A note on an identity of the gamma function and Stirling’s formula.

Abstract

Short and elementary proofs of the well-known Stirling formula for the discrete Gamma function $\Gamma(n)$ have been given by several authors. In this note, a well-known identity and Stirling's formula for the continuous Gamma function $\Gamma(x)$ are deduced in a different and short way from a simple and elementary proposition.