2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162994Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q-shifted factorials can be incorporated into the implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and Mu to prove nonterminating basic hypergeometric series identities. This observation enables us to extend the q-WZ method to identities on infinite series. As examples, we will give the q-WZ pairs for some classical identities such as the q-Gauss sum, the $_6ϕ_5$ sum, Ramanujan's $_1ψ_1$ sum and Bailey's $_6ψ_6$ sum.17 pagesCombinatoricstext