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

%I #13 Sep 08 2022 08:46:20

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

%H G. C. Greubel, <a href="/A301813/b301813.txt">Table of n, a(n) for n = 0..10000</a>

%H Peter Luschny, <a href="/A301813/a301813.pdf">Illustration of the integral</a>

%F Equals EulerGamma / Pi.

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

%e 0.183733452598307980759284468143756182827258561121282424722174416749125638699...

%p evalf(gamma/Pi, 20);

%p g := -int(log(z^2+1/4)*sech(Pi*z)^2/4, z=-10..10); evalf(g, 20);

%p # This is an approximation. For more valid decimal digits the

%p # range of integration and the precision must be increased.

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

%o (PARI) Euler/Pi \\ _Altug Alkan_, Apr 18 2018

%o (Magma) R:= RealField(100); EulerGamma(R)/Pi(R); // _G. C. Greubel_, Sep 05 2018

%Y Cf. A000796, A001620, A301816.

%K nonn,cons

%O 0,2

%A _Peter Luschny_, Apr 18 2018

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)