# New inequalities from classical Sturm theorems

## Repositorio e-Archivo

 dc.contributor.author Deaño, Alfredo dc.contributor.author Gil, Amparo dc.contributor.author Segura, Javier dc.date.accessioned 2010-01-27T11:49:16Z dc.date.available 2010-01-27T11:49:16Z dc.date.issued 2004-12 dc.identifier.bibliographicCitation Journal of Approximation Theory, 2004, vol. 131, n. 2, p. 208-230 dc.identifier.issn 0021-9045 dc.identifier.uri http://hdl.handle.net/10016/6647 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 dc.type.review PeerReviewed dc.description.status Publicado dc.relation.publisherversion http://dx.doi.org/10.1016/j.jat.2004.09.006 dc.subject.eciencia Matemáticas dc.identifier.doi 10.1016/j.jat.2004.09.006 dc.rights.accessRights openAccess
﻿

## Ficheros en el ítem

*Click en la imagen del fichero para previsualizar.(Los elementos embargados carecen de esta funcionalidad)