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%I #53 Jan 27 2021 09:24:20
%S 5,1,5,9,3,9,4,8,2,2,7,9,6,5,3,4,8,4,9,5,3,1,2,5,0,1,3,9,4,0,5,5,6,3,
%T 7,2,6,9,8,1,0,9,9,9,2,4,6,8,6,8,1,4,7,4,8,5,8,7,1,7,9,6,2,5,2,2,7,4,
%U 4,9,7,1,7,6,1,9,5,7,7,2,2,7,6,1,1,9,4,3,1,3,1,6,2,6,5,8,8,9,8,3,0,3,6
%N Decimal expansion of the constant kappa(-5) = (1/2)*sqrt(sqrt(5)*log(9+4*sqrt(5))/(3*Pi))*sqrt(A340794*A340665).
%C For general definition of the constants kappa(n) see Steven Finch 2009 p. 7, for this particular case kappa(-5) see p. 11.
%H Steven Finch, <a href="https://arxiv.org/abs/0907.4894">Quartic and Octic Characters Modulo n</a>, arXiv:0907.4894 [math.NT], 2009 p. 7-11.
%F Equals exp(-gamma/2)*log((1+sqrt(5))/2)*sqrt(5/Pi)/(2*C(5,2)*C(5,3)), where C(5,2) and C(5,3) are Mertens constants see A340839.
%F Equals 2*A340866*exp(gamma/4)*((1/5)*log((1+sqrt(5))/2))^(3/4)/sqrt(A340004).
%F Equals 2*A340866*exp(gamma/4)*log((1+sqrt(5))/2)/(sqrt(5*Pi)*A340884^(1/4)).
%F Equals 2*A340839*A340866*exp(gamma/2)*log((1+sqrt(5))/2)/sqrt(5*Pi).
%F Equals sqrt((1/3)*Pi*log(9+4*sqrt(5)))/(sqrt(5^(3/2)*A340004*A340127)). [Finch 2009 p. 11]
%e 0.51593948227965348495312501394...
%Y Cf. A340004, A340127, A340665, A340794, A340839, A340866.
%K nonn,cons
%O 0,1
%A _Artur Jasinski_, Jan 26 2021