A third-order Apery-like recursion for $ζ(5)$
| dc.creator | Zudilin, Wadim | |
| dc.date | 2002-06-18 | |
| dc.date | 2002-07-06 | |
| dc.date.accessioned | 2026-07-07T06:29:52Z | |
| dc.date.available | 2026-07-07T06:29:52Z | |
| dc.description | In 1978, Apery has given sequences of rational approximations to $ζ(2)$ and $ζ(3)$ yielding the irrationality of each of these numbers. One of the key ingredient of Apery's proof are second-order difference equations with polynomial coefficients satisfied by numerators and denominators of the above approximations. Recently, a similar second-order difference equation for $ζ(4)$ has been discovered. The note contains a possible generalization of the above results for the number $ζ(5)$. | |
| dc.description | 5 pages, AmSTeX; to appear in Mat. Zametki [Math. Notes] 72 (2002) | |
| dc.identifier | https://arxiv.org/abs/math/0206178 | |
| dc.identifier | http://arxiv.org/abs/math/0206178 | |
| dc.identifier | Mat. Zametki 72:5 (2002), 796--800 (Russian); English transl., Math. Notes 72:5 (2002), 733--737 | |
| dc.identifier | doi:10.1023/A:1021473409544 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98192 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Primary 11Y60; Secondary 11J20, 33C20 | |
| dc.title | A third-order Apery-like recursion for $ζ(5)$ | |
| dc.type | text |