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%I #15 Aug 17 2015 02:56:28
%S 1,0,0,0,0,0,0,0,0,0,0,4,8,8,5,1,0,9,0,4,1,3,8,2,5,1,5,6,2,4,3,0,7,8,
%T 8,6,9,9,9,1,1,6,7,9,6,0,8,2,6,3,8,2,8,0,4,0,1,4,7,1,1,1,6,2,8,2,6,6,
%U 2,6,0,6,3,0,5,1,1,9,7,2,0,8,1,6,6,8,5,5,1,0,0,7,2,6,9,1,3,8,0,1,2,5
%N Decimal expansion of Sum_{k=-infinity..+infinity} log(2)/(2^(-k/2) + 2^(k/2))^2.
%C Differs from 1 by 4.9*10^-11.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostInteger.html">Almost Integer</a>
%e 1.00000000004885109041382...
%t almostOne = Log[2]/4 + 2*Log[2]*NSum[1/(2^(-k/2) + 2^(k/2))^2, {k, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 100]; RealDigits[almostOne, 10, 102] // First (* _Jean-François Alcover_, Feb 07 2013 *)
%t RealDigits[Re[2 - Log[2]/4 - 2*(QPolyGamma[1, -((I*Pi)/Log[2]), Sqrt[2]] + QPolyGamma[1, (I*Pi)/Log[2], Sqrt[2]])/Log[2]],10,100][[1]] (* _Vaclav Kotesovec_, Aug 17 2015 *)
%K nonn,cons
%O 0,12
%A _Eric W. Weisstein_, Dec 15 2005
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