@article{gomez-ullateConjectureExceptionalOrthogonal2013,
 abstract = {Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunctions of Sturm-Liouville problems, but without the assumption that an eigenpolynomial of every degree is present. In this sense, they generalize the classical families of Hermite, Laguerre, and Jacobi, and include as a special case the family of CPRS orthogonal polynomials introduced by Cariñena et al. (J. Phys. A 41:085301, 2008). We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X2-OPSs. The classification includes all cases known to date plus some new examples of X2-Laguerre and X2-Jacobi polynomials. o̧pyright 2012 SFoCM.},
 author = {Gómez-Ullate, David and Kamran, Niky and Milson, Robert},
 copyright = {http://www.springer.com/tdm},
 doi = {10.1007/s10208-012-9128-6},
 issn = {1615-3375, 1615-3383},
 journal = {Foundations of Computational Mathematics},
 langid = {english},
 month = {August},
 number = {4},
 pages = {615--666},
 title = {A Conjecture on Exceptional Orthogonal Polynomials},
 urldate = {2025-10-19},
 volume = {13},
 year = {2013}
}