Application of the mathematical Graf's addition theorem to the problem of electron energy absorption in laser-irradiated plasma

The electron energy absorption in laser-irradiated plasma is determined by the sum of the rates of photon absorption and emission. These rates contain the square of the Bessel functions. It was shown that in a moderate laser field, terms with absorption and emission of several photons are large, but cancel exactly each other. Therefore, we should take into account terms with the absorption and emission of only one laser photon. This statement is proved analytically using Graf's theorem for Bessel functions. (comment)