Binomial sums related to rational approximations to $ζ(4)$
| dc.creator | Zudilin, Wadim | |
| dc.date | 2003-11-12 | |
| dc.date.accessioned | 2026-07-07T06:29:53Z | |
| dc.date.available | 2026-07-07T06:29:53Z | |
| dc.description | For the solution $\{u_n\}_{n=0}^\infty$ to the polynomial recursion $(n+1)^5u_{n+1}-3(2n+1)(3n^2+3n+1)(15n^2+15n+4)u_n -3n^3(3n-1)(3n+1)u_{n-1}=0$, where $n=1,2,...$, with the initial data $u_0=1$, $u_1=12$, we prove that all $u_n$ are integers. The numbers $u_n$, $n=0,1,2,...$, are denominators of rational approximations to $ζ(4)$ (see math.NT/0201024). We use Andrews's generalization of Whipple's transformation of a terminating ${}_7F_6(1)$-series and the method from math.NT/0311114. | |
| dc.description | 5 pages, AmSTeX | |
| dc.identifier | https://arxiv.org/abs/math/0311196 | |
| dc.identifier | http://arxiv.org/abs/math/0311196 | |
| dc.identifier | Mat. Zametki 75:4 (2004), 637--640 (Russian); English transl., Math. Notes 75:4 (2004), 594--597 | |
| dc.identifier | doi:10.1023/B:MATN.0000023341.93824.fb | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98195 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Number Theory | |
| dc.subject | 11B65, 33C20 | |
| dc.title | Binomial sums related to rational approximations to $ζ(4)$ | |
| dc.type | text |