Analytical properties of the Hurwitz–Lerch zeta function

Advances in Difference Equations

article

Nadeem, Raghib¹  Usman, Talha²  Nisar, Kottakkaran Sooppy³  Baleanu, Dumitru⁴ 

[1] Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University;Department of Mathematics, School of Basic and Applied Sciences;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University;Department of Mathematics, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University Hospital, China Medical University

关键词: Generalized;    Generating functions;    Rodrigues formula;   

DOI  :  10.1186/s13662-020-02924-2

学科分类：航空航天科学

来源: SpringerOpen

【 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.

【 授权许可】

CC BY