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arXiv:math/0302270 [math.CO]AbstractReferencesReviewsResources

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

Michael J. Schlosser

Published 2003-02-24, updated 2003-06-16Version 4

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.

Comments: 14 pages, mistake in appendix corrected; to appear in "Theory and Applications of Special Functions, A volume dedicated to Mizan Rahman", M. E. H. Ismail and E. Koelink (eds.), Dev. Math
Journal: Dev. Math. 13 (2005), 383-400
Categories: math.CO, math.CA
Subjects: 33D15, 33D67
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