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

%I A301813 #13 Sep 08 2022 08:46:20
%S A301813 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,
%T A301813 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
%N A301813 Decimal expansion of Integral_{-infinity..infinity} -log((z^2+1/4)^(1/4))* sech(Pi*z)^2 dz.
%H A301813 G. C. Greubel, <a href="/A301813/b301813.txt">Table of n, a(n) for n = 0..10000</a>
%H A301813 Peter Luschny, <a href="/A301813/a301813.pdf">Illustration of the integral</a>
%F A301813 Equals EulerGamma / Pi.
%F A301813 Equals Integral_{0..infinity} -log(sqrt(z^2 + 1/4))/cosh(Pi*z)^2 dz.
%e A301813 0.183733452598307980759284468143756182827258561121282424722174416749125638699...
%p A301813 evalf(gamma/Pi, 20);
%p A301813 g := -int(log(z^2+1/4)*sech(Pi*z)^2/4, z=-10..10); evalf(g, 20);
%p A301813 # This is an approximation. For more valid decimal digits the
%p A301813 # range of integration and the precision must be increased.
%t A301813 RealDigits[EulerGamma/Pi, 10, 40] [[1]]
%o A301813 (PARI) Euler/Pi \\ _Altug Alkan_, Apr 18 2018
%o A301813 (Magma) R:= RealField(100); EulerGamma(R)/Pi(R); // _G. C. Greubel_, Sep 05 2018
%Y A301813 Cf. A000796, A001620, A301816.
%K A301813 nonn,cons
%O A301813 0,2
%A A301813 _Peter Luschny_, Apr 18 2018