Insights into New Generalization of q-Legendre-Based Appell Polynomials: Properties and Quasi Monomiality
Year: 2025
Type: article
Abstract: In this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced. These polynomials are studied by means of generating functions, series expansions, and determinant representation. Further, by utilizing the concepts of q-quasi-monomiality, these polynomials are examined as several q-quasi-monomial and operational representations; the q-differential equations for the three-variable q-Legendre-based Appell polynomials were obtained. In addition, we established a new generalization of three-variable q-Legendre-Hermite-Appell polynomials, and we derive series expansion, determinant representation, and q-quasi-monomial and q-differential equations. Some examples are framed to better illustrate the theory of three-variable q-Legendre-based Appell polynomials, and this is characterized by the above properties.
Source: Mathematics
DOI: 10.3390/math13060955
Authors: Naeem Ahmad, Waseem Ahmad Khan
Institutions: Jouf University, Prince Mohammad bin Fahd University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408404139