Abstract

The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions satisfy linear second order differential equations with one more singularity. In this paper we compare these equations with linear differential equations isomonodromy deformations of which are described by the Painlevé equations \(P_{II}-P_{VI}\).

中文翻译：

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关于亨氏函数的导数

摘要

Heun函数满足复平面中具有某些奇点的二阶线性常微分方程。Heun函数的一阶导数满足具有一个奇点的线性二阶微分方程。在本文中，我们将这些方程与线性微分方程的等单变形进行了比较，这些变形由Painlevé方程\（P_ {II} -P_ {VI} \）描述。