Hermite-based Appell polynomials: Properties and applications

By employing certain operational methods, the authors introduce Hermite-based Appell polynomials. Some properties of Hermite–Appell polynomials are considered, which proved to be useful for the derivation of identities involving these polynomials. The possibility of extending this technique to introduce Hermite-based Sheffer polynomials (for example, Hermite–Laguerre and Hermite–Sister Celine's polynomials) is also investigated.