OFFSET
0,1
LINKS
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 179.
J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV.
FORMULA
Equals -(6/Pi^2)*Zeta'(2).
Equals 1 - 12*Zeta'(-1) - gamma - log(2*Pi).
From Amiram Eldar, Aug 14 2020: (Start)
Equals Sum_{k>=1} Lambda(k)/k^2, where Lambda is the Mangoldt function.
Equals Sum_{p prime} log(p)/(p^2 - 1). (End)
EXAMPLE
Equals 0.569960993094532806399864360019730002403482280806930979558...
MAPLE
-(6/Pi^2)*Zeta(1, 2): evalf(%, 100);
MATHEMATICA
RealDigits[- Zeta'[2] / Zeta[2], 10, 87][[1]]
PROG
(PARI) -zeta'(2)/zeta(2) \\ Michel Marcus, Jan 11 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Peter Luschny, Jun 17 2018
STATUS
approved