A366345 -id:A366345 - cp's OEIS frontend

A364821 Decimal expansion of the unique value of x such that Gamma(x + i*sqrt(1-x^2)) is an imaginary number and -1 < x < 1.

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

Offset: 0

Artur Jasinski, Oct 07 2023

Gamma(A364821 + i*sqrt(1-A364821^2)) = -i*0.5377003887835295919... see A366345.

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

			0.149965974606491...

Cf. A090986, A212877, A212878, A212880, A212879, A364355, A364356, A365317, A365318, A366345.

RealDigits[
  x /. FindRoot[Re[Gamma[x + I Sqrt[1 - x^2]]], {x, 0.15},
    WorkingPrecision -> 106]][[1]]

Last digit corrected by Vaclav Kotesovec, Sep 02 2025

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.

Original entry on oeis.org

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, 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, 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

Offset: 0

Artur Jasinski, Oct 12 2023

For Re(Gamma(-A366545 + i*sqrt(1-A366545^2))) = -0.930840199... see A366545.

			0.9565130903466545656...

Cf. A090986, A212877, A212878, A212880, A212879, A364355, A364356, A364821, A365317, A365318, A366345.

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,
         x + I Sqrt[1 - x^2]]), {x, -0.98}, WorkingPrecision -> 110]];
 RealDigits[xmin, 10, 106][[1]]

cp's OEIS Frontend

A364821 Decimal expansion of the unique value of x such that Gamma(x + i*sqrt(1-x^2)) is an imaginary number and -1 < x < 1.

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