In this paper we introduce analytical solutions of interband polarization, which is the selfenergy of the Dyson equation for the Photon Green's functions and apply them to study photoluminescence of Coulomb correlated semiconductor materials. The accuracy of the easily programmable solutions is proven by consistently explaining the low temperature s-shape of the luminescence peak of dilute bismide semiconductors. The different roles of homogeneous versus inhomogeneous broadening at low and high temperatures are described, as well as the relevance of many body effects, which are in very good agreement with experiments.