Abstract and Applied Analysis
Volume 2011 (2011), Article ID 545314, 8 pages
http://dx.doi.org/10.1155/2011/545314
Research Article

A Note on the Modified 𝑞 -Bernoulli Numbers and Polynomials with Weight 𝛼

T. Kim,1 D. V. Dolgy,2 S. H. Lee,1 B. Lee,3 and S. H. Rim4

1Division of General Education, Kwangwoon University, Seoul 139-701, Republic of Korea
2Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea
4Department of Mathematics Education, Kyungpook National University, Taegu 702-701, Republic of Korea

Received 13 July 2011; Accepted 2 October 2011

Academic Editor: Alberto d'Onofrio

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

A systemic study of some families of the modified 𝑞 -Bernoulli numbers and polynomials with weight 𝛼 is presented by using the 𝑝 -adic 𝑞 -integration ℤ 𝑝 . The study of these numbers and polynomials yields an interesting 𝑞 -analogue related to Bernoulli numbers and polynomials.