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Exceptional orthogonal polynomials and the Darboux transformation

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Published Article
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DOI: 10.1088/1751-8113/43/43/434016
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arXiv
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Abstract

We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.

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