A365319 Decimal expansion of abs(Gamma(exp(i*Pi/3))).

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

Offset: 0

Author

Artur Jasinski, Sep 01 2023

Keywords

• nonn
• cons

Comments

Also abs(Gamma(exp(i*2*Pi/3))).

For real part of Gamma(exp(i*Pi/3)) see A365317.

For negative imaginary part of Gamma(exp(i*Pi/3)) see A365318.

Examples

			0.641739372784755...
		

Links

• Juan Arias de Reyna and Jan van de Lune, On the exact location of the non-trivial zeros of Riemann's zeta function, arXiv:1305.3844 [math.NT], 2013, formula (4).

Crossrefs

Cf. A109219, A212877, A212878, A212879, A212880, A365317, A365318.

Programs

Mathematica

RealDigits[Abs[Gamma[Cos[Pi/3] + I Sin[Pi/3]]], 10, 106][[1]]
(* or *)
RealDigits[Sqrt[Pi/Cosh[Pi Sqrt[3]/2]], 10, 106][[1]]

PARI

abs(gamma(exp(I*Pi/3))) \\ Michel Marcus, Sep 01 2023

Formula

Equals sqrt(Pi/cosh(Pi*sqrt(3)/2)).

Equals 1/sqrt(3*A109219).