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arXiv · 1208.1330

On three third order mock theta functions and Hecke-type double sums

Eric Mortenson
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Abstract

We obtain four Hecke-type double sums for three of Ramanujan's third order mock theta functions. We discuss how these four are related to the new mock theta functions of Andrews' work on $q$-orthogonal polynomials and Bringmann, Hikami, and Lovejoy's work on unified Witten-Reshetikhin-Turaev invariants of certain Seifert manifolds. We then prove identities between these new mock theta functions by first expressing them in terms of the universal mock theta function.

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Eric Mortenson. 2012-08-07. On three third order mock theta functions and Hecke-type double sums. https://doi.org/10.1007/s11139-012-9376-8

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