference Equation:
 * $\Gamma \left({z+1}\right) = z \Gamma \left({z}\right)$

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

The result follows by dividing by $z$.