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• W3129294958 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." @default.
• W3129294958 created "2021-03-01" @default.
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• W3129294958 date "2021-02-20" @default.
• W3129294958 modified "2023-10-18" @default.
• W3129294958 title "Exceptional Legendre Polynomials and Confluent Darboux Transformations" @default.
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• W3129294958 doi "https://doi.org/10.3842/sigma.2021.016" @default.
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