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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

Information

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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