Resonant equations with classical orthogonal polynomials. I - Gavrilyuk, I. P.; Makarov, V. L. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
In the present paper, we study some resonant equations related to the classical orthogonal polynomials and propose analgorithm of finding their particular and general solutions in the explicit form. The algorithm is especially suitable for thecomputer algebra tools, such as Maple. The resonant equations form an essential part of various applications e.g. of theefficient functional-discrete method aimed at the solution of operator equations and eigenvalue problems. These equationsalso appear in the context of supersymmetric Casimir operators for the di-spin algebra, as well as for the square operatorequations $A^2u = f$; e.g., for the biharmonic equation.