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New Fifth and Seventh Order Mock Theta Function Identities

  • Frank G. GarvanEmail author
Article
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Abstract

We give simple proofs of Hecke–Rogers indefinite binary theta series identities for the two Ramanujan’s fifth order mock theta functions \(\chi _0(q)\) and \(\chi _1(q)\) and all three of Ramanujan’s seventh order mock theta functions. We find that the coefficients of the three mock theta functions of order 7 are surprisingly related.

Keywords

Mock theta functions Hecke–Rogers double sums Bailey pairs Conjugate Bailey pairs 

Mathematics Subject Classification

Primary 33D15 Secondary 11B65 11F27 

Notes

Acknowledgements

I would like to thank Chris Jennings-Shaffer and Jeremy Lovejoy for their comments and suggestions. Also I would like to thank the referee for corrections and suggestions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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