Mock theta functions can be represented by Eulerian forms, Hecke-type double sums, Appell–Lerch sums, and Fourier coefficients of meromorphic Jacobi forms. In view of some q-series identities, we establish three two-parameter mock theta functions, and express them in terms of Appell-Lerch sums. In addition, we find three mock theta functions in Eulerian forms. Then in light of their Hecke-type double sums, we provide the Hecke-type double sums for some third order mock theta functions, and establish the relations between these functions and some classical mock theta functions.

中文翻译：

---

一些新的模拟 theta 函数

模拟 theta 函数可以用欧拉形式、Hecke 型双和、Appell-Lerch 和和亚纯雅可比形式的傅立叶系数表示。针对一些q- series恒等式，我们建立了三个二参数mock theta函数，并用Appell-Lerch sum表示。此外，我们发现了三个欧拉形式的模拟 theta 函数。然后根据它们的Hecke型双和，我们为一些三阶模拟theta函数提供了Hecke型双和，并建立了这些函数与一些经典模拟theta函数之间的关系。