New Solutions Generating Technique to Generalized Kompaneets Equation and the Corresponding Heun Functions

摘要

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.