# Bailey-Borwein-Plouffe formula

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!