We study some resonant equations related to the classical orthogonal polynomials and propose an algorithm for finding their particular and general solutions in the explicit 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 aimed at 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 for the square operator equations A2u = f; e.g., for the biharmonic equation.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 2, pp. 190–209, February, 2019.
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Gavrilyuk, I., Makarov, V. Resonant Equations with Classical Orthogonal Polynomials. I. Ukr Math J 71, 215–236 (2019). https://doi.org/10.1007/s11253-019-01640-9
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DOI: https://doi.org/10.1007/s11253-019-01640-9