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 poi nt of view provides more efficient tools which allow the straightforward de rivation of a wraith of new and old identities. In this paper a central rol e is played by negative derivative operators and by their link with the Tri comi functions and the generalized Laguerre polynomials. (C) 1999 Academic Press.