Generic Approximation of functions by their pad\'{e} approximants, I

TL;DR

This paper explores the approximation of functions by Padé approximants, providing stronger generic results for functions on various domains, extending previous work on entire functions.

Contribution

It introduces new generic results on function approximation by Padé approximants for functions on simply connected and arbitrary connectivity domains.

Findings

Stronger generic approximation results for functions on complex domains.

Extension of previous results from entire functions to broader classes.

Improved understanding of Padé approximants' approximation capabilities.

Abstract

Approximation of entire functions by their pad\'e approximants has been examined in the past. It is true that generically such an approximation holds. However, examining this problem from another viewpoint, we obtain stronger generic results on functions defined on simply connected domains or even open sets of arbitrary connectivity.