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

Details 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 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

2005-08-09

arxiv.org/abs/math/0508170v1

Mathematics

History and Overview

5 pages, seems to be first English translation of Euler's Latin original ``De novo genere serierum rationalium et valde conver

Scientific paper

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.

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