Two-Variable q -Hermite-Based Appell Polynomials and Their Applications

Mohammed Fadel, Maryam Salem Alatawi and Waseem Ahmad Khan ()
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Mohammed Fadel: Department of Mathematics, Lahej University, Lahej 73560, Yemen
Maryam Salem Alatawi: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia

Mathematics, 2024, vol. 12, issue 9, 1-17

Abstract: A noteworthy advancement within the discipline of q -special function analysis involves the extension of the concept of the monomiality principle to q -special polynomials. This extension helps analyze the quasi-monomiality of many q -special polynomials. This extension is a helpful tool for considering the quasi-monomiality of several q -special polynomials. This study aims to identify and establish the characteristics of the 2-variable q -Hermite–Appell polynomials via an extension of the concept of monomiality. Also, we present some applications that are taken into account.

Keywords: extension of monomility principle; q -Appell polynomials; q -Hermite polynomials; q -dilatation operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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