Vol. 264, No. 1, 2013

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ISSN: 0030-8730
q-hypergeometric double sums as mock theta functions

Jeremy Lovejoy and Robert Osburn

Vol. 264 (2013), No. 1, 151–162
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
Authors
Jeremy Lovejoy
CNRS, LIAFA
Université Denis Diderot - Paris 7
Case 7014
75205 Paris Cedex 13
France
Robert Osburn
School of Mathematical Sciences
University College Dublin
Belfield
Dublin 4
Ireland