A301813 Decimal expansion of Integral_{-infinity..infinity} -log((z^2+1/4)^(1/4))* sech(Pi*z)^2 dz.

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

Offset: 0

Author

Peter Luschny, Apr 18 2018

Keywords

• nonn
• cons

Examples

			0.183733452598307980759284468143756182827258561121282424722174416749125638699...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Peter Luschny, Illustration of the integral

Crossrefs

Cf. A000796, A001620, A301816.

Programs

Magma

R:= RealField(100); EulerGamma(R)/Pi(R); // G. C. Greubel, Sep 05 2018

Maple

evalf(gamma/Pi, 20);
g := -int(log(z^2+1/4)*sech(Pi*z)^2/4, z=-10..10); evalf(g, 20);
# This is an approximation. For more valid decimal digits the
# range of integration and the precision must be increased.

Mathematica

RealDigits[EulerGamma/Pi, 10, 40] [[1]]

PARI

Euler/Pi \\ Altug Alkan, Apr 18 2018

Formula

Equals EulerGamma / Pi.

Equals Integral_{0..infinity} -log(sqrt(z^2 + 1/4))/cosh(Pi*z)^2 dz.