A NEW GENERALIZATION OF $q$-TRUNCATED EXPONENTIAL-BASED APPELL POLYNOMIALS WITHIN THE CONTEXT OF QUANTUM CALCULUS

Abstract

In this work, we set out on an exhaustive analysis of trivariate $q$-truncated exponential-based Appell polynomials (T$q$-TEbAP), which are explicitly built by a generating function with a $q$-calculus profile. First, an analysis will be provided for these polynomials by means of quasi-monomiality, which will lead to the fundamental operational relations and a simple form for the operators. Subsequently, concrete forms for the operators will be obtained, along with the related $q$-differential and partial differential equations that these polynomials obey. Last but not least, a number of summation formulas will be provided to highlight the intrinsic analytic properties of these polynomials.