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

A Note on the q-Euler Measures

Taekyun Kim1 , Kyung-Won Hwang2 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

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--series which interpolate q-Euler numbers at negative integers. Finally, we give Kummer Congruence for the q-extension of ordinary Euler numbers.