A301815 Decimal expansion of gamma / (2*Pi), where gamma is Euler's constant A001620.

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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Peter Luschny, An expansion for the Bernoulli function

Formula

Let beta(r) be the real part of Integral_{-oo..oo} (log(1/2 + i*z)^r / (exp(-Pi*z) + exp(Pi*z))^2) dz, where i denotes the imaginary unit. The constant equals -beta(1) and A301814 equals beta(1/2).

Example

Equals 0.0918667262991539903796422340718780914136292805606412123610872...

Maple

evalf(gamma(0)/(2*Pi), 100);

Mathematica

RealDigits[EulerGamma/(2*Pi), 10, 100][[1]] (* G. C. Greubel, Aug 11 2018 *)

Prog

(PARI) Euler/(2*Pi) \\ Altug Alkan, Apr 13 2018
(Magma) R:=RealField(100); EulerGamma(R)/(2*Pi(R)); // G. C. Greubel, Aug 27 2018

Crossrefs

Cf. A001620, A301814, A301816, A301817.

Sequence in context: A098783 A234468 A011111 * A191502 A109871 A087500

Adjacent sequences: A301812 A301813 A301814 * A301816 A301817 A301818

Keyword

nonn,cons

Author

Peter Luschny, Apr 13 2018

Status

approved