Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(5): 1015-1045

Online first article July 25, 2022      Printed September 1, 2022

https://doi.org/10.4134/JKMS.j220167

Copyright © The Korean Mathematical Society.

Bailey pairs and strange identities

Jeremy Lovejoy

8 Place Aur\'elie Nemours

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.

Keywords: Bailey pairs, strange identities, Andrews-Gordon identities

MSC numbers: 11F37, 11P84, 33D15

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