On Hurwitz Zeta funtion and Lommel fundtions

We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function ?(s,a) beginning with Hermite's formula. The aim is to reveal a nice connection between ?(s,a) and a special case of the Lommel function S?,?(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.