A173685 - OEIS

%I #21 Oct 31 2013 12:17:45

%S 6,0,3,9,9,0,4,2,4,8,6,5,0,7,4,7,4,3,9,5,2,9,1,8,7,1,9,9,7,8,4,0,7,9,

%T 4,0,0,2,8,3,5,9,4,3,6,8,0,8,1,1,5,1,1,3,0,0,2,6,4,3,2,1,1,1,3,4,3,4,

%U 8,7,7,0,4,6,7,3,0,5,4,0,4,9,9,9,0,4,1,5,5,1,5,3,0,5,3,0,3,8,4,9,4,0,1,5,0,2,9,4,8,0,6,9,2,2,6,5,3,5,7,8,8,6,4,9,5,0,0,8,3,1,7,2,0,4,5,6,9,6,5,7,8,5,0,1,2,8,3,5,1,9

%N Decimal expansion of negative of previously unknown transition arising in exact dynamics for fully connected nonlinear network.

%C Given on p.3 of Tsironis. The paper has a major typo. Substituting N=3 into equation 16 produces the polynomial 108 - 43x +2x^2 + 2x^3, whose real zero is about -6.0399. The exact value is given in the formula below.

%H G. P. Tsironis, <a href="http://arxiv.org/abs/1101.4721">Exact dynamics for fully connected nonlinear networks</a>, arXiv:1101.4721 Jan 25, 2011.

%F -(1 + f^(1/3)/2^(2/3) + 131/(2f)^(1/3))/3, where f=3307-387*sqrt(43).

%e Chi_c ~ -6.03990424865074743952918719978407940028359436808....

%t RealDigits[Solve[108 - 43 x + 2 x^2 + 2 x^3 == 0, x][[1, 1, 2]], 10, 150][[1]]

%t r = (3307 - 387*Sqrt@ 43); RealDigits[-(1 + (r/4)^(1/3) + 131/(2r)^(1/3))/3, 10, 111][[1]] (* _Robert G. Wilson v_, Jan 31 2011 *)

%K nonn,cons

%O 1,1

%A _Jonathan Vos Post_, Jan 27 2011