On Hurwitz zeta function and Lommel functions
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 Sμ, (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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