On Hurwitz zeta function and Lommel functions

Abstract

We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function $\hat{I}\P (s,a)$ beginning with Hermite's formula. The aim is to reveal a nice connection between $\hat{I}\P (s,a)$ and a special case of the Lommel function $S_{\hat{I}¼,\hat{I}½}(z)$. This connection is used to rephrase a modular-type transformation involving infinite series of Hurwitz zeta function in terms of those involving Lommel functions.

9 pages, submitted for publication