Higher order recurrences and row sequences of Hermite-Pad\'e approximation

TL;DR

This paper extends classical theorems for higher order recurrence relations and applies these results to analyze the asymptotic behavior of row sequences in Hermite-Padé approximation of vector power series.

Contribution

It introduces generalized Poincaré and Perron theorems for higher order recurrences and uses them to derive inverse theorems for Hermite-Padé approximation sequences.

Findings

Extended Poincaré and Perron theorems for higher order recurrences

Derived inverse theorems for Hermite-Padé approximation sequences

Enhanced understanding of asymptotic behavior of approximation sequences

Abstract

We obtain extensions of the Poincar\'e and Perron theorems for higher order recurrence relations and apply them to obtain an inverse type theorem for row sequences of (type II) Hermite-Pad\'e approximation of a vector of formal power series.