English

On Hurwitz zeta function and Lommel functions

Number Theory 2019-12-04 v1 Classical Analysis and ODEs

Abstract

We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function ζ(s,a)\zeta(s, a) beginning with Hermite's formula. The aim is to reveal a nice connection between ζ(s,a)\zeta(s, a) and a special case of the Lommel function Sμ,ν(z)S_{\mu, \nu}(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.

Keywords

Cite

@article{arxiv.1912.01199,
  title  = {On Hurwitz zeta function and Lommel functions},
  author = {Atul Dixit and Rahul Kumar},
  journal= {arXiv preprint arXiv:1912.01199},
  year   = {2019}
}

Comments

9 pages, submitted for publication

R2 v1 2026-06-23T12:33:57.074Z