Some q-extensions of the Apostol–Bernoulli and the Apostol–Euler polynomials of order n, and the multiple Hurwitz zeta function

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• 作者：Junesang Choi ; P.J. Anderson ; H.M. Srivastava
• 关键词：Gamma function ; Multiple Gamma functions ; Riemann Zeta function ; Hurwitz Zeta function ; Hurwitz– ; Lerch Zeta function ; Multiple Hurwitz– ; Lerch Zeta function ; q-Extensions of the Apostol– ; Bernoulli and the Apostol– ; Euler polyn
• 刊名：Applied Mathematics and Computation
• 出版年：2008
• 出版时间：1 June 2008
• 年：2008
• 卷：199
• 期：2
• 页码：723-737
• 全文大小：237 K

文摘

In this paper, we first investigate several further interesting properties of the multiple Hurwitz–Lerch Zeta function Φ_n(z, s, a) which was introduced recently by Choi et al. [J. Choi, D.S. Jang, H.M. Srivastava, A generalization of the Hurwitz–Lerch Zeta function, Integral Transform. Spec. Funct., 19 (2008)]. We then introduce and investigate some q-extensions of the multiple Hurwitz–Lerch Zeta function Φ_n(z, s, a), the Apostol–Bernoulli polynomials of order n, and the Apostol–Euler polynomials of order n. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely.