Journal of the
Korean Mathematical Society
JKMS

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

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J. Korean Math. Soc.

Published online July 25, 2022

Copyright © The Korean Mathematical Society.

Bailey pairs and strange identities

Jeremy Lovejoy

CNRS, Université Paris Cité

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, Rogers-Ramanujan identities

MSC numbers: 11F37, 11P84, 33D15

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