The Laguerre and Legendre polynomials from an operational point of view

摘要

The use of the monomiality principle and of the associated operational calculus allows to reformulate the theory of Laguerre and Legendre polynomials from a unified point of view. They are indeed shown to be particular cases of more general polynomials, whose usefulness in purely mathematical and applied contexts is discussed. The concepts introduced in the paper are also exploited to develop an elementary point of view on the theory of Legendre and Laguerre–Bessel functions.