Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series (1906.11997v1)

Abstract: The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of $2\psi_2$ series [ \sum{n=-\infty}^{\infty}\frac{(a,c;q)_n}{(b,d;q)_n}z^n. ] Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for both these mock theta functions and the corresponding bilateral series. \ New and existing summation formulae for these bilateral series are also used to make explicit in a number of cases the fact that for a mock theta function, say $\chi(q)$, and a root of unity in a certain class, say $\zeta$, that there is a theta function $\theta_{\chi}(q)$ such that [ \lim_{q \to \zeta}(\chi(q) - \theta_{\chi}(q)) ] exists, as $q \to \zeta$ from within the unit circle.