Abstract and Applied Analysis
Volume 2008 (2008), Article ID 914367, 7 pages
doi:10.1155/2008/914367
Research Article
On the Symmetries of the q-Bernoulli Polynomials
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.
Abstract
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.