Chudnovsky algorithm

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The Chudnovsky algorithm is a fast method for calculating the digits of π. It was used by the Chudnovsky brothers to calculate more than one billion digits.

The algorithm is based on the following rapidly convergent hypergeometric series:

 \frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}}.\!

This identity is very similar to some of Ramanujan's formulae involving π.

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