Gauss-Appell polynomials: An umbral calculus approach

This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the theoretical framework of special functions and provide powerful techniques for uncovering new extensions and relationships among these functions. This research article introduces an innovative class of special polynomials, specifically the Gauss-Appell polynomials. The fundamental attributes of this versatile family of special polynomials are outlined, including generating relations, explicit representations, and differential recurrence relations. Certain examples of the particular members that belong to the class of Gauss-Appell polynomials are also considered.