New inequalities from classical Sturm theorems

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Show simple item record Deaño, Alfredo Gil, Amparo Segura, Javier 2010-01-27T11:49:16Z 2010-01-27T11:49:16Z 2004-12
dc.identifier.bibliographicCitation Journal of Approximation Theory, 2004, vol. 131, n. 2, p. 208-230
dc.identifier.issn 0021-9045
dc.description 23 pages, no figures.-- MSC2000 codes: Primary: 33C45; Secondary: 26D20, 34C10.
dc.description MR#: MR2106538 (2006c:33007)
dc.description.abstract Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegö's bounds on the zeros of Jacobi polynomials $P_n\sp {(\alpha,\beta)}(\cos\theta)$ for $ alpha beta 1/2$ and $ 1/2$ are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with 1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions.
dc.description.sponsorship A. Gil acknowledges financial support from Ministerio de Ciencia y Tecnología (programa Ramón y Cajal). J. Segura acknowledges financial support from Project BFM2003-06335-C03-02.
dc.format.mimetype text/html
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier
dc.subject.other Sturm comparison theorem
dc.subject.other Hypergeometric functions
dc.subject.other Orthogonal polynomials
dc.title New inequalities from classical Sturm theorems
dc.type article PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.jat.2004.09.006
dc.rights.accessRights openAccess
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