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A249652
Decimal expansion of integral_{0..1} Li_3(x)^2 dx, where Li_3 is the trilogarithm function.
0
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
0,1
LINKS
Eric Weisstein's MathWorld, Trilogarithm
FORMULA
20 - 8*zeta(2) - 10*zeta(3) + (15/2)*zeta(4) - 2*zeta(2)*zeta(3) + zeta(3)^2.
EXAMPLE
0.4277147842908240881128389716127945324286...
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved