Bivariate <i>q</i> -Laguerre–Appell polynomials and their applications

Recently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered. Also, certain results including the monomiality properties of the q-Gould-Hopper polynomials are derived and applications of monomiality are explored for a few members of the q-Appell polynomial families. In this paper, the primary purpose of this paper is to define 2-variable q-Laguerre–Appell polynomials by applying the q-monomiality principle techniques and to study their quasi-monomial properties and applications. We provide some operational identities and quasi-monomial features. Also, we derive some q-differential equations of these polynomials. As applications, using the operational identity of 2-variable q-Laguerre–Appell polynomials we draw specific conclusions regarding several q-Laguerre–Appell polynomial families. Furthermore, we define the family of q-Laguerre-Sheffer polynomials by an operational approach and give some of its fundamental properties.