Pi, Euler Numbers, and Asymptotic Expansions

  • J. M. Borwein
  • P. B. Borwein
  • K. Dilcher


Gregory’s series for π, truncated at 500,000 terms, gives to forty places
$$4\sum\limits_{K = 1}^{500.000} {\tfrac{{{{( - 1)}^{k - 1}}}}{{2k - 1}} = 3.14159\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} 6535897932\underline {40} } 4626433832\underline 6 9502884197.$$


Asymptotic Expansion Infinite Series Remainder Term Euler Number Summation Formula 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • J. M. Borwein
    • 1
  • P. B. Borwein
    • 1
  • K. Dilcher
  1. 1.Dalhousie UniversityHalifaxCanada

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