On Hurwitz zeta function and Lommel functions

2019/12/03 by Dixit, Atul, Kumar, Rahul · 1 citation
#11M35 #33C47 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Primary 11M06 #Secondary 33C10

paper · doi:10.48550/arxiv.1912.01199

Abstract

We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function ζ(s, a) beginning with Hermite's formula. The aim is to reveal a nice connection between ζ(s, a) and a special case of the Lommel function S_{μ, ν}(z). This connection is used to rephrase a modular-type transformation involving infinite series of Hurwitz zeta function in terms of those involving Lommel functions.

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