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<p>In this paper, we conjecture an extension to Bressoud’s 1996 generalization of Borwein’s famous 1990 conjecture. We then state a few infinite hierarchies of non-negative <i>q</i>-series identities which are interesting examples of our proposed conjecture and Bressoud’s generalized conjecture. Finally, using certain positivity-preserving transformations for <i>q</i>-binomial coefficients, we prove the non-negativity of the infinite families.</p>

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Extension of Bressoud’s generalization of Borwein’s conjecture and some exact results

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Alexander Berkovich,
  • Aritram Dhar

摘要

In this paper, we conjecture an extension to Bressoud’s 1996 generalization of Borwein’s famous 1990 conjecture. We then state a few infinite hierarchies of non-negative q-series identities which are interesting examples of our proposed conjecture and Bressoud’s generalized conjecture. Finally, using certain positivity-preserving transformations for q-binomial coefficients, we prove the non-negativity of the infinite families.