Exceptional Legendre polynomials and confluent Darboux transformations - García-Ferrero, María Ángeles; Gómez-Ullate, David; Milson, Robert (Symmetry, integrability and geometry: methods and applications, 2021)
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.
Gesehen am 29.06.2021