Abstract:In this article, we use identities found in N.J. Fine's book Basic hypergeometric series and its applications to derive a one-parameter generalization of the product of two partial theta functions discovered by G.E. Andrews and S.O. Warnaar. We also give two different proofs of this generalization, one of which is motivated by the work of A. Berkovich and the other is given by M.E.H. Ismail.

---

中文翻译：

---

精细函数和部分theta函数

摘要：在本文中，我们使用NJ Fine的《基本超几何系列》及其应用中的恒等式推导了GE Andrews和SO Warnaar发现的两个部分theta函数的乘积的一参数归纳。我们还给出了两种不同的概括证明，一种是A. Berkovich的工作动机，另一种是MEH Ismail提出的。

---