Δ-Sobolev orthogonal polynomials of Meixner type: asymptotics and limit relation

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dc.contributor.author Area, Iván
dc.contributor.author Godoy, Eduardo
dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Moreno Balcázar, Juan José
dc.date.accessioned 2009-12-04T12:34:30Z
dc.date.available 2009-12-04T12:34:30Z
dc.date.issued 2005-06
dc.identifier.bibliographicCitation Journal of Computational and Applied Mathematics, 2005, vol. 178, n. 1-2, p. 21-36
dc.identifier.issn 0377-0427
dc.identifier.uri http://hdl.handle.net/10016/5953
dc.description 16 pages, no figures.-- MSC2000 codes: 42C05.-- Issue title: "Proceedings of the Seventh International Symposium on Orthogonal Polynomials, Special Functions and Applications" (University of Copenhagen, Denmark, Aug 18-22, 2003).
dc.description MR#: MR2127867 (2006a:33005)
dc.description Zbl#: Zbl 1060.42015
dc.description.abstract Let $\{Q_n(x)\}_n$ be the sequence of monic polynomials orthogonal with respect to the Sobolev-type inner product $$\bigl\langle (p(x),r(x)\bigr \rangle_S=\bigl\langle{\bold u}_0,p(x)r(x) \bigr\rangle+ \lambda\bigl\langle {\bold u}_1,(\Delta p)(x)(\Delta r)(x) \bigr\rangle,$$ where $\lambda\ge 0$, $(\Delta f)(x)=f(x+1)-f(x)$ denotes the forward difference operator and $({\bold u}_0,{\bold u}_1)$ is a $\Delta$-coherent pair of positive-definite linear functionals being ${\bold u}_1$ the Meixner linear functional. In this paper, relative asymptotics for the $\{Q_n(x)\}_n$ sequence with respect to Meixner polynomials on compact subsets of $\bbfC\setminus[0,+\infty)$ is obtained. This relative asymptotics is also given for the scaled polynomials. In both cases, we deduce the same asymptotics as we have for the self-$\Delta$-coherent pair, that is, when ${\bold u}_0={\bold u}_1$ is the Meixner linear functional. Furthermore, we establish a limit relation between these orthogonal polynomials and the Laguerre-Sobolev orthogonal polynomials which is analogous to the one existing between Meixner and Laguerre polynomials in the Askey scheme.
dc.description.sponsorship The work by I.A. and E.G. was partially supported by Ministerio de Ciencia y Tecnología of Spain under grant BFM2002-04314-C02-01. The work by F.M. has been supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM2003-06335-C03-02 as well as by the NATO collaborative grant PST.CLG. 979738. The work by J.J.M.B has been supported by Dirección General de Investigación of Spain under grant BFM2001-3878-C02-02 as well as by Junta de Andalucía (research group FQM0229).
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier
dc.subject.other Orthogonal polynomials
dc.subject.other Sobolev orthogonal polynomials
dc.subject.other Meixner polynomials
dc.subject.other Δ-coherent pairs
dc.subject.other Asymptotics
dc.subject.other Linear functionals
dc.title Δ-Sobolev orthogonal polynomials of Meixner type: asymptotics and limit relation
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.cam.2004.08.008
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.cam.2004.08.008
dc.rights.accessRights openAccess
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