Solution of the Kinetic Equation Taking into Account Resonance in the Compton Process in a Magnetized Medium

The solution of the kinetic equation for finding the distribution function of photons of two possible polarizations in an equilibrium nonrelativistic e^ + e^ - plasma in a relatively strong magnetic field is considered taking into account resonance on a virtual electron. Using the Laplace transform and the expansion of the distribution function in Legendre polynomials, the problem is reduced to a system of differential equations for the coefficients of this expansion. The solution is presented as an integral in the complex plane.