Bailey-Borwein-Plouffe formula

February 7, 2008 — Karthik

The Bailey-Borwein-Plouffe formula (BBP formula) provides a spigot algorithm for the computation of the nth digit of \pi. The original BBP \pi summation formula was found in 1995 by Plouffe using PSLQ. It is

\pi = \sum_{k = 0}^{\infty} \frac{1}{16^k} \left( \frac{4}{8k + 1} - \frac{2}{8k + 4} - \frac{1}{8k + 5} - \frac{1}{8k + 6}\right)

Amazingly, this formula is a digit-extraction algorithm for \pi in base 16.

It appears that there is a digit extraction algorithm even for e!

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