A New Generalization of q-Laguerre-Based Appell Polynomials and Quasi-Monomiality

In this paper, we define a new generalization of three-variable q-Laguerre polynomials and derive some properties. By using these polynomials, we introduce a new generalization of three-variable q-Laguerre-based Appell polynomials (3VqLbAP) through a generating function approach involving zeroth-order q-Bessel–Tricomi functions. These polynomials are studied by means of generating function, series expansion, and determinant representation. Also, these polynomials are further examined within the framework of q-quasi-monomiality, leading to the establishment of essential operational identities. We then derive operational representations, as well as q-differential equations for the three-variable q-Laguerre-based Appell polynomials. Some examples are constructed in terms of q-Laguerre–Hermite-based Bernoulli, Euler, and Genocchi polynomials in order to illustrate the main results.