Laguerre and generalized hermite polynomials: the point of view of the operational method

Abstract

We use computational methods based on an operational point of view to prove the existence of a link between Laguerre and generalized Hermite polynomials with many variables and many indices. Within this framework new versions of the Wicksell–Campbell–Meixner and Buchholz formulae are proposed and it is also shown that the operational method can be exploited to gain a deeper insight into the nature of the Bateman polynomials.