login
A221710
Decimal expansion of the integral of the logarithm of the Riemann zeta function from 2 to infinity.
1
5, 3, 6, 5, 2, 6, 9, 4, 5, 9, 2, 1, 1, 7, 7, 1, 0, 0, 9, 6, 1, 7, 1, 9, 0, 1, 9, 5, 4, 8, 7, 9, 4, 4, 0, 0, 6, 6, 7, 0, 0, 4, 7, 2, 8, 7, 5, 5, 0, 2, 6, 3, 6, 4, 7, 7, 3, 7, 6, 3, 9, 0, 9, 9, 9, 5, 6, 6, 2, 7, 7, 3, 6, 1, 3, 1, 0, 9, 6, 9, 9, 0, 0, 0, 3, 7, 6, 3, 5, 0, 4, 4, 3, 3, 5, 1, 6, 0, 2, 4
OFFSET
0,1
REFERENCES
Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
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
Cf. A188157.
Sequence in context: A089250 A155681 A075264 * A011504 A357467 A333009
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Jan 26 2013
EXTENSIONS
More digits from Jean-François Alcover, Jun 10 2013
STATUS
approved