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 A087491 Decimal expansion of Khinchin mean K_{-1}. 10

%I

%S 1,7,4,5,4,0,5,6,6,2,4,0,7,3,4,6,8,6,3,4,9,4,5,9,6,3,0,9,6,8,3,6,6,1,

%T 0,6,7,2,9,4,9,3,6,6,1,8,7,7,7,9,8,4,2,5,6,5,9,5,0,1,3,7,7,3,5,1,6,0,

%U 7,8,5,7,5,2,2,0,8,7,3,4,2,5,6,5,2,0,5,7,8,8,6,4,5,6,7,8,3,2,4,2,4,2

%N Decimal expansion of Khinchin mean K_{-1}.

%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>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KhinchinHarmonicMean.html">Khinchin Harmonic Mean</a>

%e 1.74540566...

%t digits = 102; exactEnd = 1000; f[n_] = (1 - 1/(n + 1)^2)^(-1/n); s[n_] = Series[Log[f[n] ], {n, Infinity, digits}] // Normal // N[#, digits]&; exactSum = Sum[Log[f[n]] , {n, 1, exactEnd}] // N[#, digits]&; extraSum = Sum[s[n] , {n, exactEnd + 1, Infinity}] // N[#, digits]&; A087491 = Log[2]/(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

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