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MOCK THETA DOUBLE SUMS

Part of: Basic hypergeometric functions Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  10 June 2016

JEREMY LOVEJOY  and
ROBERT OSBURN
JEREMY LOVEJOY
Affiliation:
CNRS, LIAFA, Université Denis Diderot - Paris 7, Case 7014, 75205 Paris Cedex 13, France e-mail: lovejoy@math.cnrs.fr
ROBERT OSBURN
Affiliation:
School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland IHÉS, Le Bois-Marie, 35, route de Chartres, F-91440 Bures-sur-Yvette, France e-mails: robert.osburn@ucd.ie, osburn@ihes.fr
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Abstract

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We prove a general result on Bailey pairs and show that two Bailey pairs of Bringmann and Kane are special cases. We also show how to use a change of base formula to pass from the pairs of Bringmann and Kane to pairs used by Andrews in his study of Ramanujan's seventh order mock theta functions. We derive several more Bailey pairs of a similar type and use these to construct a number of new q-hypergeometric double sums which are mock theta functions. Finally, we prove identities between some of these mock theta double sums and classical mock theta functions.

MSC classification

Primary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 323 - 348
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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