Borwein's algorithm

Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of 1/pi. It is one of several algorithms of this kind described in their book Pi and the AGM, A Study in Analytic Number Theory and Computational Complexity. The formulas are examples of a Ramanujan-Sato series and are related to the Chudnovsky algorithm, which uses a discriminant with class number 1. The article presents a class number 2 version dated 1989, built from constants that involve the square root of 61, in which each additional term of the partial sum yields approximately 25 digits, and a class number 4 version dated 1993. Each formula expresses 1/pi as an infinite sum of ratios of factorials and powers, so that a handful of terms already gives a very large number of correct digits of pi.