A396976 - OEIS

%I #19 Jun 17 2026 00:15:34

%S 1,1,9,5,0,9,2,9,1,9,0,5,5,6,0,7,5,5,4,4,6,7,7,8,6,5,9,4,8,7,6,8,8,4,

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

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

%N Decimal expansion of (-1)*Integral_{x=0..1} log(-log(x))/(1 + x^2 + 2*x*cos(1)) dx.

%H Robert Reynolds, <a href="https://arxiv.org/abs/2412.10395">Derivation of some definite integrals</a>, arXiv:2412.10395 [math.GM], 2024-2025, page 10, eq. 4.11.

%F Equals -(1/2)*Pi*csc(1)*log(((2 Pi)^(1/Pi)*Gamma(1/2+1/(2 Pi)))/Gamma(1/2-1/(2 Pi))).

%F Equals (Pi*log(cos(1/2)*Gamma(1/2 - 1/(2*Pi))^2/Pi) - log(2*Pi)) / (2*sin(1)). - _Vaclav Kotesovec_, Jun 13 2026

%e 0.11950929190556075544677865948768847300488651613614619...

%t RealDigits[-(1/2)*Pi Csc[1] Log[((2 Pi)^(1/Pi) Gamma[1/2+1/(2 Pi)])/Gamma[1/2-1/(2 Pi)]],10,105][[1]]

%o (PARI) -intnum(x=0, 1, log(-log(x))/(1+x^2+2*x*cos(1)))

%Y Cf. A049470, A396964.

%K nonn,cons

%O 0,3

%A _Artur Jasinski_, Jun 12 2026