ON THE STRUCTURE OF DW-APPELL DUNKL CLASSICAL ORTHOGONAL POLYNOMIALS

J. Souissi; K. A. Alanezy

doi:10.15393/j3.art.2026.20191

ON THE STRUCTURE OF D_W-APPELL DUNKL CLASSICAL ORTHOGONAL POLYNOMIALS

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate a class of classical orthogonal polynomials associated with the D_w-Dunkl operator. This class is defined via a lowering operator that combines the discrete translation operator with a reflection-invariant component. We characterize these polynomials showing that the only possible T_θ,w-Appell classical sequences are of class one. The study concludes by explicitly determining the recurrence relations and structure formulas satisfied by such polynomials.

Original language	English
Pages (from-to)	107-126
Number of pages	20
Journal	Problemy Analiza
Volume	15
Issue number	1
DOIs	https://doi.org/10.15393/j3.art.2026.20191
State	Published - 2026

Bibliographical note

Publisher Copyright:
© Petrozavodsk State University, 2026.

Keywords

Appell orthogonal polynomials
D-Dunkl operator
orthogonal polynomials

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.15393/j3.art.2026.20191

Cite this

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title = "ON THE STRUCTURE OF DW-APPELL DUNKL CLASSICAL ORTHOGONAL POLYNOMIALS",

abstract = "In this paper, we investigate a class of classical orthogonal polynomials associated with the Dw-Dunkl operator. This class is defined via a lowering operator that combines the discrete translation operator with a reflection-invariant component. We characterize these polynomials showing that the only possible Tθ,w-Appell classical sequences are of class one. The study concludes by explicitly determining the recurrence relations and structure formulas satisfied by such polynomials.",

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KW - D-Dunkl operator

KW - orthogonal polynomials

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