Exceptional Legendre Polynomials and Confluent Darboux Transformations

@article{GarcaFerrero2021ExceptionalLP,
  title={Exceptional Legendre Polynomials and Confluent Darboux Transformations},
  author={Mar{\'i}a {\'A}ngeles Garc{\'i}a‐Ferrero and Ruprecht-Karls-Universit and David G{\'o}mez‐Ullate and Robert Milson},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2021},
  volume={17},
  pages={016}
}
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… 

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