q-Legendre based Gould–Hopper polynomials and q-operational methods

Abstract The generalization of the monomiality principle for q -special polynomials has just been explained and demonstrated. This extension is used to study the monomiality features of the number of q -special polynomials, such as q -Appell polynomials, q -Gould–Hopper polynomials, two variables q -Hermite, q -Laguerre and q -Legendre polynomials. Additionally, several kinds of hybrid q -special polynomials and their monomiality features are studied, such as two-variable q -Laguerre-Appell polynomials, two-variable based q -Hermite-Appell polynomials and q -Gould–Hopper–Appell polynomials. This study seeks to generate the q -Legendre–Gould–Hopper polynomials and then describe their attributes by extending the idea of monomiality for q -polynomials. Furthermore, we propose operational representations, expansion formulae and new families of these polynomials with the aid of q -operational methods and extension for monomiality principle of q -polynomials.