On 2-variable q-Legendre polynomials: the view point of the q-operational technique

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.