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%I #9 Aug 13 2015 19:48:35
%S 1,3,1,3,5,0,7,0,7,8,6,8,7,9,8,5,7,6,6,7,1,7,3,3,9,4,4,7,0,7,2,7,8,6,
%T 8,2,8,1,5,8,1,2,9,8,6,1,4,8,4,7,9,2,0,5,8,8,0,9,8,4,9,8,0,5,4,2,3,8,
%U 8,1,3,6,0,3,3,8,8,1,5,9,2,5,0,5,2,4,2,9,1,5,4,1,1,8,2,2,0,8,6,1,1,7,2
%N Decimal expansion of Khinchin mean K_{-3}.
%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 1.31350707...
%t digits = 102; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^3*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]&; A087493 = (exactSum + extraSum)^(-1/3) // 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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