Exceptional Gegenbauer polynomials via isospectral deformation

2021/10/08 by María Ángeles García‐Ferrero, David Gómez‐Ullate, García-Ferrero, María~Ángeles +5
Mathematics · Physics and Astronomy · #33C47 #34A05 #34L10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2110.04059

openalex publication_date 2021/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show a method to construct isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, and it allows to construct Sturm-Liouville problems with polynomial eigenfunctions that have an arbitrary number of continuous parameters. We propose to call these new orthogonal polynomial systems exceptional polynomials of the second kind. We illustrate this construction by describing the class of exceptional Gegenbauer polynomials of the second kind.

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