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

  • Michael Schlosser
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 13)

Abstract

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-Saalschütz 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.

Keywords

q-series bilateral series Jacobi's triple product identity Ramanujan's 1ψ1 summation q-Rothe summation q-Abel summation Macdonald identities Ar series U(n) series 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Michael Schlosser
    • 1
  1. 1.Institute für Mathematik der Universität WienWienAustria

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