Q-hypergeometric double sums as mock theta functions

Lovejoy, JeremyJeremyLovejoyOsburn, RobertRobertOsburn2016-09-162016-09-162013Pacific Journal of Mathematicshttp://hdl.handle.net/10197/7954Recently, 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.enQ-hypergeometric seriesMock theta functionsAppell–Lerch seriesHecke-type double sumsQ-hypergeometric double sums as mock theta functionsJournal Article264115116210.2140/pjm.2013.264.1512016-08-10https://creativecommons.org/licenses/by-nc-nd/3.0/ie/