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Cookson Hills Series

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FlintHillSeries2

The Cookson Hills series is the series similar to the Flint Hills series, but with numerator sec^2n instead of csc^2n:

S_2=sum_(n=1)^infty(sec^2n)/(n^3)

(Pickover 2002, p. 268). It is not known if this series converges since sec^2n can have sporadic large values. The plots above show its behavior up to n=10^4. The positive integer values of n giving incrementally largest values of |secn| are given by 1, 2, 5, 8, 11, 344, 699, 1054, 1409, 1764, 2119, ... (OEIS A004112), corresponding to the values 1.85082, 2.403, 3.52532, 6.87285, 225.953, 227.503, ....

See also

Flint Hills Series

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References

Pickover, C. A. "Flint Hills Series." Ch. 25 in The Mathematics of Oz: Mental Gymnastics from Beyond the Edge. New York: Cambridge University Press, pp. 57-59 and 265-268, 2002.Sloane, N. J. A. Sequence A004112 in "The On-Line Encyclopedia of Integer Sequences."

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Cookson Hills Series

Cite this as:

Weisstein, Eric W. "Cookson Hills Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CooksonHillsSeries.html

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