%I #21 Feb 16 2025 08:34:02
%S 1,7,1,5,9,4,0,4,3,0,7,0,9,8,1,4,9,4,5,4,1,9,1,6,1,4,2,7,3,9,6,4,2,9,
%T 2,6,1,5,3,6,0,1,1,1,7,4,8,1,8,3,5,9,1,2,1,5,1,5,9,1,2,5,1,3,7,0,6,7,
%U 8,2,4,4,5,8,1,5,1,4,0,6,7,7,9,8,1,9,1,7,5,7,2,8,1,5,9,8,5,3,4,3,3,3,7,8,4,4
%N Decimal expansion of a limit related to the sum of reciprocals of the imaginary part of the nontrivial zeros of the Riemann zeta function (negated).
%H Richard P. Brent, David J. Platt, and Timothy S. Trudgian, <a href="https://doi.org/10.1017/S0004972720001252">A harmonic sum over nontrivial zeros of the Riemann zeta-function</a>, Bulletin of the Australian Mathematical Society, Vol. 104, No. 1 (2021), pp. 59-65; <a href="https://arxiv.org/abs/2009.05251">arXiv preprint</a>, arXiv:2009.05251 [math.NT], 2020.
%H Artur Kawalec, <a href="https://arxiv.org/abs/2403.15741">On the series expansion of the secondary zeta function</a>, arXiv:2403.15741 [math.NT], 2024; formula (70).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannZetaFunctionZeros.html">Riemann Zeta Function Zeros</a>.
%F Equals -lim_{T->oo} (Sum_{0 < gamma <= T} 1/gamma) - log(T/(2*Pi))^2/(4*Pi), where gamma denotes the imaginary part of the nontrivial zeros of the Riemann zeta function where multiple zeros (if they exist) are weighted according to their multiplicity.
%e -0.0171594043070981...
%Y Cf. A058303, A074760.
%K nonn,cons,changed
%O -1,2
%A _Amiram Eldar_, Oct 22 2021
%E More terms from _Artur Jasinski_, Apr 06 2024