cp's OEIS Frontend

A249652 Decimal expansion of integral_{0..1} Li_3(x)^2 dx, where Li_3 is the trilogarithm function.

%I A249652 #20 Feb 16 2025 08:33:24
%S A249652 4,2,7,7,1,4,7,8,4,2,9,0,8,2,4,0,8,8,1,1,2,8,3,8,9,7,1,6,1,2,7,9,4,5,
%T A249652 3,2,4,2,8,6,0,2,4,7,8,7,7,4,6,9,5,7,4,4,5,5,4,9,2,9,8,3,5,2,4,1,6,1,
%U A249652 6,5,8,8,1,5,1,6,7,4,1,4,3,2,0,4,6,5,6,6,8,1,9,8,6,3,4,5,4,2,1,2,6,9
%N A249652 Decimal expansion of integral_{0..1} Li_3(x)^2 dx, where Li_3 is the trilogarithm function.
%H A249652 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Trilogarithm.html">Trilogarithm</a>
%F A249652 20 - 8*zeta(2) - 10*zeta(3) + (15/2)*zeta(4) - 2*zeta(2)*zeta(3) + zeta(3)^2.
%e A249652 0.4277147842908240881128389716127945324286...
%t A249652 RealDigits[20 - 8*Zeta[2] - 10*Zeta[3] + (15/2)*Zeta[4] - 2*Zeta[2]*Zeta[3] + Zeta[3]^2, 10, 102] // First
%t A249652 NIntegrate[PolyLog[3,x]^2,{x,0,1},WorkingPrecision->102] (* _Vaclav Kotesovec_, Nov 03 2014 *)
%o A249652 (PARI) z2=zeta(2); z3=zeta(3); 20 - 8*z2 - 10*z3 + 15*zeta(4)/2 - 2*z2*z3 + z3^2 \\ _Charles R Greathouse IV_, Apr 20 2016
%o A249652 (Python)
%o A249652 from mpmath import mp, zeta
%o A249652 mp.dps=103
%o A249652 z2=zeta(2)
%o A249652 z3=zeta(3)
%o A249652 print([int(z) for z in list(str(20 - 8*z2 - 10*z3 + 15*zeta(4)/2 - 2*z2*z3 + z3**2)[2:-1])]) # _Indranil Ghosh_, Jul 03 2017
%Y A249652 Cf. A002117, A013661, A013662, A249649, A249651.
%K A249652 nonn,cons,easy
%O A249652 0,1
%A A249652 _Jean-François Alcover_, Nov 03 2014