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%I #9 Oct 17 2014 18:45:00
%S 1,1,0,2,5,4,3,1,3,6,6,7,0,7,2,8,0,1,3,8,3,6,0,9,3,4,0,2,5,2,2,5,6,8,
%T 3,5,1,0,2,2,2,2,1,2,8,4,1,4,9,3,1,8,4,0,2,3,3,1,3,1,9,8,4,7,6,8,6,3,
%U 2,5,6,2,6,9,4,7,4,4,6,0,3,3,3,6,4,1,3,9,2,0,7,8,7,2,3,7,1,7,8,4
%N Decimal expansion of Khinchin mean K_{-9}.
%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 1.10254313...
%t m = 9; digits = 100; exactEnd = 1000; f[n_] = -(Log[1 - (1 + n)^(-2)]/(n^m*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]&; (exactSum + extraSum)^(-1/m) // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 14 2013 *)
%Y Cf. A002210, A087491, A087492, A087493, A087494, A087495, A087496, A087497, A087498, A087499, A087500.
%K nonn,cons
%O 1,4
%A _Eric W. Weisstein_, Sep 09 2003
%E More terms from _Jean-François Alcover_, Feb 14 2013
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