In this paper, we consider the monodromy and, in particular, the isomonodromy sets of accessory parameters for the Heun class equations. We show that the Heun class equations can be obtained as limits of the linear systems associated with the Painlevé equations when the Painlevé transcendents go to one of the actual singular points of the linear systems. The isomonodromy sets of accessory parameters for the Heun class equations are described by Taylor or Laurent coefficients of the corresponding Painlevé functions, or the associated tau functions, at the positions of the critical values. As an application of these results, we derive some asymptotic approximations for the isomonodromy sets of accessory parameters in the Heun class equations, including the confluent Heun equation, the doubly‐confluent Heun equation, and the reduced biconfluent Heun equation.

中文翻译：

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Heun类方程的辅助参数的等单集

在本文中，我们考虑了Heun类方程的辅助参数的单调性，尤其是等调性。我们表明，当Painlevé先验者到达线性系统的实际奇异点之一时，Heun类方程式可以作为与Painlevé方程相关联的线性系统的极限而获得。Heun类方程式的辅助参数的等单论集在临界值的位置通过相应的Painlevé函数或关联的tau函数的Taylor或Laurent系数来描述。作为这些结果的应用，我们导出了Heun类方程组中辅助参数的等单集的渐近近似，包括合流Heun方程，双合流Heun方程，