Geodesic
Exceptional Legendre Polynomials and Confluent Darboux Transformations
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : exceptional orthogonal polynomials, Darboux transformations, isospectral deformations. 
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     author = {Mar{\'\i}a \'Angeles Garc{\'\i}a-Ferrero and David G\'omez-Ullate and Robert Milson},
     title = {Exceptional {Legendre} {Polynomials} and {Confluent} {Darboux} {Transformations}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2021},
     volume = {17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a15/}
}
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María Ángeles García-Ferrero; David Gómez-Ullate; Robert Milson. Exceptional Legendre Polynomials and Confluent Darboux Transformations. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a15/

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