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Number of cited
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.

  • Kapsamı

    Uluslararası

  • Type

    Hakemli

  • Index info

    WOS.SCI

  • Language

    English

  • Article Type

    None