We study fluctuations in the number of zeros random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When entire, we find sharp bounds for asymptotic growth rate variance large disks centered at origin. To obtain result that holds under no assumptions on employ Wiman-Valiron theory. demonstrate sharpness our studying well-behaved covariance kerne...

In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method. In the present paper, we demonstrate that such a view is only valid in very special cases, and in general the homotopy analysis method is far more robust. In particular...