%0 Journal Article
%T New Approach to q-Euler Numbers and Polynomials
%A Taekyun Kim
%A Lee-Chae Jang
%A Young-Hee Kim
%A Seog-Hoon Rim
%J Advances in Difference Equations
%D 2010
%I Springer
%R 10.1155/2010/431436
%X We give a new construction of the q-extensions of Euler numbers and polynomials. We present new generating functions which are related to the q-Euler numbers and polynomials. We also consider the generalized q-Euler polynomials attached to Dirichlet's character ¦Ö and have the generating functions of them. We obtain distribution relations for the q-Euler polynomials and have some identities involving q-Euler numbers and polynomials. Finally, we derive the q-extensions of zeta functions from the Mellin transformation of these generating functions, which interpolate the q-Euler polynomials at negative integers.
%U http://dx.doi.org/10.1155/2010/431436