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Bases of the space of solutions of some fourth-order linear difference equations: applications in rational approximation

2013-10Artigo científico Acesso restrito
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.sdg03:Saúde de Qualidade
datacite.subject.sdg07:Energias Renováveis e Acessíveis
datacite.subject.sdg11:Cidades e Comunidades Sustentáveis
dc.contributor.authorMarcellán, Francisco
dc.contributor.authorMendes, Ana
dc.contributor.authorPijeira, Héctor
dc.date.accessioned2026-03-06T11:18:48Z
dc.date.available2026-03-06T11:18:48Z
dc.date.issued2013-10
dc.description.abstractIt is very well known that a sequence of polynomials {Qn(x)}∞n=0 orthogonal with respect to a Sobolev discrete inner product 〈f,g〉s = ∫Ifg dμ+λf′(0)g′(0), λ ∈ ℝ+ where μ is a finite Borel measure and I is an interval of the real line, satisfies a five-term recurrence relation. In this contribution we study other three families of polynomials which are linearly independent solutions of such a five-term linear difference equation and, as a consequence, we obtain a polynomial basis of such a linear space. They constitute the analogue of the associated polynomials in the standard case. Their of {Qn(x)}∞n=0 explicit expression in terms of using an integral representation is given. Finally, an application of these polynomials in rational approximation is shown.eng
dc.identifier.citationMarcellán, F., Mendes, A., & Pijeira, H. (2013). Bases of the space of solutions of some fourth-order linear difference equations: applications in rational approximation. Journal of Difference Equations and Applications, 19(10), 1632–1644. https://doi.org/10.1080/10236198.2013.769531
dc.identifier.doi10.1080/10236198.2013.769531
dc.identifier.issn1023-6198
dc.identifier.issn1563-5120
dc.identifier.urihttp://hdl.handle.net/10400.8/15794
dc.language.isoeng
dc.peerreviewedyes
dc.publisherTaylor and Francis
dc.relation.hasversionhttps://www.tandfonline.com/doi/full/10.1080/10236198.2013.769531
dc.relation.ispartofJournal of Difference Equations and Applications
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectOrthogonal polynomials
dc.subjectRecurrence relation
dc.subjectDifference equations
dc.titleBases of the space of solutions of some fourth-order linear difference equations: applications in rational approximationeng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage1644
oaire.citation.issue10
oaire.citation.startPage1632
oaire.citation.titleJournal of Difference Equations and Applications
oaire.citation.volume19
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameMendes
person.givenNameAna
person.identifier.ciencia-id3C19-42EA-DDBD
person.identifier.orcid0000-0002-4161-6130
person.identifier.scopus-author-id55873199300
relation.isAuthorOfPublication3523e160-c260-47a6-89cc-eb3fca0059d9
relation.isAuthorOfPublication.latestForDiscovery3523e160-c260-47a6-89cc-eb3fca0059d9

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