Exceptional orthogonal polynomials and the Darboux transformation
Mathematical Physics
2010-12-02 v2 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 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.
Cite
@article{arxiv.1002.2666,
title = {Exceptional orthogonal polynomials and the Darboux transformation},
author = {David Gomez-Ullate and Niky Kamran and Robert Milson},
journal= {arXiv preprint arXiv:1002.2666},
year = {2010}
}
Comments
corrected abstract, added references, minor corrections