On the symmetries of the \(q\)-Bernoulli polynomials
type: Item
instance of: scholarly article
title: On the symmetries of the \(q\)-Bernoulli polynomials
zbMATH Open document ID: 1217.11022
DOI: 10.1155/2008/914367
author: Taekyun Kim
published in: Abstract and Applied Analysis
publication date: 2008-10-16T00:00:00Z
full work available at URL: https://eudml.org/doc/45293
review text: Summary: \textit{B. A. Kupershmidt} [Reflection symmetries of \(q\)-Bernoulli polynomials. J. Nonlinear Math. Phys. 12, Suppl. 1, 412--422 (2005; Zbl 1362.33021)] and \textit{H. J. H. Tuenter} [Am. Math. Mon. 108, No. 3, 258--261 (2001; Zbl 0983.11008)] have introduced reflection symmetries for the \(q\)-Bernoulli numbers and the Bernoulli polynomials, 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.
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 05A30
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 5352111
zbMATH Keywords: symmetries of the \(q\)-Bernoulli numbers and polynomials
Wikidata QID: Q58643846
MaRDI profile type: Publication
OpenAlex ID: W1555131391
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description: scientific article; zbMATH DE number 5352111