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An Asymptotic Series for Computing π

Published online by Cambridge University Press:  03 November 2016

A. P. Guinand
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Extract

The series

is the simplest known series * which could be used to compute π, but it converges far too slowly to be of any practical use for this purpose. In this paper we prove an asymptotic formula for the remainder of the series (1) after a finite number of terms. The formula is

where

Type
Research Article
Information
The Mathematical Gazette , Volume 29 , Issue 287 , December 1945 , pp. 214 - 218
Copyright
Copyright © Mathematical Association 1945

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References

* E. W. Hobson, squaring the circle(cambridge, 1913), gives many series which can be used to compute π