OFFSET
0,1
LINKS
M. Jung, Y. J. Cho, J. Choi, Euler sums evaluatable from integrals, Commun. Korean Math. Soc. 19 (2008), 545-555.
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.
EXAMPLE
-0.30601805998435855625569334368504964003212761290540536094434 ...
MATHEMATICA
RealDigits[Integrate[Log[1 - x]*Log[x]^2, {x, 0, 1}] , 10,
105] // First
PROG
(PARI) -(-6 + Pi^2/3 + 2*zeta(3)) \\ Michel Marcus, Sep 27 2015
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Sep 26 2015
STATUS
approved