q-hypergeometric double sums as mock theta functions

Jeremy Lovejoy and Robert Osburn

Vol. 264 (2013), No. 1, 151–162

DOI: 10.2140/pjm.2013.264.151

Abstract

Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums. We also prove an identity between one of these sums and two classical mock theta functions introduced by Gordon and McIntosh.

Keywords

q-hypergeometric series, mock theta functions, Appell–Lerch series, Hecke-type double sums

Mathematical Subject Classification 2010

Primary: 33D15

Secondary: 05A30, 11F03, 11F37

Milestones

Received: 11 April 2012

Revised: 19 September 2012

Accepted: 22 October 2012

Published: 5 July 2013