A346834 - OEIS

%I #6 Aug 06 2021 00:36:20

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

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

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

%N Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^4 / (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 0.0082153376812133834646401861710135371428632177816...

%Y Cf. A001620 (n=1), A346833 (n=2), A346833 (n=3), this sequence (n=4), A346835 (n=5), A346836 (n=6).

%K nonn,cons

%O 0,3

%A _Peter Luschny_, Aug 05 2021