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Exceptional Gegenbauer polynomials via isospectral deformation

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URI: http://hdl.handle.net/10498/27007

DOI: 10.1111/sapm.12510

ISSN: 0022-2526

ISSN: 1467-9590

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APC_2022_059.pdf (556.9Kb)
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Author/s
García-Ferrero, María Ángeles; Gómez-Ullate Oteiza, DavidAuthority UCA; Milson, Robert; Munday, James
Date
2022
Department
Ingeniería Informática
Source
Stud Appl Math. 2022;1–40.
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.
Subjects
confluent Darboux transformations; exceptional polynomials; Gegenbauer polynomials; isospectral deformations; Sturm–Liouville problems
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  • Artículos Científicos [5002]
  • Articulos Científicos Ing. Inf. [142]
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 Internacional

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