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 beginning with Hermite's formula. The aim is to reveal a nice connection between and a special case of the Lommel function . This connection is used to rephrase a modular-type transformation involving infinite series of Hurwitz zeta function in terms of those involving Lommel functions.
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