Well-poised generation of Apéry-like recursions
| dc.creator | Zudilin, Wadim | |
| dc.date | 2003-07-04 | |
| dc.date | 2003-11-28 | |
| dc.date.accessioned | 2026-07-07T06:29:51Z | |
| dc.date.available | 2026-07-07T06:29:51Z | |
| dc.description | The idea to use classical hypergeometric series and, in particular, well-poised hypergeometric series in diophantine problems of the values of the polylogarithms has led to several novelties in number theory and neighbouring areas of mathematics. Here we present a systematic approach to derive second-order polynomial recursions for approximations to some values of the Lerch zeta function, depending on the fixed (but not necessarily real) parameter $α$ satisfying the condition $\Re(α)<1$. Substituting $α=0$ into the resulting recurrence equations produces the famous recursions for rational approximations to $ζ(2)$, $ζ(3)$ due to Apéry, as well as the known recursion for rational approximations to $ζ(4)$. Multiple integral representations for solutions of the constructed recurrences are also given. | |
| dc.description | 8 pages; to appear in the Proceedings of the 7th OPSFA (Copenhagen, 18--22 August 2003) | |
| dc.identifier | https://arxiv.org/abs/math/0307058 | |
| dc.identifier | http://arxiv.org/abs/math/0307058 | |
| dc.identifier | J. Comput. Appl. Math. 178:1--2 (2005), 513--521 | |
| dc.identifier | doi:10.1016/j.cam.2003.11.016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98184 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 11J70, 33C20, 33F10 | |
| dc.title | Well-poised generation of Apéry-like recursions | |
| dc.type | text |