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

Author

Peter Luschny, Apr 13 2018

Keywords

• nonn
• cons

Examples

			Equals 0.0918667262991539903796422340718780914136292805606412123610872...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Peter Luschny, An expansion for the Bernoulli function

Crossrefs

Cf. A001620, A301814, A301816, A301817.

Programs

Magma

R:=RealField(100); EulerGamma(R)/(2*Pi(R)); // G. C. Greubel, Aug 27 2018

Maple

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

Mathematica

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

PARI

Euler/(2*Pi) \\ Altug Alkan, Apr 13 2018

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).