An algorithm which allows digits of a given number to be calculated without requiring the computation of earlier digits. The BBP formula for pi is the best-known such algorithm, but an algorithm also exists for e. Plouffe gives a particularly simple digit-extraction algorithm for the decimal digits of π by defining π_n = ((2(-1)^(n + 1)(2n)!)/(2^(2n) B_(2n)(1 - 2^(-n))(1 - 3^(-n))(1 - 5^(-n))(1 - 7^(-n))))^(1/(2n)).

BBP formula | pi formulas