Geodesic
Second Order Mock Theta Functions
Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 284-290

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DOI

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.
DOI : 10.4153/CMB-2007-028-9
Mots-clés : 11B65, 33D15, q-series, mock theta function, Mordell integral 
McIntosh, Richard J. Second Order Mock Theta Functions. Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 284-290. doi: 10.4153/CMB-2007-028-9
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     author = {McIntosh, Richard J.},
     title = {Second {Order} {Mock} {Theta} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {284--290},
     year = {2007},
     volume = {50},
     number = {2},
     doi = {10.4153/CMB-2007-028-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-028-9/}
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