Stirling's formula derived simply

Joseph B. Keller, Jean-Marc Vanden-Broeck

Stirling's formula, the asymptotic expansion of $n!$ for $n$ large, or of $\Gamma (z)$ for $z\to \infty$, is derived directly from the recursion equation $\Gamma (z+1)=z\Gamma (s)$ and the normali…