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.

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