Variations on a theme by James Stirling

Abstract

We review the history and various approaches to the derivation of Stirling’s series. We use a different procedure, based on the asymptotic analysis of the difference equation We use a different procedure, based on the asymptotic analysis of the difference equation Γ(z+1)=zΓ(z). The method reproduces Stirling’s series very easily and can be applied to analyze more complicated difference equations.