A262605 Decimal expansion of Integral_{0..1} log(1-x)*log(x)^2 dx (negated).
3, 0, 6, 0, 1, 8, 0, 5, 9, 9, 8, 4, 3, 5, 8, 5, 5, 6, 2, 5, 5, 6, 9, 3, 3, 4, 3, 6, 8, 5, 0, 4, 9, 6, 4, 0, 0, 3, 2, 1, 2, 7, 6, 1, 2, 9, 0, 5, 4, 0, 5, 3, 6, 0, 9, 4, 4, 3, 4, 0, 4, 3, 0, 5, 7, 6, 3, 0, 8, 6, 4, 7, 6, 2, 0, 9, 7, 2, 0, 7, 1, 9, 5, 9, 8, 3, 0, 4, 5, 1, 5, 4, 1, 8, 1, 2, 0, 7, 3, 0, 9, 9, 5, 9, 3
Offset: 0
Examples
-0.30601805998435855625569334368504964003212761290540536094434 ...
Links
- M. Jung, Y. J. Cho, J. Choi, Euler sums evaluatable from integrals, Commun. Korean Math. Soc. 19 (2008), 545-555.
Crossrefs
Programs
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Mathematica
RealDigits[Integrate[Log[1 - x]*Log[x]^2, {x, 0, 1}] , 10, 105] // First -
PARI
-(-6 + Pi^2/3 + 2*zeta(3)) \\ Michel Marcus, Sep 27 2015
Formula
Equals -6 + Pi^2/3 + 2 zeta(3).
Equals Integral_{0..Pi/2} log(cos(x)^2) * log(sin(x)^2)^2 * sin(2x) dx.