Gamma function asymptotics by an extension of the method of steepest descents

Abstract

Recent work of Berry & Howls, which reformulated the method of steepest de­scents, is exploited to derive a new representation for the gamma function. It is shown how this representation can be used to derive a number of properties of the asymptotic expansion of the gamma function, including explicit and realistic error bounds, the Berry transition between different asymptotic representations across a Stokes line, and asymptotic estimates for the late coefficients.