Polyanalytic functions with exceptional values

Abstract:

Let $f(z) = \sum \nolimits _{k = 0}^n {{{\bar z}^k}{f_k}(z)}$ where the functions ${f_0},{f_1}, \cdots ,{f_n}$ are analytic on some annular neighborhood A of the point $\infty$ and ${f_n} \equiv 1$ on A and z denotes the complex conjugate of z. If f does not vanish on A it is shown that the functions ${f_0},{f_1}, \cdots ,{f_{n - 1}}$ have a nonessential isolated singularity at the point infinity.