When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

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dc.contributor.author Alfaro, Manuel
dc.contributor.author Marcellán Español, Francisco José
dc.contributor.author Peña, Ana
dc.contributor.author Rezola, M. Luisa
dc.date.accessioned 2009-12-02T10:08:41Z
dc.date.available 2009-12-02T10:08:41Z
dc.date.issued 2010-01
dc.identifier.bibliographicCitation Journal of Computational and Applied Mathematics, 2010, vol. 233, n. 6, p. 1446-1452
dc.identifier.issn 0377-0427
dc.identifier.uri http://hdl.handle.net/10016/5900
dc.description 7 pages, no figures.-- MSC2000 codes: 33C45; 42C05.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics" (Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday).
dc.description.abstract Given {Pn}n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,
dc.description.abstract Qn(x) = Pn(x) + a1Pn-1(x) + ... + akPn-k(x), ak<>0, n>k.
dc.description.abstract Necessary and sufficient conditions are given for the orthogonality of the sequence {Qn}n≥0. An interesting interpretation in terms of the Jacobi matrices associated with {Pn}n≥0 and {Qn}n≥0 is shown.
dc.description.sponsorship MA and MLR partially supported by Ministerio de Educación y Ciencia (MEC) of Spain under Grant MTM 2006-13000-C03-03 and Diputación General de Aragón (DGA) project E-64. FM partially supported by MEC of Spain under Grant MTM 2006-13000-C03-02 and INTAS Research Network NeCCA 03-51-6637. AP partially supported by MEC of Spain under Grants MTM 2004-03036 and MTM 2006-13000-C03-03 and DGA project E-64.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier
dc.subject.other Orthogonal polynomials
dc.subject.other Recurrence relations
dc.subject.other Linear functionals
dc.subject.other Chebyshev polynomials
dc.subject.other Difference equations
dc.title When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.cam.2009.02.060
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.cam.2009.02.060
dc.rights.accessRights openAccess
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