Analytical properties of the Hurwitz–Lerch zeta function

[摘要] In the present paper, we aim to extend the Hurwitz–Lerch zeta function$\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)$ involving the extension of the beta function (Choi et al. in Honam Math. J. 36(2):357–385, 2014). We also study the basic properties of this extended Hurwitz–Lerch zeta function which comprises various integral formulas, a derivative formula, the Mellin transform, and the generating relation. The fractional kinetic equation for an extended Hurwitz–Lerch zeta function is also obtained from an application point of view. Furthermore, we obtain certain interesting relations in the form of particular cases.

[学科分类] 航空航天科学

[关键词] Generalized;Generating functions;Rodrigues formula