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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
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.
Received: September 22, 2020; in final form February 3, 2021; Published online February 20, 2021
Citation:
María Ángeles García-Ferrero, David Gómez-Ullate, Robert Milson, “Exceptional Legendre Polynomials and Confluent Darboux Transformations”, SIGMA, 17 (2021), 016, 19 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1699 https://www.mathnet.ru/eng/sigma/v17/p16
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