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Publication date

2022-06-10

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cc by-nc-nd (c) María Ángeles García-Ferrero, et al., 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193200

Exceptional Gegenbauer polynomials via isospectral deformation

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https://doi.org/10.1111/sapm.12510

Abstract

In this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, where repeated factorizations at the same eigenvalue are allowed. These factorizations allow us to construct Sturm-Liouville problems with polynomial eigenfunctions that have an arbitrary number of realvalued parameters. We illustrate this new construction by exhibiting the class of deformed Gegenbauer polynomials, which are XOP families that are isospectral deformations of classical Gegenbauer polynomials.

Subject

Funcions hipergeomètriques, Teoria de l'aproximació, Polinomis

Subject (English)

Hypergeometric functions, Approximation theory, Polynomials

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

GARCÍA-FERRERO, María Ángeles, et al. Exceptional Gegenbauer polynomials via isospectral deformation. Studies in Applied Mathematics. 2022. Vol. 149, num. 2, pags. 324-363. ISSN 0022-2526. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/193200

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