A242052 - OEIS

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

(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