Operational methods and differential equations with applications to initial-value problems

摘要

The authors present and develop a general method of operational nature in order to explore and investigate such families of orthogonal polynomials and functions as the classical and generalized Hermite and Laguerre polynomials, as well as their higher-order and multi-index cases. They also consider several applications of these operational techniques to the solutions of a wide class of partial differential equations, including (for example) the heat, wave, and transport equations, some of which involve second-order Laguerre derivatives.