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Abstract and Applied Analysis
Volume 2011, Article ID 392025, 14 pages
Research Article

On the 𝑞 -Bernoulli Numbers and Polynomials with Weight 𝜶

Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 13 May 2011; Accepted 26 July 2011

Academic Editor: Elena Litsyn

Copyright © 2011 T. Kim and J. Choi. 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.


We present a systemic study of some families of higher-order 𝑞 -Bernoulli numbers and polynomials with weight 𝛼 . From these studies, we derive some interesting identities on the 𝑞 -Bernoulli numbers and polynomials with weight 𝛼 .