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2008 On the Symmetries of the q -Bernoulli Polynomials
Taekyun Kim
Abstr. Appl. Anal. 2008: 1-7 (2008). DOI: 10.1155/2008/914367


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.


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Taekyun Kim. "On the Symmetries of the q -Bernoulli Polynomials." Abstr. Appl. Anal. 2008 1 - 7, 2008.


Published: 2008
First available in Project Euclid: 10 February 2009

zbMATH: 1217.11022
MathSciNet: MR2448390
Digital Object Identifier: 10.1155/2008/914367

Rights: Copyright © 2008 Hindawi

Vol.2008 • 2008
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