Abel-Rothe type generalizations of Jacobi's triple product identity

Details Abel-Rothe type generalizations of Jacobi's triple product identity Abel-Rothe type generalizations of Jacobi's triple product identity

2003-02-24

arxiv.org/abs/math/0302270v4

Dev. Math. 13 (2005), 383-400

Mathematics

Combinatorics

14 pages, mistake in appendix corrected; to appear in "Theory and Applications of Special Functions, A volume dedicated to Miz

Scientific paper

Using a simple classical method we derive bilateral series identities from terminating ones. In particular, we show how to deduce Ramanujan's 1-psi-1 summation from the q-Pfaff-Saalschuetz 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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