Some properties of Hermite-based Sheffer polynomials

摘要

In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite–Sheffer polynomials are considered. Further, an operational formalism providing a correspondence between Sheffer and Hermite–Sheffer polynomials is developed. Furthermore, this correspondence is used to derive several new identities and results for members of Hermite–Sheffer family.