Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 575240, 17 pages
doi:10.1155/2010/575240
Research Article

Some Identities on the Generalized q-Bernoulli Numbers and Polynomials Associated with q-Volkenborn Integrals

T. Kim,1 J. Choi,1 B. Lee,2 and C. S. Ryoo3

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 23 August 2010; Accepted 30 September 2010

Academic Editor: Alberto Cabada

Copyright © 2010 T. 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 give some interesting equation of p-adic q-integrals on ℤp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz type q-Bernoulli numbers and polynomials in p-adic number field.