Srivastava, H.M.Gaboury, SébastienBayad, Abdelmejid2015-05-222015-05-2220142014-06-23Srivastava et al.: Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus. Advances in Difference Equations 2014 2014:169.http://www.advancesindifferenceequations.com/content/2014/1/169http://dx.doi.org/10.1186/1687-1847-2014-169http://hdl.handle.net/1828/6195SpringerOpenMotivated 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: Primary 11M25; 11M35; 26A33; secondary 33C05; 33C60enAttribution-NonCommercial-NoDerivs 2.5 Canadafractional derivativesgeneralized Taylor expansiongeneralized Hurwitz-Lerch zeta functionsRiemann zeta functionLeibniz rulesArticleDepartment of Mathematics and Statistics