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Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^6 / (exp(-Pi*x) + exp(Pi*x))^2, negated.
4

%I #7 Aug 06 2021 00:36:26

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

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

%U 8,8,8,9,2,7,0,8,1,0,2,9,1,2,1,4,2,7,8,3,2

%N Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^6 / (exp(-Pi*x) + exp(Pi*x))^2, negated.

%C Let b(n) = 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^n / (exp(-Pi*x) + exp(Pi*x))^2, then B(s) = Sum_{n>=0} b(n)*s^n/n! = -s*zeta(1 - s) is the Bernoulli function.

%H Peter H. N. Luschny, <a href="https://arxiv.org/abs/2009.06743">An introduction to the Bernoulli function</a>, arXiv:2009.06743 [math.HO], 2020.

%e 0.0047599429038063762105200092646666689843892364275...

%Y Cf. A001620 (n=1), A346833 (n=2), A346833 (n=3), A346834 (n=4), A346835 (n=5), this sequence (n=6).

%K nonn,cons

%O 0,3

%A _Peter Luschny_, Aug 05 2021