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%I #19 Dec 28 2023 13:10:41
%S 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,
%T 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,
%U 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
%N Decimal expansion of the negated imaginary part of i!.
%C Also the negated real part of Gamma(i).
%F i! = gamma(1+i) = i*gamma(i).
%F Equals -Integral_{x=0..+oo} exp(-x)*sin(log(x)) dx. - _Jianing Song_, Sep 27 2023
%F A212877^2 + A212878^2 = A090986 = Pi/sinh(Pi). - _Vaclav Kotesovec_, Dec 28 2023
%e 0.15494982830181068512495513048...
%t -Gamma[I] // Re // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, May 13 2013 *)
%o (PARI) -imag(I*gamma(I))
%Y Cf. A212877 (real(i!)), A212879 (abs(i!)), A212880 (-arg(i!)), A090986.
%K nonn,cons,easy
%O 0,2
%A _Stanislav Sykora_, May 29 2012
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