Abstract and Applied Analysis
Volume 2008 (2008), Article ID 914367, 7 pages
Research Article

On the Symmetries of the q-Bernoulli Polynomials

Taekyun Kim

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

Received 25 June 2008; Accepted 29 August 2008

Academic Editor: Ferhan Merdivenci Atici

Copyright © 2008 Taekyun Kim. 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.


Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the classical Bernoulli numbers. In this paper, we study the new symmetries of the q-Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results. By using our symmetries for the q-Bernoulli polynomials, we can obtain some interesting relationships between q-Bernoulli numbers and polynomials.