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Exceptional orthogonal polynomials and the Darboux transformation (1002.2666v2)
Published 13 Feb 2010 in math-ph and math.MP
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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