2-Variable q$$ q $$-Legendre-Based Appell Polynomials and Their Applications
Waseem Ahmad Khan, Mumtaz Riyasat, Can Kizilates
article (Uluslararası, Hakemli) | Yazar(lar): Waseem Ahmad Khan, Mumtaz Riyasat, Can Kizilates | Yıl: 2026 | Dergi/Kurum: MATHEMATICAL METHODS IN THE APPLIED SCIENCES | İndeks: WOS.SCI | DOI: 10.1002/mma.70353 | Anahtar Kelimeler: extension of monomiality principle, quantum calculus, quasi monomiality, q$$ q $$-dilatat
In this paper, we introduce the theory of two-variable -Legendre-based Appell polynomials through the framework of the zeroth-order -Tricomi functions. These polynomials are investigated via their generating functions, series expansions, and determinant representations. Furthermore, employing the principles of -quasi-monomiality, we establish that these polynomials possess the -quasi-monomial property, deriving several operational representations and formulating the corresponding -differential equations. Several illustrative examples are presented to elucidate the theory of -Legendre-based Appell polynomials and to highlight the properties established above. Finally, graphical interpretations are provided, including plots, surface visualizations, and depictions of the spatial distribution of scattered zeros in the -plane for selected two-variable -Legendre-based Appell polynomials.