A249652 Decimal expansion of integral_{0..1} Li_3(x)^2 dx, where Li_3 is the trilogarithm function.
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, 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, 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
Offset: 0
Examples
0.4277147842908240881128389716127945324286...
Links
- Eric Weisstein's MathWorld, Trilogarithm
Programs
-
Mathematica
RealDigits[20 - 8*Zeta[2] - 10*Zeta[3] + (15/2)*Zeta[4] - 2*Zeta[2]*Zeta[3] + Zeta[3]^2, 10, 102] // First NIntegrate[PolyLog[3,x]^2,{x,0,1},WorkingPrecision->102] (* Vaclav Kotesovec, Nov 03 2014 *) -
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
-
Python
from mpmath import mp, zeta mp.dps=103 z2=zeta(2) z3=zeta(3) 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
Formula
20 - 8*zeta(2) - 10*zeta(3) + (15/2)*zeta(4) - 2*zeta(2)*zeta(3) + zeta(3)^2.