Multivariate q-Hermite-based Appell polynomials: structural properties and applications

Abstract

In the domain of specialized mathematical functions, the rising interest in q-calculus continues to attract researchers, offering powerful tools for modeling in fields like quantum computing, non-commutative probability, combinatorics, functional analysis, mathematical physics, and approximation theory. This study introduces the framework of multivariate q-Hermite-based Appell polynomials, employing various q-calculus techniques. Key properties and fresh insights into these polynomials are examined, such as their generating functions, series representations, recurrence relations, q-differential identities, and operational mechanisms. Additionally, it is shown that these polynomials maintain a quasi-monomial structure within the q-calculus context.