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

0,1

Comments

Also the negated imaginary part of Gamma(i).

Links

Table of n, a(n) for n=0..104.

Stanislav Sykora, Mathematical Constants, Stan's Library, Vol. II.

Wikipedia, Particular values of the Gamma function

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

Adjacent sequences: A212874 A212875 A212876 * A212878 A212879 A212880

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 29 2012

Status

approved