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

%I

%S 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,

%T 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,

%U 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

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

%H H. Cohen, <a href="http://www.math.u-bordeaux.fr/~cohen/hardylw.dvi">High-precision calculation of Hardy-Littlewood constants</a>, 1998, variable I(1).

%H R. J. Mathar, <a href="http://arxiv.org/abs/0811.4739">Twenty digits of some integrals of the prime zeta function</a>, arXiv:0811.4739, table in Section 2.4.

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

%t RealDigits[ NIntegrate[ Log[ Zeta[x]], {x, 1, Infinity}, WorkingPrecision -> 100, AccuracyGoal -> 100]][[1]] (* _Jean-Fran├žois Alcover_, Nov 08 2012 *)

%K cons,nonn

%O 1,2

%A _R. J. Mathar_, Mar 26 2011

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Last modified March 25 08:15 EDT 2019. Contains 321469 sequences. (Running on oeis4.)