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Decimal expansion of constant in Kac's formula.
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%I #11 Aug 14 2015 23:30:55

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

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

%U 5,4,8,3,6,8,2,4,6,3,3,4,8,0,0,5,9,3,6,0,2,2,6,0,6,0,4,4,2,9,6,8,3,1

%N Decimal expansion of constant in Kac's formula.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 141.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KacFormula.html">Kac's Formula</a>

%e 0.625735807...

%t (2/Pi)*(Log[2] + NIntegrate[Sqrt[1/x^2 - 4*(Exp[ -2*x]/(1 - Exp[ -2*x])^2)] - 1/(x + 1), {x, 0, Infinity}, WorkingPrecision -> 50, PrecisionGoal -> 20])

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Apr 03 2004