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%I A242071 #14 Jan 17 2020 05:44:09
%S A242071 2,0,4,1,5,4,8,1,8,6,4,1,2,1,3,2,4,1,8,0,4,5,4,9,0,1,5,8,3,8,1,4,5,5,
%T A242071 8,6,6,3,4,0,2,5,0,2,5,2,5,6,4,6,9,1,9,1,5,5,1,2,1,3,1,2,8,1,0,5,3,6,
%U A242071 2,1,0,6,3,7,6,7,0,0,1,2,0,9,7,1,1,0,5,5,6,4,3,9,7,6,4,3,2,8,6,9,5,5
%N A242071 Decimal expansion of 'beta', a constant appearing in the random links Traveling Salesman Problem.
%D A242071 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.5 Traveling Salesman constants, p. 499.
%H A242071 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 60.
%F A242071 beta = integral_{x>0} y(x) dx, where y(x) = -2 - W_(-1) (e^(-2-x) *(2-2*e^x+x)), W_k(z) being the k-th order Lambert W function (also known as ProductLog).  y(x) is implicitly defined by the equation (1+x/2)*exp(-x)+(1+y(x)/2)*exp(-y(x)) = 1.
%e A242071 2.041548186412132418045490158381455866340250252564691915512131281...
%t A242071 y[x_] := -2 - ProductLog[-1, E^(-2-x)*(2 - 2*E^x + x)]; beta = (1/2)*NIntegrate[y[x], {x, 0, Infinity}, WorkingPrecision -> 102]; beta // RealDigits // First
%Y A242071 Cf. A073008, A091505, A240717.
%K A242071 nonn,cons
%O A242071 1,1
%A A242071 _Jean-François Alcover_, Aug 14 2014

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