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A117240 Decimal expansion of solution to problem #10 in the Trefethen challenge. 0
0, 0, 0, 0, 0, 0, 3, 8, 3, 7, 5, 8, 7, 9, 7, 9, 2, 5, 1, 2, 2, 6, 1, 0, 3, 4, 0, 7, 1, 3, 3, 1, 8, 6, 2, 0, 4, 8, 3, 9, 1, 0, 0, 7, 9, 3, 0, 0, 5, 5, 9, 4, 0, 7, 2, 5, 0, 9, 5, 6, 9, 0, 3, 0, 0, 2, 2, 7, 9, 9, 1, 7, 3, 4, 3, 6, 6, 0, 6, 8, 5, 2, 7, 4, 3, 2, 7, 6, 5, 0, 0, 8, 4, 2, 8, 4, 5, 6, 4, 7, 2, 6, 9, 9, 1, 0, 1, 5, 3, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,7

REFERENCES

Bailey D. H., Borwein J. M., Calkin N. J., Girgensohn R., Luke D. R. and Moll V. H., Experimental Mathematics in Action, Wellesley, MA, A K Peters, 2007, p. 48.

S. Wagon, F. Bornemann, D. Laurie and J. Waldvogel, The SIAM 100 Digit Challenge, A Study in High-Accuracy Numerical Computing, SIAM, Philadelphia, 2004.

LINKS

Table of n, a(n) for n=0..110.

Eric Weisstein's World of Mathematics, Hundred-Dollar, Hundred-Digit Challenge Problems

FORMULA

(2*arccos(sqrt(ModularLambda(I/10))))/Pi.

EXAMPLE

0.0000003837587979251226103...

MATHEMATICA

Flatten[{0, 0, 0, 0, 0, 0, RealDigits[(2*ArcCos[Sqrt[ModularLambda[I/10]]])/Pi, 10, 100][[1]]}] (* Vaclav Kotesovec, Aug 15 2015 after Eric W. Weisstein *)

N[2/Pi * ArcSin[(3-2*Sqrt[2])^2 * (2+Sqrt[5])^2 * (Sqrt[10]-3)^2 * (5^(1/4)-Sqrt[2])^4], 100] (* Vaclav Kotesovec, Aug 15 2015 after Bornemann *)

CROSSREFS

Sequence in context: A198489 A015136 A179450 * A151857 A010706 A125025

Adjacent sequences:  A117237 A117238 A117239 * A117241 A117242 A117243

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Mar 05 2006

STATUS

approved

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Last modified May 26 09:12 EDT 2017. Contains 287093 sequences.