Pi, Euler Numbers, and Asymptotic Expansions

Borwein, J. M.; Borwein, P. B.; Dilcher, K.

doi:10.1007/978-1-4757-4217-6_65

Pi, Euler Numbers, and Asymptotic Expansions

J. M. Borwein³,
P. B. Borwein³ &
K. Dilcher

Chapter

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Abstract

Gregory’s series for π, truncated at 500,000 terms, gives to forty places

$$4\sum\limits_{K = 1}^{500.000} {\tfrac{{{{( - 1)}^{k - 1}}}}{{2k - 1}} = 3.14159\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} 6535897932\underline {40} } 4626433832\underline 6 9502884197.$$

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Research the authors supported in part by NSERC of Canada

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Authors and Affiliations

Dalhousie University, Halifax, Canada
J. M. Borwein & P. B. Borwein

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J. M. Borwein
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P. B. Borwein
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K. Dilcher
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Borwein, J.M., Borwein, P.B., Dilcher, K. (2004). Pi, Euler Numbers, and Asymptotic Expansions. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4217-6_65

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DOI: https://doi.org/10.1007/978-1-4757-4217-6_65
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1915-1
Online ISBN: 978-1-4757-4217-6
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