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A365319
Decimal expansion of abs(Gamma(exp(i*Pi/3))).
2
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
0,1
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.
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).
FORMULA
Equals sqrt(Pi/cosh(Pi*sqrt(3)/2).
Equals 1/sqrt(3*A109219).
EXAMPLE
0.641739372784755...
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]]
PROG
(PARI) abs(gamma(exp(I*Pi/3))) \\ Michel Marcus, Sep 01 2023
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Sep 01 2023
STATUS
approved