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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76003In this short paper Euler gives a highly convergent series for arctan and thus pi, which converges much faster than the Leibniz series for arctan.5 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, E706History and OverviewClassical Analysis and ODEs01A50; 40A05On a new type of rational and highly convergent series, by which the ratio of the circumference to the diameter is able to be expressedtext