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Ballantine's Series

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Ballantine's series is the series for pi given by

pi=864sum_(n=0)^infty((n!)^24^n)/((2n+1)!325^(n+1)) +1824sum_(n=0)^infty((n!)^24^n)/((2n+1)!3250^(n+1))-20cot^(-1)239

(Borwein and Bailey 2003, pp. 135-136). It has the interesting property that the terms of the second series are decimal shifts of the terms in the first, as observed by Ballantine in 1939.

See also

Pi Formulas

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References

Berggren, L.; Borwein, J.; and Borwein, P. Pi: A Source Book. New York: Springer-Verlag, 1997.Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, 2003.

Referenced on Wolfram|Alpha

Ballantine's Series

Cite this as:

Weisstein, Eric W. "Ballantine's Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BallantinesSeries.html

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