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.
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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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Dedicated to George Andrews on the occasion of his eightieth birthday
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The author was supported in part by a grant from the Simon’s Foundation (#318714).
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Garvan, F.G. New Fifth and Seventh Order Mock Theta Function Identities. Ann. Comb. 23, 765–783 (2019). https://doi.org/10.1007/s00026-019-00438-7
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DOI: https://doi.org/10.1007/s00026-019-00438-7