New Approximations for the Higher Order Coefficients in an Asymptotic Expansion for the Barnes G-Function

Abstract

In this paper, we provide new formulas for determining the coefficients appearing in the asymptotic expansion for the Barnes G-function as n tends to infinity for certain classes of asymptotic expansion for the Barnes G-function. We remark that our formulas can be used to approximate the coefficients appearing in an asymptotic expansion of the “random matrix factor” from the Keathing-Snaith conjecture and the coefficients appearing in an asymptotic expansion of the “Lévy-Khintchine type representation of the reciprocal of the Barnes G-function”.