Abstract
We give an explicit formula for the logarithmic potential of the asymptotic zero-counting measure of the sequence ${\lbrace (d^n/dz^n) (R(z) \mathrm{exp}T(z))\rbrace}^{\infty}_{n=1}$. Here, $R(z)$ is a rational function with at least two poles, all of which are distinct, and $T(z)$ is a polynomial. This is an extension of a recent measure-theoretic refinement of Pólya’s Shire theorem for rational functions.
Citation
Christian Hägg. "The asymptotic zero-counting measure of iterated derivaties of a class of meromorphic functions." Ark. Mat. 57 (1) 107 - 120, April 2019. https://doi.org/10.4310/ARKIV.2019.v57.n1.a6