Contributions to the Theory of the Barnes Function

TL;DR

This paper introduces new integral representations and asymptotic series for the Barnes gamma function, along with numerical methods for high-precision computation of the function and related constants.

Contribution

It provides novel integral formulas and asymptotic expansions for the multiple gamma function, enhancing computational techniques.

Findings

New integral representations of the Barnes gamma function

Asymptotic series for high-precision approximation

Numerical schemes for computing Glaisher's constant

Abstract

This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.