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A212880 Decimal expansion of the negated argument of i!. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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).

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!)).

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

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Last modified October 24 10:03 EDT 2021. Contains 348225 sequences. (Running on oeis4.)