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A212877
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Decimal expansion of the real part of i!, where i = sqrt(-1).
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12
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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
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OFFSET
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0,1
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COMMENTS
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Also the negated imaginary part of Gamma(i).
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LINKS
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FORMULA
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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
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EXAMPLE
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0.498015668118356042713691117462198...
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MATHEMATICA
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RealDigits[Re[Gamma[I + 1]], 10, 105] (* T. D. Noe, May 29 2012 *)
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PROG
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(PARI) real(I*gamma(I))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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