A truncated jacobi triple product theorem

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Recently, G.E. Andrews and M. Merca considered a truncated version of Euler's pentagonal number theorem and obtained a nonnegativity result. They asked the same question on a truncated Jacobi triple product identity, which can be found as a conjecture in a paper of V.J.W. Guo and J. Zeng. In this paper, we provide an answer to the question, which is purely combinatorial. We also provide a combinatorial proof of the main theorem in the paper of Andrews and Merca.

Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalJournal of Combinatorial Theory. Series A
StatePublished - Feb 1 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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