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A117240
Decimal expansion of solution to problem #10 in the Trefethen challenge.
10
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
OFFSET
0,7
REFERENCES
David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke and Victor H. Moll, Experimental Mathematics in Action, Wellesley, MA, A K Peters, 2007, p. 48.
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10007 (from Folkmar Bornemann's solution)
Folkmar Bornemann, Hitting the Ends, a web page for the book The SIAM 100-Digit Challenge.
Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing, SIAM, Philadelphia, 2004.
Eric Weisstein's World of Mathematics, Hundred-Dollar, Hundred-Digit Challenge Problems.
FORMULA
Equals (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 *)
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Mar 05 2006
STATUS
approved