A301814 - OEIS

%I #18 Apr 14 2018 01:35:07

%S 0,3,7,6,2,5,4,9,2,0,4,8,2,6,0,4,3,2,6,4,9,9,4,3,7,2,7,2,8,9,7,8,7,6,

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

%U 6,6,9,0,2,0,7,5,0,1,1,6,5,8,7,0,1,1,7

%N Decimal expansion of Re((1/4)*Integral_{-infinity..+infinity} sqrt(log(1/2 + i*z))* sech(Pi*z)^2).

%C See the references given in A301815.

%F Let beta(r) be the real part of Integral_{-oo..oo} (log(1/2 + i*z)^r / (exp(-Pi*z) + exp(Pi*z))^2) dz, where i denotes the imaginary unit. The constant equals beta(1/2) and A301815 equals -beta(1).

%e Equals

%e 0.03762549204826043264994372728978762248544767906044519708664851302092...

%p Re((1/2)*int(sqrt(log(1/2 + I*z))*sech(Pi*z)^2, z=0..64)): evalf(%, 100);

%Y Cf. A301815.

%K nonn,cons

%O 0,2

%A _Peter Luschny_, Apr 13 2018