Two-step Darboux transformations and exceptional Laguerre polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:387

Article

Gomez-Ullate, David¹  Kamran, Niky²  Milson, Robert³ 

[1] Univ Complutense Madrid, Dept Fis Teor 2, E-28040 Madrid, Spain

[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

[3] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada

关键词: Orthogonal polynomials;    Darboux transformations;    Sturm-Liouville problems;    Exceptional polynomials;   

DOI  :  10.1016/j.jmaa.2011.09.014

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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