Finding the q -Appell Convolution of Certain Polynomials Within the Context of Quantum Calculus

Waseem Ahmad Khan (), Khidir Shaib Mohamed (), Francesco Aldo Costabile (), Can Kızılateş and Cheon Seoung Ryoo
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Waseem Ahmad Khan: Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Khidir Shaib Mohamed: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Francesco Aldo Costabile: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy
Can Kızılateş: Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100 Zonguldak, Turkey
Cheon Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea

Mathematics, 2025, vol. 13, issue 13, 1-24

Abstract: This article introduces the theory of three-variable q -truncated exponential Gould–Hopper-based Appell polynomials by employing a generating function approach that incorporates q -calculus functions. This study further explores these polynomials by using a computational algebraic approach. The determinant form, recurrences, and differential equations are proven. Relationships with the monomiality principle are given. Finally, graphical representations are presented to illustrate the behavior and potential applications of the three-variable q -truncated exponential Gould–Hopper-based Appell polynomials.

Keywords: quantum calculus; q -truncated polynomials; q -truncated Gould–Hopper–Appell polynomials; quasi-monomiality; extension of monomiality principle; q -dilatation operator; partial differential equations; differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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