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A346832 Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^2 / (exp(-Pi*x) + exp(Pi*x))^2. 1
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, 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, 2, 8, 6, 7, 1, 4, 3, 0, 2, 2, 9, 6, 9, 7, 5, 6, 1, 7 (list; constant; graph; refs; listen; history; text; internal format)
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.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..85.

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

Peter Luschny, Illustrating A346832, A346833, A346834, A346835.

EXAMPLE

0.1456316909673534497211727517498026382754726766686759...

CROSSREFS

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

Sequence in context: A305006 A338688 A010665 * A200362 A309750 A096291

Adjacent sequences:  A346829 A346830 A346831 * A346833 A346834 A346835

KEYWORD

nonn,cons

AUTHOR

Peter Luschny, Aug 05 2021

STATUS

approved

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Last modified May 22 04:12 EDT 2022. Contains 353933 sequences. (Running on oeis4.)