of redundant decimal places. Where possible, all the asymptotic forms yield the same values as the LogGamma routine in Mathematica.'
author:
- |
    **Victor Kowalenko\
    ARC Centre of Excellence for Mathematics\
    and Statistics of Complex Systems\
    Department of Mathematics and Statistics\
    The University of Melbourne\
    Victoria 3010, Australia.**
title: '**Exactification of Stirling’s Approximation for the Logarithm of the Gamma Function**'
---

[*Keywords*]{}: Asymptotic series, Asymptotic form, Borel summation, Complete asymptotic expansion, Discontinuity, Divergent series, Domain of Convergence, Exactification, Gamma function, Mellin-Barnes regularization, Regularization, Remainder, Stokes discontinuity, Stokes line, Stokes phenomenon, Stokes sector, Stirling’s approximation

[*email*]{}: vkowa@unimelb.edu.au

Introduction
============

In asymptotics exactification is defined as the process of obtaining the exact values of a function/integral from its complete asymptotic expansion and has already been achieved in two notable cases. For those unfamiliar with the concept, a complete asymptotic expansion is defined as a power series expansion for a function or integral that not only possesses all the terms in a dominant asymptotic series, but also all the terms in frequently neglected subdominant or transcendental asymptotic series, should they exist. The latter series are said to lie beyond all orders, while the methods and theory behind them belong to the discipline or 