Wiman-Valiron theory for a class of functions meromorphic in the unit disc

TL;DR

This paper extends Wiman-Valiron theory to certain meromorphic functions in the unit disc, providing local approximations and growth behavior insights based on an approach adapted from plane setting results.

Contribution

It introduces a novel adaptation of Wiman-Valiron theory for meromorphic functions in the unit disc, including local approximation results and growth estimates.

Findings

Local approximations for functions and their logarithmic derivatives

Results for functions with positive order of growth

Extension of Wiman-Valiron theory to the unit disc setting

Abstract

Analogues of the key results of Wiman-Valiron theory are proved for a class of functions meromorphic in the unit disc, based on an approach developed by Bergweiler, Rippon and Stallard for the plane setting. The results give local approximations for the function and its logarithmic derivative and, in the case of positive order of growth, for higher order logarithmic derivatives as well.