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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some modular identities of Ramanujan useful in approximating $ \pi$


Author: Jon Borwein
Journal: Proc. Amer. Math. Soc. 95 (1985), 365-371
MSC: Primary 11F03; Secondary 11J72, 41A25
MathSciNet review: 806072
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Abstract: We show how various modular identities due to Ramanujan may be used to produce simple high order approximations to $ \pi $. Various specializations are considered and the Gaussian arithmetic geometric mean formula for $ \pi $ is rederived as a consequence.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806072-6
PII: S 0002-9939(1985)0806072-6
Article copyright: © Copyright 1985 American Mathematical Society