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.

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

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 * A344765 A259356 A137302

Adjacent sequences: A242049 A242050 A242051 * A242053 A242054 A242055

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 13 2014

Status

approved