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A Limiting form of the q-Dixon 4φ3 Summation and Related Partition Identities

  • Krishnaswami Alladi
  • Alexander Berkovich
Part of the Developments in Mathematics book series (DEVM, volume 8)

Abstract

By considering a limiting form of the q-Dixon 4φ3 summation, we prove a weighted partition theorem involving odd parts differing by ≥ 4. A two parameter refinement of this theorem is then deduced from a quartic reformulation of Göllnitz’s (Big) theorem due to Alladi, and this leads to a two parameter extension of Jacobi’s triple product identity for theta functions. Finally, refinements of certain modular identities of Alladi connected to the Göllnitz-Gordon series are shown to follow from a limiting form of the q-Dixon 4φ3 summation.

Keywords

q-Dixon sum q-Dougall Sum weighted partition identities Göllnitz’s (Big) theorem quartic reformulation Jacobi’s triple product GöllnitzGordon identities modular relations 

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Krishnaswami Alladi
    • 1
  • Alexander Berkovich
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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