It is explained how the Mordell integral ∫ R e πiτ x 2 − 2 πzx cosh ( πx ) dx $$\int_{\mathbb R} \frac{e^{\pi i \tau x^{2} - 2\pi zx}}{\cosh(\pi x)} dx $$
unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z.
Mathematics Subject Classification: 11P55, 05A17