A136130 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].

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..103.

Emeric Deutsch, The expected value of the spectral radius...

Formula

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.

Mathematica

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 *)

Crossrefs

Sequence in context: A195480 A175619 A342683 * A144668 A340222 A021505

Adjacent sequences: A136127 A136128 A136129 * A136131 A136132 A136133

Keyword

nonn,cons

Author

Emeric Deutsch, Feb 26 2008

Status

approved