Recently, Choi et al. (2008) have studied the -extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order and multiple Hurwitz zeta function. In this paper, we define Apostol's type -Euler numbers and -Euler polynomials . We obtain the generating functions of and , respectively. We also have the distribution relation for Apostol's type -Euler polynomials. Finally, we obtain -zeta function associated with Apostol's type -Euler numbers and Hurwitz's type -zeta function associated with Apostol's type -Euler polynomials for negative integers.
"On the -Extension of Apostol-Euler Numbers and Polynomials." Abstr. Appl. Anal. 2008 1 - 10, 2008. https://doi.org/10.1155/2008/296159