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Some New Positive Observations

We revisit Bressoud's generalized Borwein conjecture. Making use of new positivity-preserving transformations for q-binomial coefficients we establish the truth of infinitely many cases of the Bressoud conjecture. In addition, we prove new bounded version of Lebesgue's identity and of Euler's Pentagonal Number Theorem. Finally, we discuss new companions to Andrews-Gordon mod 21 and Bressoud mod 20 identities.

preprint2020arXivOpen access
Alexander Berkovich
math.NT
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Alexander Berkovich

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