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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 948050, 6 pages
Research Article

On the Modified 𝑞-Bernoulli Numbers of Higher Order with Weight

1Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Division of General Education, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Mathematics Education, Kyungpook National University, Daegu 702-701, Republic of Korea

Received 11 August 2011; Revised 24 November 2011; Accepted 13 December 2011

Academic Editor: Ferhan M. Atici

Copyright © 2012 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.


The purpose of this paper is to give some properties of the modified 𝑞-Bernoulli numbers and polynomials of higher order with weight. In particular, by using the bosonic 𝑝-adic 𝑞-integral on 𝑝, we derive new identities of 𝑞-Bernoulli numbers and polynomials with weight.