On the Symmetries of the ð ‘ž -Bernoulli Polynomials

Taekyun Kim

Abstract and Applied Analysis, 2008, vol. 2008, 1-7

Abstract:

Kupershmidt and Tuenter have introduced reflection symmetries for the ð ‘ž -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 ð ‘ž -Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results. By using our symmetries for the ð ‘ž -Bernoulli polynomials, we can obtain some interesting relationships between ð ‘ž -Bernoulli numbers and polynomials.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:914367

DOI: 10.1155/2008/914367

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