Analytic representations of the dielectric function epsilon are needed for the analysis of optical data of complex materials and structures. Here, we examine various harmonic-oscillator-based representations of the dielectric functions of the silicon-related materials, crystalline Si, amorphous Si, and silicon nitride. For crystalline semiconductors we develop a new representation with a prefactor proportional to omega(-2), the expected response for materials with wavefunctions that are eigenfunctions of the momentum operator.