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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 (list; constant; graph; refs; listen; history; text; internal format)
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 *)
CROSSREFS
Sequence in context: A333287 A360199 A360851 * A151857 A359200 A125025
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Mar 05 2006
STATUS
approved

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Last modified May 20 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)