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, 3

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..105.

Example

0.149965974606491...

Mathematica

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

Crossrefs

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

Sequence in context: A011512 A200642 A209674 * A157300 A100555 A250126

Adjacent sequences: A364818 A364819 A364820 * A364822 A364823 A364824

Keyword

nonn,cons

Author

Artur Jasinski, Oct 07 2023

Status

approved