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

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  • S. Gaboury
  • A. Bayad

Abstract

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 well as a new expansion formula for the generalized Hurwitz‐Lerch zeta function obtained recently by Gaboury and Bayad , in this paper we present some series representations for these polynomials at rational arguments. These results provide extensions of those obtained by Apostol (1951) and by Srivastava (2000).

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:975615
DOI: 10.1155/2013/975615
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