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

  title={On three third order mock theta functions and Hecke-type double sums},
  author={Eric T. Mortenson},
  journal={The Ramanujan Journal},
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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