A346833 Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^3 / (exp(-Pi*x) + exp(Pi*x))^2.

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

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..88.

Peter H. N. Luschny, An introduction to the Bernoulli function, arXiv:2009.06743 [math.HO], 2020.

Example

0.0290710895786169554535911581056375880771974183040...

Crossrefs

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

Sequence in context: A221245 A340009 A021348 * A192938 A188619 A020817

Adjacent sequences: A346830 A346831 A346832 * A346834 A346835 A346836

Keyword

nonn,cons

Author

Peter Luschny, Aug 05 2021

Status

approved