The q-WZ method for infinite series
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 (305 sum, the Ramanujan's (1)psi(1) sum and Bailey's (6)psi(6) sum. (C) 2009 Published by Elsevier Ltd
the q-wz method the q-zeilberger algorithm basic hypergeometric series the q-gosper algorithm