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A262606 Decimal expansion of Integral_{0..1} log(1-x)^2*log(x)^2 dx (negated).

%I A262606 #8 Sep 27 2015 11:19:00
%S A262606 1,4,1,7,4,9,0,0,6,2,2,6,2,9,6,0,3,3,5,0,6,7,6,9,6,7,8,1,9,9,0,3,0,6,
%T A262606 5,7,3,5,3,7,5,9,4,9,9,7,0,2,8,9,4,5,3,6,0,9,4,3,8,5,5,0,6,8,6,1,1,1,
%U A262606 3,9,7,4,2,9,6,9,1,9,4,4,1,2,8,2,4,1,2,1,7,0,2,2,5,5,4,8,3,7,5,1,6,5,3,8,1
%N A262606 Decimal expansion of Integral_{0..1} log(1-x)^2*log(x)^2 dx (negated).
%H A262606 M. Jung, Y. J. Cho, J. Choi, <a href="http://dx.doi.org/10.4134/CKMS.2004.19.3.545">Euler sums evaluatable from integrals</a>, Commun. Korean Math. Soc. 19 (2008), 545-555.
%F A262606 Equals 24 - 4 Pi^2/3 - Pi^4/90 - 8 zeta(3).
%F A262606 Also equals Integral_{0..Pi/2} log(cos(x)^2)^2 * log(sin(x)^2)^2 * sin(2x) dx.
%e A262606 0.141749006226296033506769678199030657353759499702894536 ...
%t A262606 RealDigits[24 - 4*Pi^2/3 - Pi^4/90 - 8 Zeta[3], 10, 105] // First
%o A262606 (PARI) 24 - 4*Pi^2/3 - Pi^4/90 - 8*zeta(3) \\ _Michel Marcus_, Sep 27 2015
%Y A262606 Cf. A152416 (Integral_{0..1} log(1-x)*log(x) dx), A262605 (Integral_{0..1} log(1-x)*log(x)^2 dx).
%K A262606 nonn,cons,easy
%O A262606 0,2
%A A262606 _Jean-François Alcover_, Sep 26 2015