%I #7 Nov 03 2014 09:26:43
%S 5,5,7,1,2,2,8,3,6,3,1,1,3,6,7,8,4,8,9,2,7,3,2,2,9,9,4,8,6,5,4,2,4,8,
%T 0,1,5,4,6,0,3,6,3,9,1,1,3,3,7,0,0,4,4,4,0,5,6,7,1,3,3,2,5,9,7,1,8,3,
%U 0,7,3,5,3,8,3,1,1,2,2,1,6,3,5,2,8,2,6,9,7,2,9,8,9,5,7,6,5,5,2,8,4,2
%N Decimal expansion of integral_{0..1} Li_3(x) dx, where Li_3 is the trilogarithm function.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Trilogarithm.html">Trilogarithm</a>
%F int_{0..1} Li_3(x) dx = 1 - zeta(2) + zeta(3) = 1 - Pi^2/6 + zeta(3).
%F Compare with the same integral of the dilogarithm:
%F int_{0..1} Li_2(x) dx = zeta(2) - 1 = Pi^2/6 - 1 = 0.644934...
%e 0.5571228363113678489273229948654248015460363911337...
%t RealDigits[1 - Zeta[2] + Zeta[3], 10, 102] // First
%Y Cf. A002117, A013661.
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Nov 03 2014