Dixit, AtulAtulDixitKumar, RahulRahulKumar2025-08-282025-08-282019-12-01http://arxiv.org/abs/1912.01199http://repository.iitgn.ac.in/handle/IITG2025/20056We 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.en-USNumber Theory (math.NT)Classical AnalysisODEs (math.CA)e-Printe-Print123456789/555