A269063 - OEIS

%I #14 Feb 25 2021 21:25:53

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

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

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

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

%C Also the second 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... (A268464) and 2.4956029... (this sequence).

%e 2.4956029635171933815428456493853820634653641719500480...

%p Digits:= 150: fsolve(Psi(x)^2-Psi(1,x)=0, x=2.5);

%t FindRoot[PolyGamma[x]^2-PolyGamma[1,x]==0, {x, 2.5}, WorkingPrecision -> 120][[1, 2]] // RealDigits[#, 10, 103]& // First

%Y Cf. A268464, A268895, A268911.

%K nonn,cons

%O 1,1

%A _Iaroslav V. Blagouchine_, Feb 18 2016