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A257406 Decimal expansion of Integral_{0..infinity} log(x)/cosh(x) dx (negated).

%I A257406 #16 Feb 05 2025 18:21:15
%S A257406 5,2,0,8,8,5,6,1,2,6,0,1,9,7,6,8,9,1,0,8,0,1,8,7,7,3,7,5,7,9,4,5,4,4,
%T A257406 3,9,0,6,3,6,3,8,3,5,5,4,4,6,2,8,5,3,4,9,9,7,5,3,7,5,5,8,4,2,1,1,5,4,
%U A257406 3,2,0,7,6,2,9,4,6,3,4,7,8,5,3,9,7,8,6,6,4,1,6,0,8,0,1,8,2,9,9,6,2,3,4
%N A257406 Decimal expansion of Integral_{0..infinity} log(x)/cosh(x) dx (negated).
%H A257406 G. C. Greubel, <a href="/A257406/b257406.txt">Table of n, a(n) for n = 0..5000</a>
%H A257406 Victor Adamchik, <a href="https://citeseerx.ist.psu.edu/pdf/b52172a954833c11fd0b3a1b581187a24e750055">A Class of Logarithmic Integrals</a> (1997) Proc. of ISSAC'97
%F A257406 (Pi/2)*log(4*Pi^3/Gamma(1/4)^4).
%F A257406 Also equals 2*Integral_{0..1} (1/(x^2+1))*log(log(1/x)) dx.
%F A257406 Also equals 2*Integral_{Pi/4..Pi/2} log(log(tan(x))) dx.
%e A257406 -0.5208856126019768910801877375794544390636383554462853499753755842...
%t A257406 RealDigits[(Pi/2)*Log[4*Pi^3/Gamma[1/4]^4], 10, 103] // First
%t A257406 RealDigits[Integrate[-Log[x]/Cosh[x],{x,0,\[Infinity]}],10,120][[1]] (* _Harvey P. Dale_, Feb 05 2025 *)
%o A257406 (PARI) (Pi/2)*log(4*Pi^3/gamma(1/4)^4) \\ _Michel Marcus_, Apr 22 2015
%Y A257406 Cf. A068466, A115252.
%K A257406 nonn,cons,easy
%O A257406 0,1
%A A257406 _Jean-François Alcover_, Apr 22 2015