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On All Symmetric and Nonsymmetric Exceptional Orthogonal X 1 -Polynomials Generated by a Specific Sturm–Liouville Problem

Author

Listed:
  • Mohammad Masjed-Jamei

    (Department of Mathematics, K. N. Toosi University of Technology, Tehran P.O. Box 16315-1618, Iran
    These authors contributed equally to this work.)

  • Zahra Moalemi

    (Department of Mathematics, K. N. Toosi University of Technology, Tehran P.O. Box 16315-1618, Iran
    These authors contributed equally to this work.)

  • Nasser Saad

    (School of Mathematical and Computational Sciences, University of Prince Edward Island, Charlottetown, PE C1A 4P3, Canada)

Abstract

Exceptional orthogonal X 1 -polynomials of symmetric and nonsymmetric types can be considered as eigenfunctions of a Sturm–Liouville problem. In this paper, by defining a generic second-order differential equation, a unified classification of all these polynomials is presented, and 10 particular cases of it are then introduced and analyzed.

Suggested Citation

  • Mohammad Masjed-Jamei & Zahra Moalemi & Nasser Saad, 2022. "On All Symmetric and Nonsymmetric Exceptional Orthogonal X 1 -Polynomials Generated by a Specific Sturm–Liouville Problem," Mathematics, MDPI, vol. 10(14), pages 1-30, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2464-:d:863516
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    Cited by:

    1. Sergei Sitnik, 2023. "Editorial for the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”," Mathematics, MDPI, vol. 11(15), pages 1-7, August.

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