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A212878
Decimal expansion of the negated imaginary part of i!.
12
1, 5, 4, 9, 4, 9, 8, 2, 8, 3, 0, 1, 8, 1, 0, 6, 8, 5, 1, 2, 4, 9, 5, 5, 1, 3, 0, 4, 8, 3, 8, 8, 6, 6, 0, 5, 1, 9, 5, 8, 7, 9, 6, 5, 2, 0, 7, 9, 3, 2, 4, 9, 3, 0, 2, 6, 5, 8, 8, 0, 2, 7, 6, 7, 9, 8, 8, 6, 0, 8, 0, 1, 4, 9, 1, 1, 3, 8, 5, 3, 9, 0, 1, 2, 9, 5, 1, 3, 6, 6, 4, 7, 9, 4, 6, 3, 0, 7, 0, 7, 4, 9, 5, 9, 2
OFFSET
0,2
COMMENTS
Also the negated real part of Gamma(i).
FORMULA
i! = gamma(1+i) = i*gamma(i).
Equals -Integral_{x=0..+oo} exp(-x)*sin(log(x)) dx. - Jianing Song, Sep 27 2023
A212877^2 + A212878^2 = A090986 = Pi/sinh(Pi). - Vaclav Kotesovec, Dec 28 2023
EXAMPLE
0.15494982830181068512495513048...
MATHEMATICA
-Gamma[I] // Re // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, May 13 2013 *)
PROG
(PARI) -imag(I*gamma(I))
CROSSREFS
Cf. A212877 (real(i!)), A212879 (abs(i!)), A212880 (-arg(i!)), A090986.
Sequence in context: A125057 A021186 A195705 * A376258 A092302 A002389
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, May 29 2012
STATUS
approved