Two-step Darboux transformations and exceptional Laguerre polynomials



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Gómez-Ullate Otaiza, David and Kamran, Niky and Milson, Robert (2012) Two-step Darboux transformations and exceptional Laguerre polynomials. Journal of mathematical analysis and applications, 387 (1). pp. 410-418. ISSN 0022-247X

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It has been recently discovered that exceptional families of Sturm-Liouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of exceptional orthogonal polynomials can be constructed by means of multiple-step algebraic Darboux transformations. The construction is illustrated with an example of a 2-step Darboux transformation of the classical Laguerre polynomials, which gives rise to a new orthogonal polynomial system indexed by two integer parameters. For particular values of these parameters, the classical Laguerre and the type II X(l)-Laguerre polynomials are recovered.

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© 2011 Elsevier Inc. All rights reserved.
The research of DGU was supported in part by MICINN-FEDER grant MTM2009- 06973 and CUR-DIUE grant 2009SGR859. The research of NK was supported in part by NSERC grant RGPIN 105490-2004. The research of RM was supported in part by NSERC grant RGPIN-228057-2004.

Uncontrolled Keywords:Shape-invariant potentials; Orthogonal polynomials
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30775
Deposited On:11 Jun 2015 10:16
Last Modified:10 Dec 2018 15:09

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