Abstract
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.
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Kapsamı
Uluslararası
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Type
Hakemli
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Index info
WOS.SCI
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Language
English
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Article Type
None