The paper deals with the problem of convergence of special classes of branched continued fractions including the multidimensional A- and J-fractions with independent variables, which are generalizations of A-fractions (associated fractions) and J-fractions (Jakobi’s fractions), respectively. These branched continued fractions are used for the approximation of analytic functions of several complex variables. We have used a research method is to extend convergence, already known for a small domain, to a larger domain. As a result, we have established some new convergence criteria for the above mentioned branched continued fractions.

中文翻译：

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具有独立变量的多维A-和J-分形的收敛性

本文讨论了特殊类别的分支连续分数的收敛问题，包括具有独立变量的多维A-和J-分数，它们分别是A-分数（关联分数）和J-分数（雅各比分数）的推广。这些分支的连续分数用于近似几个复杂变量的解析函数。我们使用的一种研究方法是将已经为小领域而广为人知的融合扩展到更大的领域。结果，我们为上述分支连续分数建立了一些新的收敛准则。