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 Φn(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 Φn(z, s, a), the Apostol-Bernoulli polynomials Bk(n)(x;λ) of order n, and the Apostol-Euler polynomials Ek(n)(x;λ) of order n. Relevant connections of the results presented here with those obtained in earlier works are also indicated precisely.