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A249651 Decimal expansion of Integral_{0..1} Li_2(x)^2 dx, where Li_2 is the dilogarithm function.

%I A249651 #19 Feb 16 2025 08:33:24
%S A249651 6,0,7,7,1,2,3,3,7,9,4,3,0,1,5,4,6,4,2,4,6,2,2,6,2,6,2,0,1,5,0,6,9,4,
%T A249651 1,5,4,3,9,0,3,2,4,0,8,0,2,1,2,2,4,8,6,6,5,6,7,2,3,7,8,5,8,5,0,2,9,3,
%U A249651 3,7,7,6,5,1,5,7,6,8,0,0,7,9,7,9,1,9,2,7,9,4,1,7,7,3,9,1,3,4,9,8,8,9,6,7,1,7
%N A249651 Decimal expansion of Integral_{0..1} Li_2(x)^2 dx, where Li_2 is the dilogarithm function.
%H A249651 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Dilogarithm.html">Dilogarithm</a>
%F A249651 6 - 2*zeta(2) - 4*zeta(3) + zeta(2)^2.
%e A249651 0.607712337943015464246226262015069415439032408...
%t A249651 RealDigits[6 - 2*Zeta[2] - 4*Zeta[3] + Zeta[2]^2, 10, 106] // First
%t A249651 NIntegrate[PolyLog[2,x]^2,{x,0,1},WorkingPrecision->110] (* _Vaclav Kotesovec_, Nov 03 2014 *)
%o A249651 (Python)
%o A249651 from mpmath import *
%o A249651 mp.dps=107
%o A249651 f=lambda x: polylog(2, x)**2
%o A249651 I=quad(f, [0, 1])
%o A249651 print([int(n) for n in list(str(I)[2:-1])]) # _Indranil Ghosh_, Jul 04 2017
%Y A249651 Cf. A002117, A013661, A249649.
%K A249651 nonn,cons,easy
%O A249651 0,1
%A A249651 _Jean-François Alcover_, Nov 03 2014