Poles near the origin produce lower bounds for coefficients of meromorphic univalent functions (Q1885568)

Let \(r\), \(0<r<1\), be a fixed number and let \(U_r\) denote the class of functions \(f(z)=z+\sum^\infty_{n=2} a_n(f)z^n\), \(|z|<r\), that are univalent in the unit disc and have a simple pole at \(z=p\), \(|p|=r\). The main objective of this paper is to show that the variability region of \(a_n(f)\), \(f\in U_r\) at least for small values of \(r\), is an annulus.