On 2-variable q-Legendre polynomials: the view point of the q-operational technique - Raza, N.; Fadel, M.; Cesarano, C. (Carpathian Mathematical Publications, 2025)
In this work, we exploit the methods of an operational formality and extension of quasi-monomials to describe and realize 2-variable q-Legendre polynomials. We introduce the generating function of 2-variable q-Legendre polynomials with a context of 0^th order q-Bessel Tricomi functions and obtain their properties such as series definition and q-differential equations. Also, we establish the q-multiplicative and q-derivative operators of these polynomials. The operational representations of 2-variable q-Legendre polynomials are obtained.