On the convergence of type I Hermite-Pad\'e approximants for a class of meromorphic functions

TL;DR

This paper investigates the convergence properties of type I Hermite-Padé approximants for a specific class of meromorphic functions formed by combining rational functions with Nikishin systems, advancing understanding in approximation theory.

Contribution

It introduces new convergence results for type I Hermite-Padé approximants applied to functions combining rational components with Nikishin systems.

Findings

Established convergence conditions for the approximants.

Extended previous results to a broader class of meromorphic functions.

Provided theoretical insights into approximation behavior for complex functions.

Abstract

We study the convergence of type I Hermite-Pad\'e approximation for a class of meromorphic functions obtained by adding a vector of rational functions with real coefficients to a Nikishin system of functions.