A366345 Decimal expansion of y such that Gamma(A364821 + i*sqrt(1-A364821^2)) = -y*i.

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

Offset

0,1

Comments

x = A364821 = 0.149965974606491089853... is the only real number x such that Gamma(x + i*sqrt(1-x^2)) is an imaginary number and -1 < x < 1.

Links

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

Example

0.53770038878352959190460079577395025549442775617415...

Mathematica

RealDigits[With[{x0 = x /. FindRoot[Re[Gamma[x + Sqrt[1-x^2]*I]], {x, 0}, WorkingPrecision -> 120]}, Im[Gamma[x0 + Sqrt[1-x0^2]*I]]]][[1]] (* Amiram Eldar, Apr 12 2026 *)

Crossrefs

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

Sequence in context: A275415 A021190 A186905 * A109694 A259068 A219336

Adjacent sequences: A366342 A366343 A366344 * A366346 A366347 A366348

Keyword

nonn,cons,less

Author

Artur Jasinski, Oct 07 2023

Status

approved