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A249651
Decimal expansion of Integral_{0..1} Li_2(x)^2 dx, where Li_2 is the dilogarithm function.
1
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, 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, 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
OFFSET
0,1
LINKS
Eric Weisstein's MathWorld, Dilogarithm
FORMULA
6 - 2*zeta(2) - 4*zeta(3) + zeta(2)^2.
EXAMPLE
0.607712337943015464246226262015069415439032408...
MATHEMATICA
RealDigits[6 - 2*Zeta[2] - 4*Zeta[3] + Zeta[2]^2, 10, 106] // First
NIntegrate[PolyLog[2, x]^2, {x, 0, 1}, WorkingPrecision->110] (* Vaclav Kotesovec, Nov 03 2014 *)
PROG
(Python)
from mpmath import *
mp.dps=107
f=lambda x: polylog(2, x)**2
I=quad(f, [0, 1])
print([int(n) for n in list(str(I)[2:-1])]) # Indranil Ghosh, Jul 04 2017
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved