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arXiv · 2402.15886

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

Alexander Berkovich·Aritram Dhar
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Abstract

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.

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Alexander Berkovich, Aritram Dhar. 2025-05-04. Extension of Bressoud's generalization of Borwein's conjecture and some exact results. https://doi.org/10.1007/s11139-025-01063-0

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