OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.
FORMULA
sum(k>0, (-1)^k*log(k)^2/k) = -log(2)^3/3 + gamma*log(2)^2 + gamma(1)*log(4).
EXAMPLE
0.065372592558898599146207399388201...
MATHEMATICA
-Log[2]^3/3 + EulerGamma*Log[2]^2 + StieltjesGamma[1]*Log[4] // RealDigits[#, 10, 100]& // First
PROG
(PARI) sumalt(k=1, (-1)^k*log(k)^2/k) \\ Charles R Greathouse IV, Mar 10 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 16 2014
STATUS
approved