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Cubic and Higher Order Algorithms for π

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein  and
P. B. Borwein
J. M. Borwein
Affiliation:
Department of Mathematics., Statistics and Computing Science, Dalhousie University, Halifax, N.S., B3H 4H8
P. B. Borwein
Affiliation:
Department of Mathematics., Statistics and Computing Science, Dalhousie University, Halifax, N.S., B3H 4H8
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Abstract

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We show that the theory of elliptic integral transformations may be employed to construct iterative approximations for π of order p (p any prime). Details are provided for two, three and seven. The cubic case proves amenable to surprisingly complete analysis.

Keywords

10A3033A25PiElliptic IntegralsAlgorithmsModular Equations
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 436 - 443
Copyright
Copyright © Canadian Mathematical Society 1984

References

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