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%I #11 Jul 08 2015 04:06:11
%S 9,9,5,9,8,7,2,1,1,2,3,3,6,8,2,0,0,3,8,6,6,1,4,6,7,1,4,0,5,0,3,2,6,8,
%T 5,1,5,6,5,4,1,3,2,7,6,2,5,4,0,4,7,5,7,5,9,6,9,9,8,0,1,9,6,1,1,6,2,8,
%U 4,2,0,2,9,5,1,7,1,6,0,6,5,0,2,8,5,5,4,8,0,8,0,2,0,0,2,7,9,6,0,3,8,2,4,2
%N Decimal expansion of the expected value of the spectral radius of a 2 X 2 matrix, whose entries are independent random variables, uniformly distributed over [0,1].
%H Emeric Deutsch, <a href="/A136130/a136130.pdf">The expected value of the spectral radius...</a>
%F 1/2 + (1/2)Int[sqrt((x-u)^2 +4yz)] over the 4-dimensional cube 0<=x,y,u,v<=1 = (29/60)log((1+sqrt(5))/2) - 43*sqrt(5)/720 + 3229/3600 =~ 0.995987211233682003866.
%t 1/2 + (1/2)*(ArcCoth[Sqrt[5]] + (1429 - 215*Sqrt[5] - 60*ArcCsch[2])/1800) // RealDigits[#, 10, 104]& // First (* _Jean-François Alcover_, Mar 04 2013 *)
%K nonn,cons
%O 0,1
%A _Emeric Deutsch_, Feb 26 2008