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Decimal expansion of the third negative root of the equation Gamma(x) + Psi(x) = 0, negated.
3

%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