The exceptional Bessel polynomials

Gomez-Ullate, Kamran and Milson have found polynomial eigenfunctions of a Sturm-Liouville problem. These polynomials, denoted by X 1 -Laguerre and X 1 -Jacobi and starting with degree one, are eigenfunctions of a second-order linear differential operator. In this paper, we investigate the X 1 -Besse...

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Bibliographic Details
Published in:	Integral transforms and special functions Vol. 25; no. 6; pp. 470 - 480
Main Authors:	Atia, M.J., Chneguir, S.
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 03-06-2014 Taylor & Francis Ltd
Subjects:	Bessel polynomials Carlitz formula Eigenfunctions Functions (mathematics) Mathematical analysis Operators orthogonal polynomials Orthogonality Polynomials Primary: 33C45 Secondary: 42C05 Sturm-Liouville problem Transforms
Online Access:	Get full text
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Summary:	Gomez-Ullate, Kamran and Milson have found polynomial eigenfunctions of a Sturm-Liouville problem. These polynomials, denoted by X 1 -Laguerre and X 1 -Jacobi and starting with degree one, are eigenfunctions of a second-order linear differential operator. In this paper, we investigate the X 1 -Bessel case which we denote by . We wrote these polynomials as explicit functions of n, decompose it for the basis (x−b) 2 x i , and we expand in terms of Bessel orthogonal polynomials , using generalized Carlitz formula. Finally, we give a non-hermitian orthogonality satisfied by these polynomials.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1065-2469 1476-8291
DOI:	10.1080/10652469.2013.876020