OFFSET
0,1
REFERENCES
Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
LINKS
Henri Cohen, High-precision calculation of Hardy-Littlewood constants, 1998, see I(2).
Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission]
R. J. Mathar, Twenty digits of some integrals of the Prime Zeta Function, arXiv:0811.4739, Section 2.4.
EXAMPLE
Integral_{s=2..infinity} log zeta(s) ds = 0.536526945921177100961719019548794400667....
MATHEMATICA
NIntegrate[ Log[ Zeta[s]], {s, 2, Infinity}, WorkingPrecision -> 110] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Jun 10 2013 *)
PROG
(PARI) intnum(s=2, [oo, log(2)], log(zeta(s))) \\ Charles R Greathouse IV, Dec 12 2013
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Jan 26 2013
EXTENSIONS
More digits from Jean-François Alcover, Jun 10 2013
STATUS
approved