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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 approximation
Multiple orthogonal polynomials
Irrationality
Recurrence relations |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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