On the q-Extension of Apostol-Euler Numbers and Polynomials. (4th January 2009)

• Record Type: Journal Article
• Authors: Kim, Young-Hee; Kim, Wonjoo; Jang, Lee-Chae
• Other Names: Littlejohn Lance Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2008(2008)
• Publication Date: 2009-01-04
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2008/296159
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Recently, Choi et al. (2008) have studied theq -extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of ordern and multiple Hurwitz zeta function. In this paper, we define Apostol's typeq -Euler numbersE n, q, ξ andq -Euler polynomialsE n, q, ξ ( x ) . We obtain the generating functions ofE n, q, ξ andE n, q, ξ ( x ), respectively. We also have the distribution relation for Apostol's typeq -Euler polynomials. Finally, we obtainq -zeta function associated with Apostol's typeq -Euler numbers and Hurwitz's typeq -zeta function associated with Apostol's typeq -Euler polynomials for negative integers.