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arXiv · 1204.2431

q-hypergeometric double sums as mock theta functions

Jeremy Lovejoy·Robert Osburn
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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. Additionally, we prove an identity between one of these sums and two classical mock theta functions introduced by Gordon and McIntosh.

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Jeremy Lovejoy, Robert Osburn. 2012-10-23. q-hypergeometric double sums as mock theta functions. https://doi.org/10.2140/pjm.2013.264.151

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