Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 358986, 13 pages
doi:10.1155/2010/358986
Research Article

On Carlitz's Type q-Euler Numbers Associated with the Fermionic P-Adic Integral on ℤp

Min-Soo Kim,1 Taekyun Kim,2 and Cheon-Seoung Ryoo3

1Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-Gu, Daejeon 305-701, Republic of Korea
2Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 2 August 2010; Accepted 28 September 2010

Academic Editor: Jewgeni Dshalalow

Copyright © 2010 Min-Soo 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

We consider the following problem in the paper of Kim et al. (2010): “Find Witt's formula for Carlitz's type q-Euler numbers.” We give Witt's formula for Carlitz's type q-Euler numbers, which is an answer to the above problem. Moreover, we obtain a new p-adic q-l-function lp,q(s,χ) for Dirichlet's character χ, with the property that lp,q(−n,χ)=En,χn,q−χn(p)[p]qnEn,χn,qp for n=0,1,… using the fermionic p-adic integral on ℤp.