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A family of WZ pairs and q-identities

  • Yan-Ping MuEmail author
Article
  • 35 Downloads

Abstract

We observe that \((F(n+k+1,k)+G(n+k,k), G(n+k,k))\) is a WZ pair provided that (F(nk), G(nk)) is a WZ pair. This observation enables us to construct a bilateral sequence of WZ pairs starting from a single WZ pair. As an application, we give a one-line proof of the Rogers–Fine identity. Moreover, combing this observation and the q-WZ method for infinite series, we are able to derive a series of identities from a single q-identity. We illustrate this approach by Euler’s identity and the q-Gauss sum.

Keywords

WZ pair Basic hypergeometric series Rogers–Fine identity Euler’s identity q-Gauss sum 

Mathematics Subject Classification

33F10 33D15 65B10 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of ScienceTianjin University of TechnologyTianjinPeople’s Republic of China

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