Haloragaceae

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) of the Bailey–Borwein–Plouffe formula.

Bellard's formula was discovered by Fabrice Bellard in 1997.

Formula

$\begin{array}{rl}\pi =\frac{1}{2^6}\sum _{n=0}^{\mathrm{\infty }}\frac{(-1{)}^n}{2^{10n}}(-\frac{2^5}{4n+1}& -\frac{1}{4n+3}+\frac{2^8}{10n+1}-\frac{2^6}{10n+3}-\frac{2^2}{10n+5}-\frac{2^2}{10n+7}+\frac{1}{10n+9})\end{array}$

External links

• Fabrice Bellard's PI page
• PiHex web site
• David Bailey, Peter Borwein, and Simon Plouffe's BBP formula (On the rapid computation of various polylogarithmic constants) (PDF)