The dynamics of luminescence decay is analyzed within the general scenario of randomly distributed ions with whatever multipole interaction, taking into account energy transfer and migration processes among them. By applying Pade approximants to the Allinger and Blumen expression for the excited state population, a simple expression has been obtained which can be easily fitted to experimental data. This expression can be considered a generalization of the dipole-dipole Yokota-Tanimoto equation. On the other hand, the decay curves from the D-5(3) level of the Tb3+ ions in fluorozincate glasses have been measured for different Tb3+ concentrations. The results are analyzed in the framework of the proposed expression.