Finding the <i>q</i>-Appell Convolution of Certain Polynomials Within the Context of Quantum Calculus
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/math13132073 | Anahtar Kelimeler: quantum calculus, <italic>q</italic>-truncated polynomials, <italic>
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.