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GómezUllate Otaiza, David and Kamran, Niky and Milson, Robert (2013) A conjecture on exceptional orthogonal polynomials. Foundations of computational mathematics, 13 (4). pp. 615666. ISSN 16153375

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Official URL: http://dx.doi.org/10.1007/s1020801291286
URL  URL Type 

http://link.springer.com  Publisher 
http://arxiv.org/abs/1203.6857  Organisation 
Abstract
Exceptional orthogonal polynomial systems (XOPSs) arise as eigenfunctions of SturmLiouville 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 Cariena 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 DarbouxCrum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2OPs). As a byproduct of this analysis, we prove a Bochnertype theorem classifying all possible X2OPSs. The classification includes all cases known to date plus some new examples of X2Laguerre and X2Jacobi polynomials.
Item Type:  Article 

Additional Information:  © Springer. The research of DGU was supported in part by MICINNFEDER grant MTM2009 06973 and CURDIUE grant 2009SGR859. The research of NK was supported in part by NSERC grant RGPIN 1054902011. The research of RM was supported in part by NSERC grant RGPIN2280572009. 
Uncontrolled Keywords:  Shapeinvariant potentials; Quasiexact solvability; XL laguerre; Darboux transformations; Differentialequation; Supersymmetry; Operators 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  30772 
Deposited On:  11 Jun 2015 10:02 
Last Modified:  10 Dec 2018 15:09 
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