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MathGroup Archive 1994

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Re: Arbitrary Precision Calculation Of Pi

  • To: MATHGROUP at
  • 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
Wolfram Research, Inc.

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