Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6439

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 Title: Orthogonal forms: a simple tool for proving the irartionality of $\zeta (3)$ Author(s): Arvesú, Jorge Publisher: Elsevier Issued date: Aug-2009 Citation: Journal of Approximation Theory (submitted) URI: http://hdl.handle.net/10016/6439 ISSN: 0021-9045 Description: 33 pages, no figures.-- MSC2000 codes: Primary 42C05, 11B37, 11J72, 11M06; Secondary 30B70, 11A55, 11J70, 33C47.Submitted to: Journal of Approximation Theory 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. Sponsor: 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. Review: NonPeerReviewed Keywords: Simultaneous rational approximationMultiple orthogonal polynomialsIrrationalityRecurrence relations Appears in Collections: DM - GAMA - Artículos de Revistas