We apply Heine’s method—the key idea Heine used in 1846 to derive his famous transformation formula for \(_2\phi _1\) series—to multiple basic series over the root system of type A. In the classical case, this leads to a bibasic extension of Heine’s formula, which was implicit in a paper of Andrews which he wrote in 1966. As special cases, we recover extensions of many of Ramanujan’s \(_2\phi _1\) transformations. In addition, we extend previous work of the author regarding a bibasic extension of Andrews’ q-Lauricella function, and show how to obtain very general transformation formulas of this type. The results obtained include transformations of an n-fold sum into an m-fold sum.

中文翻译：

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Heine方法和A n至A m转换公式。

我们将Heine的方法（Heine在1846年用来推导他著名的\（_ 2 \ phi _1 \）级数转换公式的关键思想）应用于A型根系统上的多个基本级数。在经典情况下，这导致Heine公式的二元扩展，这在Andrews于1966年撰写的论文中隐含了。作为特殊情况，我们恢复了许多Ramanujan的\（_ 2 \ phi _1 \）变换的扩展。此外，我们扩展了作者先前关于安德鲁斯q -Lauricella函数的二元扩展的先前工作，并展示了如何获得这种类型的非常通用的转换公式。获得的结果包括将n倍和转换为m倍和。