Abstract and Applied Analysis

On the Symmetries of the q -Bernoulli Polynomials

Taekyun Kim

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 914367, 7 pages.

Dates
First available in Project Euclid: 10 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1234298991

Digital Object Identifier
doi:10.1155/2008/914367

Mathematical Reviews number (MathSciNet)
MR2448390

Zentralblatt MATH identifier
1217.11022

Citation

Kim, Taekyun. On the Symmetries of the $q$ -Bernoulli Polynomials. Abstr. Appl. Anal. 2008 (2008), Article ID 914367, 7 pages. doi:10.1155/2008/914367. https://projecteuclid.org/euclid.aaa/1234298991


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