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Some discrete multiple orthogonal polynomials

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorArvesú Carballo, Jorge
dc.contributor.authorCoussement, J.
dc.contributor.authorVan Assche, W.
dc.date.accessioned2010-01-14T12:32:58Z
dc.date.available2010-01-14T12:32:58Z
dc.date.issued2003-04-01
dc.description27 pages, no figures.-- MSC2000 codes: 33C45, 33C10, 42C05, 41A28.-- Issue title: "Proceedings of the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications" (OPSFA-VI, Rome, Italy, 18-22 June 2001).
dc.descriptionMR#: MR1985676 (2004g:33015)
dc.descriptionZbl#: Zbl 1021.33006
dc.description.abstractIn this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317–347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
dc.description.sponsorshipThis research was supported by INTAS project 00-272, Dirección General de Investigación del Ministerio de Ciencia y Tecnología of Spain under grants BFM-2000-0029 and BFM-2000-0206-C04-01, Dirección General de Investigación de la Comunidad Autónoma de Madrid, and by project G.0184.02 of FWO-Vlaanderen.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Computational and Applied Mathematics, 2003, vol. 153, n. 1-2, p. 19-45
dc.identifier.doi10.1016/S0377-0427(02)00597-6
dc.identifier.issn0377-0427
dc.identifier.urihttps://hdl.handle.net/10016/6409
dc.language.isoeng
dc.publisherElsevier
dc.relation.publisherversionhttp://dx.doi.org/10.1016/S0377-0427(02)00597-6
dc.rights© Elsevier
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherMultiple orthogonal polynomials
dc.subject.otherDiscrete orthogonality
dc.subject.otherCharlier polynomials
dc.subject.otherMeixner polynomials
dc.subject.otherKravchuk polynomials
dc.subject.otherHahn polynomials
dc.titleSome discrete multiple orthogonal polynomials
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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