A New Generalization of <i>q</i>-Truncated Polynomials Associated with <i>q</i>-General Polynomials
Waseem Ahmad Khan, Khidir Shaib Mohamed, Francesco Aldo Costabile, Can Kizilates, Cheon Seoung Ryoo
article (Uluslararası, Hakemli) | Yazar(lar): Waseem Ahmad Khan, Khidir Shaib Mohamed, Francesco Aldo Costabile, Can Kizilates, Cheon Seoung Ryoo | Yıl: 2025 | Dergi/Kurum: MATHEMATICS | İndeks: WOS.SCI | DOI: 10.3390/math13121964 | Anahtar Kelimeler: quantum calculus, <italic>q</italic>-truncated polynomials, <italic>
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.