# 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…

## 6 Citations

### Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters

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### Determinantal Formulas for Exceptional Orthogonal Polynomials

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. We present determinantal formulas for families of exceptional X m -Laguerre and exceptional X m -Jacobi polynomials and also for exceptional X 2 -Hermite polynomials. The formulas resemble…

### Complete classification of rational solutions of A2-Painlevé systems

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