New Approaches to Certain Identities Involving Differential Operators

The authors develop certain new approaches to finding and proving numerous identities involving the derivative operator D = d/dx, and apply the resulting operator calculus to obtain (among other things) various known (or seemingly new) operational representations for the classical Laguerre and Hermite polynomials. The inter-relationships between many of these operational representations, and the potential for their applications in other related areas of interest, are also pointed out