A212877 Decimal expansion of the real part of i!, where i = sqrt(-1).

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

Offset: 0

Author

Stanislav Sykora, May 29 2012

Keywords

• nonn
• cons
• easy

Comments

Also the negated imaginary part of Gamma(i).

Examples

			0.498015668118356042713691117462198...
		

Links

• Stanislav Sykora, Mathematical Constants, Stan's Library, Vol. II.
• Wikipedia, Particular values of the Gamma function

Crossrefs

Cf. A212878 (-imag(i!)), A212879 (abs(i!)), A212880 (-arg(i!)), A090986.

Programs

Mathematica

RealDigits[Re[Gamma[I + 1]], 10, 105] (* T. D. Noe, May 29 2012 *)

PARI

real(I*gamma(I))

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