Some new formulas for $π$

dc.creatorAlmkvist, Gert
dc.creatorKrattenthaler, Christian
dc.creatorPetersson, Joakim
dc.date2001-10-22
dc.date2002-10-10
dc.date.accessioned2026-07-07T04:43:59Z
dc.date.available2026-07-07T04:43:59Z
dc.descriptionWe 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.description28 pages, LaTeX; some important references added
dc.identifierhttps://arxiv.org/abs/math/0110238
dc.identifierhttp://arxiv.org/abs/math/0110238
dc.identifierExperiment. Math. 12 (2003), 441-456.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62461
dc.subjectNumber Theory
dc.subjectClassical Analysis and ODEs
dc.subject40A25 (Primary) 11B65 11Y60 65B10 (Secondary)
dc.titleSome new formulas for $π$
dc.typetext

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