Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus

Advances in Difference Equations

Sbastien Gaboury³  Hari M Srivastava⁴  Abdelmejid Bayad⁷ 

[1] d’DéDepartment of Mathematics and Computer Science, University of QuéDepartment of Mathematics and Statistics, University of Victoria, Victoria, Canada;Essonne, Evry Cedex, France;Evry Val D’bec at Chicoutimi, Chicoutimi, Canada;matiques, Universitépartement de Mathé

关键词: fractional derivatives;    generalized Taylor expansion;    generalized Hurwitz-Lerch zeta functions;    Riemann zeta function;    Leibniz rules;   

DOI  :  10.1186/1687-1847-2014-169

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Motivated by the recent investigations of several authors, in this paper, we derive several new expansion formulas involving a generalized Hurwitz-Lerch zeta function introduced and studied recently by Srivastava et al. (Integral Transforms Spec. Funct. 22:487-506, 2011). These expansions are obtained by using some fractional calculus theorems such as the generalized Leibniz rules for the fractional derivatives and the Taylor-like expansions in terms of different functions. Several (known or new) special cases are also considered. MSC:11M25, 11M35, 26A33, 33C05, 33C60.

【 授权许可】

CC BY