Discrete Appell-Dunkl sequences and Bernoulli-Dunkl polynomials of the second kind

In a similar way that the Appell sequences of polynomials can be extended to the Dunkl context, where the ordinary derivative is replaced by Dunkl operator on the real line, and the exponential function is replaced by the so-called Dunkl kernel, one can expect that the discrete Appell sequences can...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 507; no. 2; p. 125832
Main Authors Extremiana Aldana, José Ignacio, Labarga, Edgar, Mínguez Ceniceros, Judit, Varona, Juan Luis
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2022
Subjects
Appell-Dunkl sequences
Bernoulli-Dunkl polynomials
Bernoulli-Dunkl polynomials of the second kind
Dunkl transform
Dunkl transform
Bernoulli-Dunkl polynomials
Appell-Dunkl sequences
Bernoulli-Dunkl polynomials of the second kind
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Summary:In a similar way that the Appell sequences of polynomials can be extended to the Dunkl context, where the ordinary derivative is replaced by Dunkl operator on the real line, and the exponential function is replaced by the so-called Dunkl kernel, one can expect that the discrete Appell sequences can be extended to the Dunkl context. In this extension, the role of the ordinary translation is played by the Dunkl translation, that is a much more intricate operator. In this paper, we define discrete Appell-Dunkl sequences of polynomials, and we give some properties and examples. In particular, we show which is the suitable definition for the Bernoulli polynomials of the second kind in the Dunkl context.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125832