Resonant Equations with Classical Orthogonal Polynomials. II

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 for finding their particular and general solutions in the closed form. This 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 and in the solution of square operator equations, such as A(2)u = f (e.g., of the biharmonic equation).