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A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a second-order eigenvalue equation. We extend Bochner's result by dropping the assumption that the first element of the orthogonal polynomial sequence be a constant. This approach gives rise to new families of complete orthogonal polynomial systems(More)
Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunc-tions of Sturm–Liouville problems, but without the assumption that an eigenpolyno-mial of every degree is present. In this sense, they generalize the classical families of Hermite, Laguerre, and Jacobi, and include as a special case the family of CPRS orthogonal polynomials introduced by(More)
Exceptional orthogonal polynomials were introduced by Gomez-Ullate, Kam-ran and Milson as polynomial eigenfunctions of second order differential equations with the remarkable property that some degrees are missing, i.e., there is not a polynomial for every degree. However, they do constitute a complete orthogonal system with respect to a weight function(More)
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