Second Order Mock Theta Functions

McIntosh, Richard J.

Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 284-290

Résumé

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.

Détail

DOI : 10.4153/CMB-2007-028-9

Mots-clés : 11B65, 33D15, q-series, mock theta function, Mordell integral

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