A262606 Decimal expansion of Integral_{0..1} log(1-x)^2*log(x)^2 dx (negated).
1, 4, 1, 7, 4, 9, 0, 0, 6, 2, 2, 6, 2, 9, 6, 0, 3, 3, 5, 0, 6, 7, 6, 9, 6, 7, 8, 1, 9, 9, 0, 3, 0, 6, 5, 7, 3, 5, 3, 7, 5, 9, 4, 9, 9, 7, 0, 2, 8, 9, 4, 5, 3, 6, 0, 9, 4, 3, 8, 5, 5, 0, 6, 8, 6, 1, 1, 1, 3, 9, 7, 4, 2, 9, 6, 9, 1, 9, 4, 4, 1, 2, 8, 2, 4, 1, 2, 1, 7, 0, 2, 2, 5, 5, 4, 8, 3, 7, 5, 1, 6, 5, 3, 8, 1
Offset: 0
Examples
0.141749006226296033506769678199030657353759499702894536 ...
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[24 - 4*Pi^2/3 - Pi^4/90 - 8 Zeta[3], 10, 105] // First
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PARI
24 - 4*Pi^2/3 - Pi^4/90 - 8*zeta(3) \\ Michel Marcus, Sep 27 2015
Formula
Equals 24 - 4 Pi^2/3 - Pi^4/90 - 8 zeta(3).
Also equals Integral_{0..Pi/2} log(cos(x)^2)^2 * log(sin(x)^2)^2 * sin(2x) dx.