A construction method for WZ seeds

TL;DR

This paper introduces a systematic method for constructing Wilf-Zeilberger seeds, presents seven specific seeds, and extends the approach to q-analogues, enabling derivation of hypergeometric identities.

Contribution

It provides a new systematic construction method for WZ seeds and extends it to q-analogues, facilitating the derivation of hypergeometric identities.

Findings

Seven WZ seeds constructed and demonstrated.

Method to generate WZ seeds from existing ones.

Extension of construction to q-analogues.

Abstract

We propose a systematic method for constructing Wilf-Zeilberger (WZ) seeds and present seven WZ seeds. We also demonstrate how to construct WZ seeds from existing ones. With these WZ seeds, several hypergeometric identities are derived. The construction can be extended to the $q$-cases, leading to the $q$-analogues of the seven WZ seeds.