New approximations for the higher order coefficients in an asymptotic expansion for the Barnes G-function

2018/10/31 by Aziz Issaka, Issaka, Aziz
Mathematics · #Analytic Number Theory Research #Advanced Algebra and Geometry #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1810.13336

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".

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