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%I #9 Oct 17 2014 18:44:40
%S 1,1,1,5,9,6,4,4,0,8,9,7,8,7,1,6,6,9,0,6,1,9,1,5,6,4,1,9,3,4,5,3,4,9,
%T 6,9,5,7,6,9,4,9,1,1,8,2,2,3,0,4,0,0,9,3,7,0,6,3,5,3,3,1,1,0,0,3,3,7,
%U 0,9,5,7,5,0,5,0,2,0,3,1,1,8,9,1,5,0,1,1,3,9,6,4,6,7,1,5,1,7,0,0
%N Decimal expansion of Khinchin mean K_{-8}.
%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 1.11596440...
%t m = 8; 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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