# Orthogonal forms: a simple tool for proving the irartionality of $\zeta (3)$

## Repositorio e-Archivo

 dc.contributor.author Arvesú, Jorge dc.date.accessioned 2010-01-15T10:04:39Z dc.date.available 2010-01-15T10:04:39Z dc.date.issued 2009-08 dc.identifier.bibliographicCitation Journal of Approximation Theory (submitted) dc.identifier.issn 0021-9045 dc.identifier.uri http://hdl.handle.net/10016/6439 dc.description 33 pages, no figures.-- MSC2000 codes: Primary 42C05, 11B37, 11J72, 11M06; Secondary 30B70, 11A55, 11J70, 33C47. dc.description Submitted to: Journal of Approximation Theory dc.description.abstract A new proof of the irrationality of $\zeta(3)$ is given. The orthogonality relation among certain known forms [17] constitutes a novel ingredient used in the present approach. Here, the same sequences of integers obtained in [10] appear. Apéry’s recurrence relation for the sequence of rational approximants to $\zeta(3)$ are constructively obtained. A simultaneous rational approximation problem is used for such purposes. dc.description.sponsorship This research was partially supported by ‘Ramón y Cajal’ research program of Spain, the research project MTM2006-13000-C03-02 of the Ministerio de Educación y Ciencia of Spain, and Projects CCG07-UC3M/ESP-3339 and CCG08-UC3M/ESP-4516 from Comunidad Autónoma de Madrid. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Elsevier dc.subject.other Simultaneous rational approximation dc.subject.other Multiple orthogonal polynomials dc.subject.other Irrationality dc.subject.other Recurrence relations dc.title Orthogonal forms: a simple tool for proving the irartionality of $\zeta (3)$ dc.type article dc.type.review NonPeerReviewed dc.description.status No publicado dc.subject.eciencia Matemáticas dc.rights.accessRights openAccess
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