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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

Leonhard Euler
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Abstract

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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Leonhard Euler. 2005-08-09. 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. https://arxiv.org/abs/math/0508170

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