Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function | Zendy

Sébastien Gaboury | Zendy; Abdelmejid Bayad | Zendy

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Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function

Author(s) -

Sébastien Gaboury,

Abdelmejid Bayad

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/975615

Subject(s) - mathematics , bernoulli polynomials , pure mathematics , riemann zeta function , polylogarithm , order (exchange) , arithmetic zeta function , algebra over a field , orthogonal polynomials , discrete orthogonal polynomials , prime zeta function , finance , economics

By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch zeta function as wellas a new expansion formula for the generalized Hurwitz-Lerch zeta functionobtained recently by Gaboury and Bayad , in this paper we present some series representations for these polynomials at rational arguments. These resultsprovide extensions of those obtained by Apostol (1951) and by Srivastava (2000)

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