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A249649 Decimal expansion of Integral_{x = 0..1} Li_3(x) dx, where Li_3 is the trilogarithm function.

%I A249649 #13 Aug 04 2025 10:01:57
%S A249649 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 A249649 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 A249649 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 A249649 Decimal expansion of Integral_{x = 0..1} Li_3(x) dx, where Li_3 is the trilogarithm function.
%H A249649 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Trilogarithm.html">Trilogarithm</a>
%F A249649 Integral_{x = 0..1} Li_3(x) dx = 1 - zeta(2) + zeta(3) = 1 - Pi^2/6 + zeta(3).
%F A249649 Compare with the same integral of the dilogarithm:
%F A249649 Integral_{x = 0..1} Li_2(x) dx = zeta(2) - 1 = Pi^2/6 - 1 =  0.644934...
%F A249649 Equals Sum_{n >= 1} 1/(n^4 + n^3). - _Peter Bala_, Aug 04 2025
%e A249649 0.5571228363113678489273229948654248015460363911337...
%t A249649 RealDigits[1 - Zeta[2] + Zeta[3], 10, 102] // First
%Y A249649 Cf. A002117, A013661.
%K A249649 nonn,cons,easy
%O A249649 0,1
%A A249649 _Jean-François Alcover_, Nov 03 2014