On the Existence of Telescopers for Mixed Hypergeometric Terms

TL;DR

This paper establishes a criterion for determining when telescopers exist for mixed hypergeometric terms, aiding in understanding the termination of Zeilberger's algorithms for such inputs.

Contribution

It introduces a new criterion based on decompositions to decide the existence of telescopers for mixed hypergeometric terms, advancing symbolic summation methods.

Findings

Criterion for existence of telescopers established

Determines termination conditions for Zeilberger's algorithms

Applicable to mixed hypergeometric terms

Abstract

We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed hypergeometric inputs.