Cyclotron resonance lineshape function obtained by using a combined projection operator technique in the continued fraction representation

We review the formula for the linear-nonlinear response by using combined p rojection operators. We also review the continued fraction representation w hich is free from the danger of divergence which exists in the usual series expansion of scattering factors. In this paper, we calculate the lowest or der scattering factor (the cyclotron resonance lineshape function) of the c ontinued fraction representation in the linear response scheme of an electr on-phonon interacting system, and we compare the result with those derived from some other theories.