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A212877 Decimal expansion of the real part of i!, where i = sqrt(-1). 12
4, 9, 8, 0, 1, 5, 6, 6, 8, 1, 1, 8, 3, 5, 6, 0, 4, 2, 7, 1, 3, 6, 9, 1, 1, 1, 7, 4, 6, 2, 1, 9, 8, 0, 9, 1, 9, 5, 2, 9, 6, 2, 9, 6, 7, 5, 8, 7, 6, 5, 0, 0, 9, 2, 8, 9, 2, 6, 4, 2, 9, 5, 4, 9, 9, 8, 4, 5, 8, 3, 0, 0, 4, 3, 5, 9, 8, 1, 9, 3, 4, 5, 0, 7, 8, 9, 4, 5, 0, 4, 2, 8, 2, 6, 7, 0, 5, 8, 1, 4, 0, 5, 6, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Also the negated imaginary part of Gamma(i).
LINKS
Stanislav Sykora, Mathematical Constants, Stan's Library, Vol. II.
FORMULA
i! = gamma(1+i) = i*gamma(i).
Equals (1/2)*Integral_{x=-1/e..0} LambertW(x)*sin(log(-LambertW(x)))-LambertW(-1,x)*sin(log(-LambertW(-1,x))) dx. - Gleb Koloskov, Oct 01 2021
Equals Integral_{x=0..+oo} exp(-x)*cos(log(x)) dx. - Jianing Song, Sep 27 2023
A212877^2 + A212878^2 = A090986 = Pi/sinh(Pi). - Vaclav Kotesovec, Dec 28 2023
EXAMPLE
0.498015668118356042713691117462198...
MATHEMATICA
RealDigits[Re[Gamma[I + 1]], 10, 105] (* T. D. Noe, May 29 2012 *)
PROG
(PARI) real(I*gamma(I))
CROSSREFS
Cf. A212878 (-imag(i!)), A212879 (abs(i!)), A212880 (-arg(i!)), A090986.
Sequence in context: A365906 A256174 A096982 * A205297 A159643 A200398
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, May 29 2012
STATUS
approved

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)