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%I #9 Aug 13 2015 19:16:12
%S 1,4,5,0,3,4,0,3,2,8,4,9,5,6,3,0,4,0,6,0,5,2,9,8,3,0,7,6,6,8,0,6,9,7,
%T 8,8,1,4,0,8,2,9,9,9,7,9,6,0,5,9,0,4,1,8,2,1,7,1,7,4,9,0,7,1,7,5,1,7,
%U 6,2,8,1,3,5,5,6,8,6,8,7,6,5,9,8,4,1,3,1,4,2,0,8,2,9,3,4,1,8,8,6,9,4,7
%N Decimal expansion of Khinchin mean K_{-2}.
%C Khinchin's constant is K_0.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KhinchinsConstant.html">Khinchin's Constant</a>
%e 1.45034032...
%t digits = 102; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^2*Log[2])); s[n_] = Series[f[n] , {n, Infinity, digits}] // Normal // N[#, digits]&; exactSum = Sum[f[n] , {n, 1, exactEnd}] // N[#, digits]&; extraSum = Sum[s[n] , {n, exactEnd + 1, Infinity}] // N[#, digits]&; A087492 = 1/Sqrt[exactSum + extraSum] // RealDigits // First (* _Jean-François Alcover_, Feb 06 2013 *)
%Y Cf. A002210, A087491, A087492, A087493, A087494, A087495, A087496, A087497, A087498, A087499, A087500.
%K nonn,cons
%O 1,2
%A _Eric W. Weisstein_, Sep 09 2003
%E More terms from _Jean-François Alcover_, Feb 06 2013
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