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

机译:广义Hurwitz-Lerch Zeta函数特殊值的级数表示

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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).
机译:通过利用高阶Apostol-Bernoulli,Apostol-Euler,Apostol-Genocchi和Apostol-Frobenius-Euler多项式之间的一些显式关系以及广义Hurwitz-Lerch zeta函数以及广义Hurwitz- Gaboury和Bayad最近获得了Lerch zeta函数,在本文中,我们以有理论据给出了这些多项式的一些级数表示。这些结果提供了Apostol(1951)和Srivastava(2000)获得的结果的扩展。

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