Abel-Rothe Type Generalizations of Jacobi's Triple Product Identity

Using a simple classical method we derive bilateral series identities from terminating ones. In particular, we show how to deduce Ramanujan's 1ψ1 summation from the q-Pfaff-Saalschutz summation. Further, we apply the same method to our previous q-Abel-Rothe summation to obtain, for the first time, Abel-Rothe type generalizations of Jacobi's triple product identity. We also give some results for multiple series.

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