Advances in Difference Equations
Volume 2010 (2010), Article ID 801580, 13 pages
Research Article

A Note on Symmetric Properties of the Twisted q-Bernoulli Polynomials and the Twisted Generalized q-Bernoulli Polynomials

1Department of Mathematics and Computer Science, KonKuk University, Chungju 138-70, Republic of Korea
2Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Mathematics, Yuvaraja's College, University of Mysore, Mysore 570# 005, India
4Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
5Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 11 September 2009; Revised 14 April 2010; Accepted 31 May 2010

Academic Editor: Abdelkader Boucherif

Copyright © 2010 L.-C. Jang 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.


We define the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomials attached to χ of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain some relationships between twisted q-Bernoulli numbers and polynomials and between twisted generalized q-Bernoulli numbers and polynomials.