Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus
Date
2014-06-23
Authors
Srivastava, H.M.
Gaboury, Sébastien
Bayad, Abdelmejid
Journal Title
Journal ISSN
Volume Title
Publisher
Advances in Difference Equations
Abstract
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: Primary 11M25; 11M35; 26A33; secondary 33C05; 33C60
Description
SpringerOpen
Keywords
fractional derivatives, generalized Taylor expansion, generalized Hurwitz-Lerch zeta functions, Riemann zeta function, Leibniz rules
Citation
Srivastava et al.: Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus. Advances in Difference Equations 2014 2014:169.