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

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.