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
Abstract
Description
In 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, E706
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, E706