A New Generalization of q -Truncated Polynomials Associated with q -General Polynomials

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 12, 1-19

Abstract: This article presents the theory of trivariate q -truncated Gould–Hopper polynomials through a generating function approach utilizing q -calculus functions. These polynomials are subsequently examined within the framework of quasi-monomiality, leading to the establishment of fundamental operational identities. Operational representations are then derived, and q -differential and partial differential equations are formulated for the trivariate q -truncated Gould–Hopper polynomials. Summation formulae are presented to elucidate the analytical properties of these polynomials. Finally, graphical representations are provided to illustrate the behavior of trivariate q -truncated Gould–Hopper polynomials and their potential applications.

Keywords: quantum calculus; q -truncated polynomials; q -truncated-Gould-Hopper polynomials; q -quasi monomiality; fractional derivatives; differential equations; partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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