New families of mock theta functions and partial fraction decomposition

Abstract

In 2000, Andrews challenged mathematicians in the 21st century to elucidate the overlap between classes of q-series and modular forms. Motivated by Andrews' challenge, seeking q-hypergeometric series which are mock theta functions in the modern sense and finding their alternative representations have attracted the attention of many mathematicians in recent years. In this paper, we use partial fraction decomposition to give rise to several families of two-parameter mock theta functions and express them in the form of Appell-Lerch sums. In particular, we establish some identities involving several families of mock theta functions and Appell-Lerch sums which imply three identities proved by Cui and Gu.