A346832 - OEIS

%I #12 Jun 07 2023 19:08:19

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

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

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

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

%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.

%D F. Johansson and I. V. Blagouchine, Computing Stieltjes constants using complex integration, Mathematics of Computation, 88:318, 1829-1850, (2019).

%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.

%H F. Johansson and I. V. Blagouchine, <a href="https://arxiv.org/abs/1804.01679">Computing Stieltjes constants using complex integration</a>, arXiv:1804.01679 [math.CA], 2018.

%H Peter Luschny, <a href="/A346832/a346832.jpg">Illustrating A346832, A346833, A346834, A346835.</a>

%e 0.1456316909673534497211727517498026382754726766686759...

%Y Cf. A001620 (n=1), this sequence (n=2), A346833 (n=3), A346834 (n=4), A346835 (n=5), A346836 (n=6).

%K nonn,cons

%O 0,2

%A _Peter Luschny_, Aug 05 2021