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.