Bellard's formula

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Bellard's formula, as used by PiHex, the now-completed distributed computing project, is used to calculate the nth digit of π in base 2. It is a faster version (about 43% faster[1]) of the BBP formula. Bellard's formula was discovered by Fabrice Bellard.

[edit] Formula

\pi={{\frac1{2^6}}\,{\sum_{n=0}^\infty {{{\frac{{({-1})}^n}{2^{{10}\, n}}}\,{\left({{\frac{-{2^5}}{{4\, n}+1}}-{\frac1{{4\, n}+3}}+{\frac{2^8}{{{10}\, n}+1}}-{\frac{2^6}{{{10}\, n}+3}}-{\frac{2^2}{{{10}\, n}+5}}-{\frac{2^2}{{{10}\, n}+7}}+{\frac1{{{10}\, n}+9}}}\right)}}}}}

[edit] Notes

  1. ^ PiHex Credits

[edit] External links