Advances in Difference Equations
Volume 2009 (2009), Article ID 956910, 8 pages
doi:10.1155/2009/956910
Research Article

A Note on the q-Euler Measures

Taekyun Kim,1 Kyung-Won Hwang,2 and Byungje Lee3

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139701, South Korea
2General Education Department, Kookmin University, Seoul 136702, South Korea
3Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139701, South Korea

Received 6 March 2009; Accepted 20 May 2009

Academic Editor: Patricia J. Y. Wong

Copyright © 2009 Taekyun Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Properties of q-extensions of Euler numbers and polynomials which generalize those satisfied by Ek and Ek(x) are used to construct q-extensions of p-adic Euler measures and define p-adic q-ℓ-series which interpolate q-Euler numbers at negative integers. Finally, we give Kummer Congruence for the q-extension of ordinary Euler numbers.