A242052 - OEIS

%I #17 Jan 17 2020 05:41:28

%S 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,

%T 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,

%U 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

%N Decimal expansion of the expected number of zeros of a+b*e^z satisfying |z|<1, a and b being random complex Gaussian coefficients.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> 2.15 p. 20.

%H Gregorio Malajovich, <a href="http://arxiv.org/pdf/1106.6014.pdf">On the expected number of zeros of nonlinear equations .</a> arXiv:1106.6014v5 [math.AG] 28 Jun 2013 - arXiv.org

%F (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.

%e 2.029189212828897412828477207614873524683217519244552631788...

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

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Aug 13 2014