Infinite matrix products and hypergeometric zeta series

TL;DR

This paper explores the deep connections between hypergeometric identities, infinite matrix products, and zeta values, revealing new structures and a novel matrix subgroup called the Gosper group.

Contribution

It uncovers the relationship between hypergeometric identities and infinite matrix products for zeta values, introducing the Gosper group as a new matrix subgroup.

Findings

Many WZ-accelerated series for zeta values correspond to infinite matrix products

The Gosper group is a new matrix subgroup encompassing these products

The correspondence between identities and matrix products is more profound than previously known

Abstract

An unpublished identity of Gosper restates a hypergeometric identity for odd zeta values in terms of an infinite product of matrices. We show that this correspondence runs much deeper, and show that many examples of WZ-accelerated series for zeta values lift to infinite matrix products. We also introduce a new matrix subgroup, the Gosper group, which all of our matrix products fall into.