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Asymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomials

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorGómez-Ullate, Davides
dc.contributor.authorMarcellán Español, Francisco Josées
dc.contributor.authorMilson, Roberten
dc.date.accessioned2016-06-30T07:55:11Z
dc.date.available2016-06-30T07:55:11Z
dc.date.issued2012-03-01
dc.description.abstractIn this paper we state and prove some properties of the zeros of exceptional Jacobi and Laguerre polynomials. Generically, the zeros of exceptional polynomials fall into two classes: the regular zeros, which lie in the interval of orthogonality and the exceptional zeros, which lie outside that interval. We show that the regular zeros have two interlacing properties: one is the natural interlacing between zeros of consecutive polynomials as a consequence of their Sturm-Liouville character, while the other one shows interlacing between the zeros of exceptional and classical polynomials. A Heine-Mehler type formula is provided for the exceptional polynomials, which allows to derive the asymptotic behaviour of their regular zeros for large degree n and fixed codimension m. We also describe the location and the asymptotic behaviour of the m exceptional zeros, which converge for large n to fixed values.en
dc.description.sponsorshipThe research of the first author (DGU) has been supported by Dirección General de Investigación, Ministerio de Ciencia e Innovación of Spain, under grant MTM2009- 06973. The work of the second author (FM) has been supported by Direccioón General de Investigaci ón, Ministerio de Ciencia e Innovación of Spain, grant MTM2009-12740-C03-01. The research of the third author (RM) was supported in part by NSERC grant RGPIN-228057-2009.en
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Mathematical Analysis and Applications, 399 (Issue 2), pp. 480-495
dc.identifier.doi10.1016/j.jmaa.2012.10.032
dc.identifier.issn0022-247X
dc.identifier.publicationfirstpage480
dc.identifier.publicationlastpage495
dc.identifier.publicationtitleJournal of Mathematical Analysis and Applicationsen
dc.identifier.publicationvolume399
dc.identifier.urihttp://hdl.handle.net/10016/23256
dc.identifier.uxxiAR/0000011294
dc.language.isoeng
dc.relation.projectIDGobierno de España. MTM2012- 36732- C03-01es
dc.relation.projectIDGobierno de España. MTM2012-06973es
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.jmaa.2012.10.032
dc.rights© Elsevier 2013
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherzerosen
dc.subject.otherouter relative asymptoticsen
dc.subject.otherHeine-Mehler formulasen
dc.subject.otherSturm-Liouville problemsen
dc.subject.otheralgebraic Darboux transformationsen
dc.subject.otherexceptional orthogonal polynomialsen
dc.titleAsymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomialsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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