On a new type of rational and highly convergent series, by which the ratio of the circumference to the diameter is able to be expressed

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dc.creatorEuler, Leonhard
dc.date2005-08-09
dc.date.accessioned2026-07-07T05:22:17Z
dc.date.available2026-07-07T05:22:17Z
dc.descriptionIn this short paper Euler gives a highly convergent series for arctan and thus pi, which converges much faster than the Leibniz series for arctan.
dc.description5 pages, seems to be first English translation of Euler's Latin original ``De novo genere serierum rationalium et valde convergentium, quibus ratio peripheriae ad diametrum exprimi potest'', Nova Acta Academiae Scientarum Imperialis Petropolitinae 11 (1798), 150-154, E706
dc.identifierhttps://arxiv.org/abs/math/0508170
dc.identifierhttp://arxiv.org/abs/math/0508170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76003
dc.subjectHistory and Overview
dc.subjectClassical Analysis and ODEs
dc.subject01A50; 40A05
dc.titleOn a new type of rational and highly convergent series, by which the ratio of the circumference to the diameter is able to be expressed
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