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arXiv · 2509.21230

Bailey pairs and quantum $q$-series identites. I. The classical identities

Jehanne Dousse·Jeremy Lovejoy
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Abstract

We use Bailey pairs to prove $q$-series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the study of mock theta functions. In addition to the standard Bailey lemma, we require some changes-of-base established by Bressoud-Ismail-Stanton. We then embed the identities in infinite families using the Bailey chain.

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Jehanne Dousse, Jeremy Lovejoy. 2025-09-25. Bailey pairs and quantum $q$-series identites. I. The classical identities. https://arxiv.org/abs/2509.21230

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