Non-minimality of minimal telescopers explained by residues

TL;DR

This paper investigates why creative telescoping sometimes fails to find minimal telescopers, explaining the phenomenon through the analysis of residues, building on recent approaches by van Hoeij.

Contribution

It provides a residue-based explanation for the non-minimality of telescopers, advancing understanding of the limitations of creative telescoping methods.

Findings

Residue analysis explains non-minimal telescopers

Builds on van Hoeij's recent approach

Enhances understanding of creative telescoping limitations

Abstract

Elaborating on an approach recently proposed by Mark van Hoeij, we continue to investigate why creative telescoping occasionally fails to find the minimal-order annihilating operator of a given definite sum or integral. We offer an explanation based on the consideration of residues.