Asymptotic behavior of the Hurwitz-Lerch multiple zeta function at non-positive integer points

TL;DR

This paper investigates the asymptotic behavior of the Hurwitz-Lerch multiple zeta function at non-positive integers, providing methods to evaluate its limit values using Apostol-Bernoulli polynomials.

Contribution

It introduces a new approach to analyze the asymptotics of the Hurwitz-Lerch multiple zeta function at non-positive integers using Apostol-Bernoulli polynomials.

Findings

Asymptotic formulas near non-positive integer points

Limit values of the zeta function at these points

Application of Apostol-Bernoulli polynomials

Abstract

We give a result on the asymptotic behavior of the Hurwitz-Lerch multiple zeta functions near non-positive integer points by using the Apostol-Bernoulli polynomials. From this result, we can evaluate limit values at non-positive integer points.