The q-WZ Method for Infinite Series
William Y. C. Chen and Ernest X. W. Xia
Abstract: Motivated 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. We give the q-WZ pairs for some classical identities such as the q-Gauss sum, the 6φ5 sum, Ramanujan's 1ψ1 sum and Bailey's 6ψ6 sum.
AMS Classification: 33D15, 33F10
Keywords: basic hypergeometric series, the q-Gosper algorithm, the q-Zeilberger algorithm, the q-WZ method.