On convergence of basic hypergeometric series

TL;DR

This paper investigates the convergence properties of basic hypergeometric series specifically when the parameter q lies on the unit circle, expanding understanding of their behavior in this boundary case.

Contribution

It provides new insights into the convergence criteria of q-hypergeometric series for |q|=1, a case less explored in prior research.

Findings

Identifies conditions for convergence when |q|=1

Characterizes divergence scenarios for certain series

Extends existing theory to boundary case |q|=1

Abstract

We examine the convergence of $q$-hypergeometric series when $|q|=1$.