# 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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