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Research Article | Open Access

Advancements in q-Hermite-Appell polynomials: a three-dimensional exploration

Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India
Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58, 55-66, Barranquilla 080002, Colombia
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, Rome 00186, Italy
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Abstract

In this research, we leverage various q-calculus identities to introduce the notion of q-Hermite-Appell polynomials involving three variables, elucidating their formalism. We delve into numerous properties and unveil novel findings regarding these q-Hermite-Appell polynomials, encompassing their generating function, series representation, summation equations, recurrence relations, q-differential formula, and operational principles. Our investigation sheds light on the intricate nature of these polynomials, elucidating their behavior and facilitating deeper understanding within the realm of q-calculus.

Keywords

special polynomialsq-calculusmonomiality principleexplicit formoperational connectiondeterminant formsymmetric identitiessummation formulae
CLC number: 33E20, 33C45, 33B10, 33E30, 11T23

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 26799-26824
DOI: 10.3934/math.20241303

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Cite this article:
Zayed M, Wani SA, Ramírez W, et al. Advancements in q-Hermite-Appell polynomials: a three-dimensional exploration. AIMS Mathematics, 2024, 9(10): 26799-26824. https://doi.org/10.3934/math.20241303

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Received: 29 April 2024
Revised: 15 July 2024
Accepted: 26 July 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)