The Borweins’ Cubic Theta Functions and q-Elliptic Functions

  • Richard Lewis
  • Zhi-Guo Liu
Part of the Developments in Mathematics book series (DEVM, volume 4)


We give two identities; one, originally due to Weierstrass, is old and one appears to be new. We use these identities to give proofs of some relations between the functions a(q), b (q) and c (q) of Borwein, Borwein and Garvan [4].


q-elliptic function the power series (z; q) and [z; q] the Borweins’ identities 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Richard Lewis
    • 1
  • Zhi-Guo Liu
    • 2
    • 3
  1. 1.SMSThe University of SussexBrightonUK
  2. 2.Mathematics Dept.Xinxiang Education CollegeXinxiang, HenanP.R. China
  3. 3.Nanjing Institute of MeteorologyNanjingP.R. China

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