Re: Arbitrary Precision Calculation Of Pi

*To*: MATHGROUP at yoda.physics.unc.edu*Subject*: Re: Arbitrary Precision Calculation Of Pi*From*: keiper (Jerry Keiper)*Date*: Sat, 12 Mar 1994 15:13:06 -0600

> A colleague of mine asked me how Mathematica calculates Pi > to an arbitrary precision. I haven't a clue. Do any > of you know?! It is based on the Chudnovsky formula: 640320^(3/2)/(6541681608 Pi) == Sum[(n + 13591409/545140134) (6n)! (-1)^n/ ((3n)! (n!)^3 640320^(3n)), {n, 0, Infinity}] The sum converges like a geometric series with ratio nearly 10^-14. Jerry B. Keiper keiper at wri.com Wolfram Research, Inc.