Exceptional orthogonal polynomials and the Darboux transformation

Details Exceptional orthogonal polynomials and the Darboux transformation Exceptional orthogonal polynomials and the Darboux transformation

2010-02-13

arxiv.org/abs/1002.2666v2

J. Phys. A 43 (2010) 434016

Physics

Mathematical Physics

corrected abstract, added references, minor corrections

Scientific paper

10.1088/1751-8113/43/43/434016

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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