Recently, the stretched exponential decay of multiple correlations in a periodic Lorentz gas has been used to show the convergence of a series of correlations which has a physical interpretation as the fourth-order Burnett coefficient, a generalization of the diffusion coefficient. Here the result is extended to include all higher-order Burnett coefficients and a plausible argument is given that the expansion constructed from the Burnett coefficients has a finite radius of convergence.