A212880 Decimal expansion of the negated argument of i!.

3, 0, 1, 6, 4, 0, 3, 2, 0, 4, 6, 7, 5, 3, 3, 1, 9, 7, 8, 8, 7, 5, 3, 1, 6, 5, 7, 7, 9, 6, 8, 9, 6, 5, 4, 0, 6, 5, 9, 8, 9, 9, 7, 7, 3, 9, 4, 3, 7, 6, 5, 2, 3, 6, 9, 4, 0, 7, 4, 4, 0, 0, 5, 3, 8, 3, 0, 6, 0, 5, 8, 1, 4, 3, 9, 5, 0, 2, 9, 5, 3, 3, 9, 9, 8, 9, 8, 2, 2, 6, 9, 7, 2, 7, 9, 5, 0, 1, 1, 9, 4, 2, 3, 4, 4

Offset

0,1

Comments

The value is in radians.

Links

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

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020, p. 5.

Mircea Ivan, Problem 11592, The American Mathematical Monthly, Vol. 118, No. 7 (2011), p. 654; Arggh! Eye Factorial ... Arg(i!), Solutions to problem 11592 by Nora Thornbe, Omran Kouba and Denis Constales, ibid., Vol. 120, No. 7 (2013), p. 662-664.

Cornel Ioan Vălean, Problema 327, La Gaceta de la Real Sociedad Matemática Española, Vol. 21, No. 2 (2018), pp. 331-343.

Formula

Equals -arg(i*Gamma(i)), since i! = Gamma(1+i) = i*Gamma(i).

Equals lim_{n->infinity} ((Sum_{k=1..n} arctan(1/k)) - log(n)). - Jean-François Alcover, Aug 07 2014, after Steven Finch

Equals arctan(A212878/A212877). - Vaclav Kotesovec, Dec 10 2015

From Amiram Eldar, Jun 12 2021: (Start)

Equals 1 - Integral_{x=0..Pi/2} frac(cot(x)) dx, where frac(x) = x - floor(x) is the fractional part of x.

Equals gamma - Sum_{k>=1} (-1)^(k+1)*zeta(2*k+1)/(2*k+1) = A001620 - A352619.

Both formulae are from Vălean (2018). (End)

Equals log((Gamma(1-i)/Gamma(1+i))^(-i/2)). - Vaclav Kotesovec, Jun 12 2021

Example

0.30164032046753319788753165779...

Mathematica

RealDigits[-Arg[Gamma[1 + I]], 10, 105] // First (* Jean-François Alcover, Aug 07 2014 *)

Crossrefs

Cf. A212877 (real(i!)), A212878 (-imag(i!)), A212879 (abs(i!)).

Cf. A001620 (gamma), A352619.

Sequence in context: A105147 A335262 A111924 * A211510 A243984 A100485

Adjacent sequences: A212877 A212878 A212879 * A212881 A212882 A212883

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 29 2012

Status

approved