The work is devoted to obtaining explicit formulas for analytic continuation of quite general hypergeometric series depending on three variables and belonging to the Horn class. We have derived such continuation formulas with respect to one variable for an arbitrary series belonging to the class under consideration. In addition, on the base of several examples we have demonstrated the use of the obtained formulas for construction of analytic continuation with respect to all three variables. The obtained continuation formulas give representations for a triple hypergeometric series outside the domain of its convergence in the form of a combination of other hypergeometric series that also belong to the Horn class. These series satisfy to the same system of partial differential equations as the initial series. The results of the paper are useful for qualitative analysis and calculation of triple hypergeometric functions.

这项工作致力于获得明确的公式，以根据三个变量并属于Horn类，对相当普通的超几何级数进行解析延续。我们已经针对属于所考虑类别的任意系列的一个变量推导了这样的连续公式。此外，在几个示例的基础上，我们已经证明了使用所获得的公式来构造关于所有三个变量的解析连续性。所获得的连续公式以其收敛域之外的三重超几何级数表示形式，也以其他也属于Horn类的超几何级数组合的形式给出。这些级数满足与初始级数相同的偏微分方程组。