Two-Variable <i>q</i>-Hermite-Based Appell Polynomials and Their Applications

Abstract

A noteworthy advancement within the discipline of q-special function analysis involves the extension of the concept of the monomiality principle to q-special polynomials. This extension helps analyze the quasi-monomiality of many q-special polynomials. This extension is a helpful tool for considering the quasi-monomiality of several q-special polynomials. This study aims to identify and establish the characteristics of the 2-variable q-Hermite–Appell polynomials via an extension of the concept of monomiality. Also, we present some applications that are taken into account.

Keywords

• extension of monomility principle
• <i>q</i>-Appell polynomials
• <i>q</i>-Hermite polynomials
• <i>q</i>-dilatation operator