Some relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol-type polynomials

Advances in Difference Equations

Sebastien Gaboury¹ 

[1] Department of Mathematics and Computer Science, University of Quebec, Chicoutimi, Canada

关键词: fractional derivatives;    generalized Taylor expansion;    generalized Hurwitz-Lerch zeta functions;    Riemann zeta function;    generalized Apostol-Bernoulli polynomials;    generalized Apostol-Euler polynomials;   

DOI  :  10.1186/1687-1847-2013-361

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we present three new expansion formulas for the generalized Hurwitz-Lerch zeta function. These expansions are obtained by using Taylor-like expansions involving fractional derivatives. Finally, interesting special cases involving the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials are also given. MSC:26A33, 11M35, 33C05, 11B68.

【 授权许可】

CC BY