Gamma Function

The Gamma function is defined as::$\Gamma (p)={\int }_0^{\infty }{e}^{-u}{u}^{p-1}du$, where $p>0$.

The Gamma function is related to the factorial by::$\Gamma (n+1)=n!$ for positive integers, where the $\gamma$ function generalises the factorial for non-integers.

The Gamma function can be simplified from $\Gamma (p+1)$ to::$p\Gamma (p+1)$, by direct evaluation.

The Gamma function evaluated for $\Gamma (1)$ is equal to::$1$, by direct evaluation.