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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 016, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.016
(Mi sigma1699)
 

This article is cited in 6 scientific papers (total in 6 papers)

Exceptional Legendre Polynomials and Confluent Darboux Transformations

María Ángeles García-Ferreroa, David Gómez-Ullatebc, Robert Milsond

a Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neunheimer Feld 205, 69120 Heidelberg, Germany
b Departamento de Ingeniería Informática, Escuela Superior de Ingenierıa, Universidad de Cádiz, 11519 Puerto Real, Spain
c Departamento de Física Teórica, Universidad Complutense de Madrid, 28040 Madrid, Spain
d Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada
Full-text PDF (542 kB) Citations (6)
References:
Abstract: Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm–Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of “exceptional” degrees. In this paper we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator. Using confluent Darboux transformations and a technique from inverse scattering theory, we obtain a fully explicit description of the operators and polynomials in question. The main novelty of the paper is the novel construction that allows for exceptional polynomial families with an arbitrary number of real parameters.
Keywords: exceptional orthogonal polynomials, Darboux transformations, isospectral deformations.
Funding agency Grant number
Ministerio de Ciencia e Innovación de España PGC2018-096504-B-C33
RTI2018-100754-B-I00
Federación Española de Enfermedades Raras FEDERUCA18-108393
DGU acknowledges support from the Spanish MICINN under grants PGC2018-096504-B-C33 and RTI2018-100754-B-I00 and the European Union under the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia (project FEDERUCA18-108393).
Received: September 22, 2020; in final form February 3, 2021; Published online February 20, 2021
Bibliographic databases:
Document Type: Article
MSC: 33C47, 34L10, 34A05
Language: English
Citation: María Ángeles García-Ferrero, David Gómez-Ullate, Robert Milson, “Exceptional Legendre Polynomials and Confluent Darboux Transformations”, SIGMA, 17 (2021), 016, 19 pp.
Citation in format AMSBIB
\Bibitem{GarGomMil21}
\by Mar{\'\i}a~\'Angeles~Garc{\'\i}a-Ferrero, David~G\'omez-Ullate, Robert~Milson
\paper Exceptional Legendre Polynomials and Confluent Darboux Transformations
\jour SIGMA
\yr 2021
\vol 17
\papernumber 016
\totalpages 19
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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