In the present paper, we are developing an analytical method for solving the time-dependent Kompaneets equation in its generalized form. The technique is generalizing the Dubinov and Kitayev method. In the particular case of a low photon number density, for the corresponding linear equation, the solutions are expressed in terms of Heun functions.

中文翻译：

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广义 Kompaneets 方程及其对应 Heun 函数的新解生成技术

在本文中，我们正在开发一种解析方法，用于求解广义形式的瞬态 Kompaneets 方程。该技术是对 Dubinov 和 Kitayev 方法的推广。在低光子数密度的特殊情况下，对于相应的线性方程，解用 Heun 函数表示。