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Jacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorArvesú Carballo, Jorge
dc.contributor.authorÁlvarez Nodarse, Renato
dc.contributor.authorMarcellán Español, Francisco José
dc.contributor.authorPan, K.
dc.date.accessioned2010-01-14T11:38:42Z
dc.date.available2010-01-14T11:38:42Z
dc.date.issued1998-04-17
dc.description22 pages, 4 figures.-- MSC1991 codes: 33C45; 33A65; 42C05.-- Dedicated to Professor Mario Rosario Occorsio on his 65th birthday.
dc.descriptionMR#: MR1624329 (99h:33029)
dc.descriptionZbl#: Zbl 0924.33006
dc.description.abstractWe obtain an explicit expression for the Sobolev-type orthogonal polynomials $\{Q_n\}$ associated with the inner product $\langle p,q\rangle=\int^1_{-1}p(x)q(x)\rho(x)dx+A_1p(1)q(1)+B_1p(-1)q(-1)+A_2p'(1)q'(1)+B_2p'(-1)q'(-1)$, where $\rho(x)=(1-x)^\alpha(1+x)^\beta$ is the Jacobi weight function, $\alpha,\beta>-1$, $A_1,B_1,A_2,B_2\geq 0$ and $p,q\in\bold P$, the linear space of polynomials with real coefficients. The hypergeometric representation $({}_6F_5)$ and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in $[-1,1]$ is studied. Furthermore, we obtain some estimates for the largest zero of $Q_n(x)$. Such a zero is located outside the interval $[-1,1]$. We deduce its dependence on the masses. Finally, the WKB analysis for the distribution of zeros is presented.
dc.description.sponsorshipThe research of the first author (J.A.) was supported by a grant of Ministerio de Educación y Cultura (MEC) of Spain. The research of the three first authors (J.A., R.A.N. and F.M.) was supported by Dirección General de Enseñanza Superior (DGES) of Spain under Grant PB 96-0120-C03-01 and INTAS Project INTAS 93-0219 Ext.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Computational and Applied Mathematics, 1998, vol. 90, n. 2, p. 135-156
dc.identifier.doi10.1016/S0377-0427(98)00005-3
dc.identifier.issn0377-0427
dc.identifier.urihttps://hdl.handle.net/10016/6405
dc.language.isoeng
dc.publisherElsevier
dc.relation.publisherversionhttp://dx.doi.org/10.1016/S0377-0427(98)00005-3
dc.rights© Elsevier
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherOrthogonal polynomials
dc.subject.otherJacobi polynomials
dc.subject.otherHypergeometric function
dc.subject.otherSobolev-type orthogonal polynomials
dc.subject.otherWKB method
dc.titleJacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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