Some new formulas for $π$
| dc.creator | Almkvist, Gert | |
| dc.creator | Krattenthaler, Christian | |
| dc.creator | Petersson, Joakim | |
| dc.date | 2001-10-22 | |
| dc.date | 2002-10-10 | |
| dc.date.accessioned | 2026-07-07T04:43:59Z | |
| dc.date.available | 2026-07-07T04:43:59Z | |
| dc.description | We show how to find series expansions for $π$ of the form $π=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$, where S(n) is some polynomial in $n$ (depending on $m,p,a$). We prove that there exist such expansions for $m=8k$, $p=4k$, $a=(-4)^k$, for any $k$, and give explicit examples for such expansions for small values of $m$, $p$ and $a$. | |
| dc.description | 28 pages, LaTeX; some important references added | |
| dc.identifier | https://arxiv.org/abs/math/0110238 | |
| dc.identifier | http://arxiv.org/abs/math/0110238 | |
| dc.identifier | Experiment. Math. 12 (2003), 441-456. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62461 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 40A25 (Primary) 11B65 11Y60 65B10 (Secondary) | |
| dc.title | Some new formulas for $π$ | |
| dc.type | text |