Operational Methods for Hermite Polynomials with Applications

We exploit methods of operational nature to derive a set of new identities involving families of polynomials associated with operators providing different realizations of the Weyl group. The identities, we will deal with, extend the Nielsen formulae, valid for ordinary Hermite to families of Hermitelike polynomials. It will also be shown that the underlying formalism yields the possibility of obtaining further identities relevant to multi-variable and multi-index polynomials. Applications of higher order Hermite polynomials have been underlined for purpose of numerical simulation in continuous damage mechanics.