A257406 - OEIS

%I #14 Aug 06 2024 10:57:14

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

%H G. C. Greubel, <a href="/A257406/b257406.txt">Table of n, a(n) for n = 0..5000</a>

%H Victor Adamchik, <a href="https://citeseerx.ist.psu.edu/pdf/b52172a954833c11fd0b3a1b581187a24e750055">A Class of Logarithmic Integrals</a> (1997) Proc. of ISSAC'97

%F (Pi/2)*log(4*Pi^3/Gamma(1/4)^4).

%F Also equals 2*Integral_{0..1} (1/(x^2+1))*log(log(1/x)) dx.

%F Also equals 2*Integral_{Pi/4..Pi/2} log(log(tan(x))) dx.

%e -0.5208856126019768910801877375794544390636383554462853499753755842...

%t RealDigits[(Pi/2)*Log[4*Pi^3/Gamma[1/4]^4], 10, 103] // First

%o (PARI) (Pi/2)*log(4*Pi^3/gamma(1/4)^4) \\ _Michel Marcus_, Apr 22 2015

%Y Cf. A068466, A115252.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Apr 22 2015