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%I #24 Jan 02 2023 03:28:18
%S 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,
%T 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,
%U 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
%N Decimal expansion of solution to problem #10 in the Trefethen challenge.
%D 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.
%H Amiram Eldar, <a href="/A117240/b117240.txt">Table of n, a(n) for n = 0..10007</a> (from Folkmar Bornemann's solution)
%H Folkmar Bornemann, <a href="http://www-m3.ma.tum.de/foswiki/pub/M3/Allgemeines/FolkmarBornemannPublications/short.pdf">Short remarks on the solution of the SIAM 100-digit challenge</a>, 2002.
%H Folkmar Bornemann, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/Chapter10/">Hitting the Ends</a>, a web page for the book The SIAM 100-Digit Challenge.
%H Folkmar Bornemann, Dirk Laurie, Stan Wagon, and Jörg Waldvogel, <a href="https://www-m3.ma.tum.de/m3old/bornemann/challengebook/">The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing</a>, SIAM, Philadelphia, 2004.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html">Hundred-Dollar, Hundred-Digit Challenge Problems</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hundred-dollar,_Hundred-digit_Challenge_problems">Hundred-dollar, Hundred-digit Challenge problems</a>.
%F Equals (2*arccos(sqrt(ModularLambda(I/10))))/Pi.
%e 0.0000003837587979251226103...
%t 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_ *)
%t 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 *)
%Y Cf. A117231, A117232, A117233, A117234, A117235, A117236, A117237, A117238, A117239.
%K nonn,cons
%O 0,7
%A _Eric W. Weisstein_, Mar 05 2006
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