In 1991, Andrews and Hickerson established a new Bailey pair and combined it with the constant term method to prove some results related to sixth-order mock theta functions. In this paper, we study how this pair gives rise to new mock theta functions in terms of Appell–Lerch sums. Furthermore, we establish some relations between these new mock theta functions and some second-order mock theta functions. Meanwhile, we obtain an identity between a second-order and a sixth-order mock theta functions. In addition, we provide the mock theta conjectures for these new mock theta functions. Finally, we discuss the dual nature between the new mock theta functions and partial theta functions.

Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsom et al. for mock theta functions. Here we see that Mortenson's previous work on the dual nature of Appell–Lerch sums and partial theta functions and on constructing bilateral q-series with mixed mock modular behaviour is well suited for such radial limits. We present five more radial limit results, which follow from mixed mock modular bilateral q-hypergeometric series. We also obtain the mixed mock modular bilateral series for a universal mock theta function of Gordon and McIntosh. The later bilateral series can be used to compute radial limits for many classical second-, sixth-, eighth- and tenth-order mock theta functions.