Some new mock theta functions

New mock theta functions and formulas for basic hypergeometric series

“…Very recently, Yao [30] used partial fraction decomposition to give rise to several families of two-parameter mock theta functions and expressed them in the form of Appell-Lerch sums. In particular, she established some identities involving several families of mock theta functions and Appell–Lerch sums, which imply three identities proved by Cui and Gu [10]. Very recently, Mortenson et al.…”

“…Very recently, Yao [30] used partial fraction decomposition to give rise to several families of two-parameter mock theta functions and expressed them in the form of Appell-Lerch sums. In particular, she established some identities involving several families of mock theta functions and Appell-Lerch sums, which imply three identities proved by Cui and Gu [10]. Very recently, Mortenson et al [27] obtained new symmetries for string functions by exploiting their natural setting of Hecke-type double sums, where special double sums are expressed in terms of Appell-Lerch sums and theta functions.…”

“…Cui et al [11], Gu and Hao [16], Gu and Liu [17] and Zhang and Li [32] also discovered several new mock theta functions on Bailey pairs. Recently, Cui and Gu [10] established three two-parameter mock theta functions and represented them in terms of Appell-Lerch sums by using some formulas of basic hypergeometric series. Very recently, Yao [30] used partial fraction decomposition to give rise to several families of two-parameter mock theta functions and expressed them in the form of Appell-Lerch sums.…”