A364355 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, 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, 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, 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

Offset

0,1

Comments

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

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.

Links

Table of n, a(n) for n=0..104.

Example

x = 0.54197987169489060244332278779...

Mathematica

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

Crossrefs

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

Sequence in context: A308714 A213055 A005752 * A365465 A098494 A008955

Adjacent sequences: A364352 A364353 A364354 * A364356 A364357 A364358

Keyword

nonn,cons

Author

Artur Jasinski, Jul 20 2023

Status

approved