Abstract and Applied Analysis
Volume 2011 (2011), Article ID 361484, 8 pages
http://dx.doi.org/10.1155/2011/361484
Research Article

Some Identities on the 𝑞 -Bernoulli Numbers and Polynomials with Weight 0

T. Kim, J. Choi, and Y. H. Kim

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

Received 16 August 2011; Accepted 27 September 2011

Academic Editor: Josef Diblík

Copyright © 2011 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

Recently, Kim (2011) has introduced the 𝑞 -Bernoulli numbers with weight 𝛼 . In this paper, we consider the 𝑞 -Bernoulli numbers and polynomials with weight 𝛼 = 0 and give 𝑝 -adic 𝑞 -integral representation of Bernstein polynomials associated with 𝑞 -Bernoulli numbers and polynomials with weight 0 . From these integral representation on ℤ 𝑝 , we derive some interesting identities on the 𝑞 -Bernoulli numbers and polynomials with weight 0 .