Gamma Function Extends Factorial

Theorem

 * $\forall n \in \N: \Gamma \left({n + 1}\right) = n!$

Proof
For $n = 0$:

Then by Gamma Difference Equation:
 * $\forall z \in \Z_{> 0}: \Gamma \left({z+1}\right) = z \Gamma \left({z}\right)$

Hence the result.