%I #9 Feb 24 2016 11:26:56
%S 3,6,5,5,7,2,9,2,4,7,3,9,1,4,6,3,0,0,6,5,1,1,4,1,1,0,4,3,4,2,7,6,6,2,
%T 2,1,9,9,9,2,4,9,1,9,6,6,5,3,4,4,1,3,4,5,8,7,2,5,9,2,8,5,0,1,1,8,7,0,
%U 3,4,9,8,0,2,5,9,0,9,8,6,4,5,8,0,1,9,3,0,6,5,9,3,9,3,8,1,0,7,4,2,2,0,6
%N Decimal expansion of the third negative root of the equation Gamma(x) + Psi(x) = 0, negated.
%C Gamma(x) stands for the gamma function (Euler's integral of the second kind), Psi(x) denotes the digamma function (logarithmic derivative of the gamma function).
%e -3.6557292473914630065114110434276622199924919665344134...
%p Digits:= 150: fsolve(GAMMA(x)+Psi(x)=0, x=-3.65);
%t FindRoot[Gamma[x]+PolyGamma[x]==0, {x,-3.65}, WorkingPrecision->120][[1, 2]] // RealDigits[#, 10, 103]& // First
%o (PARI) default(realprecision, 120); solve(x = -3.7,-3.6, gamma(x)+psi(x))
%Y Cf. A268893, A268979, A268980.
%K nonn,cons
%O 1,1
%A _Iaroslav V. Blagouchine_, Feb 16 2016