A249651 Decimal expansion of Integral_{0..1} Li_2(x)^2 dx, where Li_2 is the dilogarithm function.
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
Examples
0.607712337943015464246226262015069415439032408...
Links
- Eric Weisstein's MathWorld, Dilogarithm
Programs
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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 *) -
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
Formula
6 - 2*zeta(2) - 4*zeta(3) + zeta(2)^2.