A New Generalization of q-Truncated Polynomials Associated with q-General Polynomials - Waseem Ahmad Khan; Khidir Shaib Mohamed; Francesco Aldo Costabile; Can Kızılateş; Cheon Seoung Ryoo (Mathematics)
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.