OFFSET
1,2
FORMULA
Sum_{k >=1 } log(k+eps)/k^2 = -Zeta'(2) - Sum_{i=1} (-eps)^i *Zeta(i+2)/i at eps=1/2, weighted sum over Riemann-Zeta.
EXAMPLE
1.435062...
PROG
(PARI) sumpos(k=1, log(k+1/2)/k^2) \\ Michel Marcus, May 04 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, May 04 2021
STATUS
approved