On the Symmetries of the $q$-Bernoulli Polynomials
Taekyun Kim
Source: Abstr. Appl. Anal. Volume 2008 (2008), 7 pages.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1234298991
Digital Object Identifier: doi:10.1155/2008/914367
Mathematical Reviews number (MathSciNet):
MR2448390
Zentralblatt MATH identifier:
05352111
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Abstract and Applied Analysis
