ABSTRACT We construct formulas for analytic continuation of the Lauricella functions , and into the exterior of the domains, where they are initially defined by N-multiple hypergeometric series. To construct the analytic continuation, we use a new method, which allows to obtain continuation formulas for arbitrary hypergeometric series belonging to Horn's class, which, in particular, contains Lauricella's functions. The obtained formulas give effective apparatus for qualitative analysis and computation of these functions. Thus the results of the paper useful for numerous applications, where Lauricella's functions appear.

中文翻译：

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Lauricella 函数的解析延拓，以及

摘要我们构建了月桂树函数的解析延拓公式，并进入域的外部，它们最初由 N 多重超几何级数定义。为了构造解析延拓，我们使用了一种新方法，该方法允许获得属于 Horn 类的任意超几何级数的延拓公式，该类尤其包含 Lauricella 的函数。得到的公式为这些函数的定性分析和计算提供了有效的工具。因此，该论文的结果可用于出现 Lauricella 函数的众多应用。