%I #14 May 04 2018 11:26:27
%S 2,1,7,9,9,9,9,7,6,4,4,9,9,9,8,8,1,4,6,8,6,2,8,8,1,3,9,5,7,7,9,3,6,0,
%T 9,8,9,0,7,2,6,7,9,7,8,9,0,9,7,3,0,0,5,6,5,4,8,3,2,8,8,5,2,1,2,2,4,0,
%U 4,2,3,7,7,2,0,9,6,4,2,6,1,4,9,8,3,9,2,3,1,1,2,6,8,1,5,0,7,1,6,5,3,3,0,8,6
%N Decimal expansion of Gamma(delta)^2 where delta is the Feigenbaum bifurcation velocity constant (A006890).
%C Let x be this constant, then Integral_{t=1..x} sin(t)/sqrt(t) dt = 0.655555692248871113068...
%C delta^2 = 21.8014436664499573..., (delta/Gamma(delta))^2 = 0.10000663312663433933000349...
%C If s is solution of Gamma(s) - sqrt(218) = 0 then 1/((s - delta)*Gamma(delta)^6) = 2.5555951358396... whereas a^(Pi/4) = 2.055596478435... where a is Feigenbaum alpha constant (A006891), the difference = 0.4999986574... ~ 1/(2 + 10^-5.27)
%C 10*cos(Gamma(delta)^2) + Pi = -0.199999019922688714710053...
%H D. Broadhurst, <a href="http://www.plouffe.fr/simon/constants/feigenbaum.txt">Feigenbaum constants to 1018 decimal places</a>
%e 217.99997644999881468628813957793609890726797890973...
%t Set delta then RealDigits[Gamma[delta]^2, 10, 110][[1]]
%o (PARI) acos(Pi/10+.0199999019922688714710053)+69*Pi \\ Yields ~ 30 digits. Using (2e5-1)/(1e7-1) yields ~ 15 digits. For a better value use, e.g., delta from the Broadhurst link. - _M. F. Hasler_, Apr 30 2018
%Y Cf. A006890, A006891.
%K cons,nonn
%O 3,1
%A _Gerald McGarvey_, Feb 26 2005