On the q-Extension of Apostol-Euler Numbers and Polynomials

Young-Hee Kim; Wonjoo Kim; Lee-Chae Jang
January 2008
Abstract & Applied Analysis;2008, p1
Academic Journal
Recently, Choi et al. (2008) have studied the q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol's type q-Euler numbers En,q,ξ and q-Euler polynomials En,q,ξ(x). We obtain the generating functions of En,q,ξ and En,q,ξ(x), respectively. We also have the distribution relation for Apostol's type q-Euler polynomials. Finally,we obtain q-zeta function associated with Apostol's type q-Euler numbers and Hurwitz's type q-zeta function associated with Apostol's type q-Euler polynomials for negative integers.


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