Two-Variable q -General-Appell Polynomials Within the Context of the Monomiality Principle

Noor Alam, Waseem Ahmad Khan (), Can Kızılateş and Cheon Seoung Ryoo
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Noor Alam: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Waseem Ahmad Khan: Department Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Can Kızılateş: Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey
Cheon Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea

Mathematics, 2025, vol. 13, issue 5, 1-21

Abstract: In this study, we consider the two-variable q -general polynomials and derive some properties. By using these polynomials, we introduce and study the theory of two-variable q -general Appell polynomials (2V q gAP) using q -operators. The effective use of the q -multiplicative operator of the base polynomial produces the generating equation for 2V q gAP involving the q -exponential function. Furthermore, we establish the q -multiplicative and q -derivative operators and the corresponding differential equations. Then, we obtain the operational, explicit and determinant representations for these polynomials. Some examples are constructed in terms of the two-variable q -general Appell polynomials to illustrate the main results. Finally, graphical representations are provided to illustrate the behavior of some special cases of the two-variable q -general Appell polynomials and their potential applications.

Keywords: quantum calculus; two-variable q-general polynomials; two-variable q-general Appell polynomials; q-quasi monomiality principle; dilatation operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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