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Decimal expansion of the unique value of x such that Gamma(-x + i*sqrt(1-x^2)) is a real number and -1 < x < 1.
5

%I #32 Aug 26 2023 15:37:32

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

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

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

%N Decimal expansion of the unique value of x such that Gamma(-x + i*sqrt(1-x^2)) is a real number and -1 < x < 1.

%C Gamma(-A364355 + i*sqrt(1-A364355^2)) = -0.6749332470449905963531... see A364356.

%C Also decimal expansion of the unique value of x in the range -1 < x < 1 for which the function Re(Gamma(-x + i*sqrt(1-x^2)))/abs(Gamma(-x + i*sqrt(1-x^2))) is minimized.

%e x = 0.54197987169489060244332278779...

%t RealDigits[x /. FindRoot[Im[Gamma[-x + I Sqrt[1 - x^2]]], {x, 0.5}, WorkingPrecision -> 106]][[1]]

%Y Cf. A090986, A212877, A212878, A212880, A212879, A364356.

%K nonn,cons

%O 0,1

%A _Artur Jasinski_, Jul 20 2023