A212878 Decimal expansion of the negated imaginary part of i!.

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, 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, 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

Offset

0,2

Comments

Also the negated real part of Gamma(i).

Links

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

Formula

i! = gamma(1+i) = i*gamma(i).

Equals -Integral_{x=0..+oo} exp(-x)*sin(log(x)) dx. - Jianing Song, Sep 27 2023

A212877^2 + A212878^2 = A090986 = Pi/sinh(Pi). - Vaclav Kotesovec, Dec 28 2023

Example

0.15494982830181068512495513048...

Mathematica

-Gamma[I] // Re // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, May 13 2013 *)

Prog

(PARI) -imag(I*gamma(I))

Crossrefs

Cf. A212877 (real(i!)), A212879 (abs(i!)), A212880 (-arg(i!)), A090986.

Sequence in context: A125057 A021186 A195705 * A092302 A002389 A196758

Adjacent sequences: A212875 A212876 A212877 * A212879 A212880 A212881

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 29 2012

Status

approved