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

Alexander Berkovich, Aritram Dhar

Published 2024-02-24, updated 2024-03-18Version 2

In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state three 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 three infinite families.