A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation

Jihad Souissi; Khalid Ali Alanezy

doi:10.3390/sym17091526

A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation

Jihad Souissi^*, Khalid Ali Alanezy

^*Corresponding author for this work

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

Abstract

This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the (Formula presented.) -analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of its q-Dunkl derivatives, offering a new effective classification method. We derive explicit structure relations for the (Formula presented.) -analogue of generalized Hermite and the (Formula presented.) -analogue of generalized Gegenbauer polynomials.

Original language	English
Article number	1526
Journal	Symmetry
Volume	17
Issue number	9
DOIs	https://doi.org/10.3390/sym17091526
State	Published - Sep 2025

Bibliographical note

Publisher Copyright:
© 2025 by the authors.

Keywords

orthogonal polynomials
q-Dunkl operator
q-semiclassical polynomials
q-series and q-polynomials
symmetric forms

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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10.3390/sym17091526

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title = "A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation",

abstract = "This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the (Formula presented.) -analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of its q-Dunkl derivatives, offering a new effective classification method. We derive explicit structure relations for the (Formula presented.) -analogue of generalized Hermite and the (Formula presented.) -analogue of generalized Gegenbauer polynomials.",

keywords = "orthogonal polynomials, q-Dunkl operator, q-semiclassical polynomials, q-series and q-polynomials, symmetric forms",

author = "Jihad Souissi and Alanezy, \{Khalid Ali\}",

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year = "2025",

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doi = "10.3390/sym17091526",

language = "English",

volume = "17",

journal = "Symmetry",

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T1 - A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation

AU - Souissi, Jihad

AU - Alanezy, Khalid Ali

PY - 2025/9

Y1 - 2025/9

N2 - This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the (Formula presented.) -analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of its q-Dunkl derivatives, offering a new effective classification method. We derive explicit structure relations for the (Formula presented.) -analogue of generalized Hermite and the (Formula presented.) -analogue of generalized Gegenbauer polynomials.

AB - This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the (Formula presented.) -analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of its q-Dunkl derivatives, offering a new effective classification method. We derive explicit structure relations for the (Formula presented.) -analogue of generalized Hermite and the (Formula presented.) -analogue of generalized Gegenbauer polynomials.

KW - orthogonal polynomials

KW - q-Dunkl operator

KW - q-semiclassical polynomials

KW - q-series and q-polynomials

KW - symmetric forms

UR - https://www.scopus.com/pages/publications/105017301694

U2 - 10.3390/sym17091526

DO - 10.3390/sym17091526

M3 - Article

AN - SCOPUS:105017301694

SN - 2073-8994

VL - 17

JO - Symmetry

JF - Symmetry

IS - 9

M1 - 1526

ER -

A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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