Operational Identities and Properties of Ordinary and Generalized Special Functions

The theory of Hermite, Laguerre, and of the associated generating functions is reformulated within the framework of an operational formalism. This point of view provides more efficient tools which allow the straightforward derivation of a wealth of new and old identities. In this paper a central role is played by negative derivative operators and by their link with the Tricomi functions and the generalized Laguerre polynomials