Bailey pairs and strange identities

DOI10.4134/JKMS.J220167zbMATH Open1509.11035arXiv2203.14391MaRDI QIDQ6394819

Publication date: 27 March 2022

Abstract: Zagier introduced the term "strange identity" to describe an asymptotic relation between a certain

q

-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.

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Partition identities; identities of Rogers-Ramanujan type (11P84)

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