Analytical properties of the Hurwitz-Lerch zeta function

被引：4

作者：

Nadeem, Raghib ^{[1
]}

Usman, Talha ^{[2
]}

Nisar, Kottakkaran Sooppy ^{[3
]}

Baleanu, Dumitru ^{[4
,5
,6
]}

机构：

[1] Aligarh Muslim Univ, Fac Engn & Technol, Dept Appl Math, Aligarh 202002, Uttar Pradesh, India

[2] Lingayas Vidyapeeth, Sch Basic & Appl Sci, Dept Math, Faridabad 121002, Haryana, India

[3] Prince Sattam bin Abdulaziz Univ, Dept Math, Coll Arts & Sci, Wadi Aldawaser 11991, Saudi Arabia

[4] Cankaya Univ, Dept Math, TR-06790 Ankara, Turkey

[5] Inst Space Sci, Magurele 077125, Romania

[6] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40447, Taiwan

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Generalized; Generating functions; Rodrigues formula; 33C05; 33C45; 33C47; 33C90; FEYNMAN-INTEGRALS;

D O I：

10.1186/s13662-020-02924-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we aim to extend the Hurwitz-Lerch zeta function Phi delta,sigma;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.

引用

页数：15

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