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A242052 Decimal expansion of the expected number of zeros of a+b*e^z satisfying |z|<1, a and b being random complex Gaussian coefficients. 0
2, 0, 2, 9, 1, 8, 9, 2, 1, 2, 8, 2, 8, 8, 9, 7, 4, 1, 2, 8, 2, 8, 4, 7, 7, 2, 0, 7, 6, 1, 4, 8, 7, 3, 5, 2, 4, 6, 8, 3, 2, 1, 7, 5, 1, 9, 2, 4, 4, 5, 5, 2, 6, 3, 1, 7, 8, 8, 1, 6, 2, 3, 8, 6, 9, 5, 5, 6, 2, 7, 3, 1, 4, 8, 5, 9, 5, 4, 2, 6, 7, 3, 5, 1, 3, 8, 9, 9, 8, 2, 4, 6, 7, 4, 6, 3, 0, 9, 5, 2, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants. 2.15 p. 20.

Gregorio Malajovich, On the expected number of zeros of nonlinear equations . arXiv:1106.6014v5 [math.AG] 28 Jun 2013 - arXiv.org

FORMULA

(1/Pi)*integral_{x^2+y^2<1} exp(2*x)/(1+exp(2*x))^2 dx dy = (1/(2*Pi))*integral_{x=-1..1} sqrt(1 - x^2)*sech(x)^2 dx.

EXAMPLE

2.029189212828897412828477207614873524683217519244552631788...

MATHEMATICA

(1/(2*Pi))*NIntegrate[Sqrt[1 - x^2]*Sech[x]^2, {x, -1, 1}, WorkingPrecision -> 102] // RealDigits // First

CROSSREFS

Sequence in context: A211930 A212026 A246003 * A259356 A137302 A265607

Adjacent sequences:  A242049 A242050 A242051 * A242053 A242054 A242055

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Aug 13 2014

STATUS

approved

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Last modified October 23 05:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)