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Discrete Appell-Dunkl sequences and Bernoulli-Dunkl polynomials of the second kind
- Source :
- RIUR. Repositorio Institucional de la Universidad de La Rioja, instname
- Publication Year :
- 2022
- Publisher :
- Academic Press Inc., 2022.
-
Abstract
- 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.
- Subjects :
- Pure mathematics
Applied Mathematics
Mathematics::Classical Analysis and ODEs
Context (language use)
Bernoulli polynomials
Exponential function
Kernel (algebra)
symbols.namesake
Bernoulli's principle
Operator (computer programming)
Mathematics::Quantum Algebra
symbols
Mathematics::Representation Theory
Real line
Analysis
Dunkl operator
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- RIUR. Repositorio Institucional de la Universidad de La Rioja, instname
- Accession number :
- edsair.doi.dedup.....4eac660ffe8e6b62bb2f95fc06cb0575