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Published online by Cambridge University Press:  21 December 2018

Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China email
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China email


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.

Research Article
© 2018 Australian Mathematical Publishing Association Inc. 

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The authors were supported by the National Natural Science Foundation of China and the Fundamental Research Funds for the Central Universities of China.


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