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

In this paper, we first investigate several further interesting properties of the multiple Hurwitz-Lerch Zeta function Phi(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 Phi(n)( z, s, a), the Apostol-Bernoulli polynomials B-k((n)) (x; lambda) of order n, and the Apostol-Euler polynomials E-k((n)) (x; lambda) of order n. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely. (C) 2007 Elsevier Inc. All rights reserved.