Bailey pairs and strange identities

preprint2022arXivOpen access

Abstract

Zagier introduced the term "strange identity" to describe an asymptotic relation between a certain qq-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.

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