Overconvergent series of rational functions and universal Laurent series
Let \(f\) be some analytic function on a closed connected subset \(\Gamma\) of \(\mathbb{C}\) and \(\{ P_n\}\) a polynomial sequence converging to \(f\) on \(\Gamma\) with geometric rate, then, it was proved previously by first and last authors, the convergence of \(\{ P_n\}\) extends to certain maximal domain. The present paper generalizes this result to sequences of rational functions with fixed poles. It is shown that this result implies that two classes of universal Laurent-type series coincide.
scientific article; zbMATH DE number 5320476