Resonant equations with classical orthogonal polynomials. II

Abstract

UDC 517.9
We study some resonant equations related to the classical orthogonal polynomials on infinite intervals, i.e., the Hermite and the Laguerre orthogonal polynomials, and propose an algorithm of finding their particular and general solutions in the closed form. The algorithm is especially suitable for the computer-algebra tools, such as Maple. The resonant equations form an essential part of various applications, e.g., of the efficient functional-discrete method for the solution of operator equations and eigenvalue problems. These equations also appear in the context of supersymmetric Casimir operators for the di-spin algebra, as well as of the square operator equations $A^2u = f$ , e.g., of the biharmonic equation.