cp's OEIS Frontend

A366545 Decimal expansion of the value x for which the function Re(Gamma(-x + i*sqrt(1-x^2))) is minimized for -1 < x < 1.

%I A366545 #18 Mar 28 2025 03:44:42
%S A366545 9,5,6,5,1,3,0,9,0,3,4,6,6,5,4,5,6,5,6,0,3,6,3,6,6,0,1,5,9,2,5,6,5,4,
%T A366545 4,4,9,3,0,6,8,3,2,2,6,1,4,9,5,4,1,1,1,2,5,7,6,3,2,8,7,6,6,0,5,4,8,0,
%U A366545 3,1,9,7,3,5,7,6,8,6,8,6,5,1,2,3,6,0,9,8,4,8,5,7,1,4,0,0,7,5,2,8,1,9,9,9,1,7
%N A366545 Decimal expansion of the value x for which the function Re(Gamma(-x + i*sqrt(1-x^2))) is minimized for -1 < x < 1.
%C A366545 For Re(Gamma(-A366545 + i*sqrt(1-A366545^2))) = -0.930840199... see A366545.
%e A366545 0.9565130903466545656...
%t A366545 xmin = Re[x /. FindRoot[1/(2 Sqrt[1 - x^2]) I (Gamma[1 + x - I Sqrt[1 - x^2]] PolyGamma[0, x - I Sqrt[1 - x^2]] - Gamma[1 + x + I Sqrt[1 - x^2]] PolyGamma[0,
%t A366545          x + I Sqrt[1 - x^2]]), {x, -0.98}, WorkingPrecision -> 110]];
%t A366545  RealDigits[xmin, 10, 106][[1]]
%Y A366545 Cf. A090986, A212877, A212878, A212880, A212879, A364355, A364356, A364821, A365317, A365318, A366345.
%K A366545 nonn,cons
%O A366545 0,1
%A A366545 _Artur Jasinski_, Oct 12 2023