A188157 Decimal expansion of the integral of the logarithm of the Riemann zeta function from 1 to infinity.

1, 7, 9, 7, 5, 6, 9, 9, 5, 8, 6, 2, 8, 7, 3, 9, 4, 0, 7, 9, 3, 0, 2, 5, 0, 7, 8, 2, 1, 2, 1, 5, 3, 1, 6, 5, 8, 6, 4, 6, 0, 5, 1, 8, 3, 0, 7, 5, 7, 0, 8, 7, 1, 6, 7, 9, 8, 2, 0, 3, 4, 8, 4, 8, 3, 1, 5, 5, 4, 1, 7, 0, 5, 1, 9, 8, 6, 6, 1, 0, 6, 6, 7, 9, 1, 3, 0, 5, 9, 6, 8, 9, 1, 5, 5, 2, 6, 1, 3, 4

Offset

1,2

References

Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.

Links

Table of n, a(n) for n=1..100.

Henri Cohen, High-precision computation of Hardy-Littlewood constants, 1998, variable I(1).

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, table in Section 2.4.

Example

Equals 1.79756995862873940793025078... = Integral_{s=1..infinity} log zeta(s) ds.

Mathematica

RealDigits[ NIntegrate[ Log[ Zeta[x]], {x, 1, Infinity}, WorkingPrecision -> 100, AccuracyGoal -> 100]][[1]] (* Jean-François Alcover, Nov 08 2012 *)

Prog

(PARI) intnum(s=1, [oo, log(2)], log(zeta(s))) \\ after Charles R Greathouse IV in A221710, Dec 12 2013

Crossrefs

Cf. A221710.

Sequence in context: A248674 A108743 A177271 * A135000 A257239 A345384

Adjacent sequences: A188154 A188155 A188156 * A188158 A188159 A188160

Keyword

cons,nonn

Author

R. J. Mathar, Mar 26 2011

Status

approved