On the Symmetries of the q‐Bernoulli Polynomials

Taekyun Kim

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

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.

Date: 2008
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https://doi.org/10.1155/2008/914367

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:914367

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