Gamma Function Extends Factorial

Theorem

 * $\forall n \in \N: \map \Gamma {n + 1} = n!$

Proof
For $n = 0$:

Then by Gamma Difference Equation:
 * $\forall z \in \Z_{> 0}: \map \Gamma {z + 1} = z \, \map \Gamma z$

Hence the result.