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%I #11 Jul 15 2013 13:45:41
%S 2,1,1,0,2,3,3,9,6,6,1,2,1,5,7,2,1,9,6,4,6,6,8,2,8,1,5,6,6,6,3,8,4,5,
%T 1,8,9,6,4,2,1,1,3,0,2,9,4,1,5,0,6,4,8,4,2,2,3,5,2,3,1,2,1,6,2,6,5,8,
%U 9,7,0,5,8,1,4,4,0,1,3,3,4,3,7,3,6,2,9,1,8,6,2,8,3,3,0,1,2,2,3,3,9
%N Decimal expansion of 'B', a Young-Fejér-Jackson constant linked to the positivity of certain sine sums.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 242.
%F Given lambda from A227423, 'b' is the unique positive solution to (1+lambda)*Pi*((b-1)*psi(1+(b-1)/2)-2*b*psi(1+b/2)+(b+1)*psi(1+(b+1)/2)) = 2*sin(lambda*Pi), where psi is the digamma function.
%e 2.110233966121572196466828156663845189642113029415064842235231216265897058...
%t b /. FindRoot[(1 + lambda) Pi == Tan[lambda*Pi] && (1 + lambda)*Pi*((b - 1)*PolyGamma[1 + (b - 1)/2] - 2*b*PolyGamma[1 + b/2] + (b + 1) PolyGamma[1 + (b + 1)/2]) == 2*Sin[lambda*Pi], {lambda, 2/5}, {b, 2}, WorkingPrecision -> 105] // RealDigits[#][[1, 1;;101]&
%Y Cf. A227422, A227423, A227424.
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Jul 11 2013
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