A268464 - OEIS

%I #34 Feb 25 2021 21:28:24

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

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

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

%N Decimal expansion of the first inflection point of 1/Gamma(x) on the interval x=[0,infinity).

%C Also the first positive root of the equation Psi(x)^2-Psi(1,x)=0.

%C Function 1/Gamma(x) has only two inflection points on the interval x=[0,infinity): 0.30214172... (this sequence) and 2.4956029... (A269063).

%e 0.3021417247147373772612122942128464237734291035585021...

%p Digits:= 150; fsolve(Psi(x)^2-Psi(1,x)=0, x=0.3);

%t FindRoot[PolyGamma[x]^2-PolyGamma[1,x]==0, {x, 0.3}, WorkingPrecision -> 120][[1, 2]] // RealDigits[#, 10, 104]& // First

%Y Cf. A269063, A268895, A268911.

%K nonn,cons

%O 0,1

%A _Iaroslav V. Blagouchine_, Feb 18 2016