Second Order Mock Theta Functions

@article{McIntosh2007SecondOM,
  title={Second Order Mock Theta Functions},
  author={Richard J. McIntosh},
  journal={Canadian Mathematical Bulletin},
  year={2007},
  volume={50},
  pages={284 - 290}
}
Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right)$ , where $\left| q \right|<1$ . He called them mock theta functions, because as $q$ radially approaches any point ${{e}^{2\pi ir}}\left( r\,\text{rational} \right)$ , there is a theta function ${{F}_{r}}\left( q \right)$ with $F\left( q \right)-{{F}_{r}}\left( q \right)=O\left( 1 \right)$ . In this paper we establish the relationship between two families of mock theta functions. 
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In his last letter to Hardy, Ramanujan defined 17 f unctions F(q), where | q | < 1. He called them moc k theta functions, because as q radially approaches any poi nt Γ Πi e 2 (r rational), there is a
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