A268893 - OEIS

%I #14 Feb 27 2016 07:31:55

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

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

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

%N Decimal expansion of the unique positive root of the equation Gamma(x) + Psi(x) = 0.

%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 0.6388787411601983229952762472475406150969427223844435...

%p Digits:= 150; fsolve(GAMMA(x)+Psi(x)=0, x);

%t FindRoot[Gamma[x]+PolyGamma[x]==0, {x,0.6}, WorkingPrecision->120][[1, 2]] // RealDigits[#, 10, 106]& // First

%o (PARI) default(realprecision, 120); solve(x = 0.60, 0.68, gamma(x)+psi(x))

%Y Cf. A268895, A268979, A268980, A268981.

%K nonn,cons

%O 0,1

%A _Iaroslav V. Blagouchine_, Feb 15 2016