The theoretical analysis of the energy distribution function of electrons in weakly ionised gases is developed in a relatively high E/N by using the three-term approximation of the distribution function in the Boltzmann equation. The continuity equation of the electron swarm with an anisotropic distribution function is also derived. The present analysis is applied to the steady-state electron swarm in neon: the energy distribution functions and the swarm parameters are computed numerically over a range of E/N from 141.3 to 1130 Td. Also the distribution functions are solved from the usual two-term Lorentz approximation. The range of the validity of the Lorentz approximation is investigated by the comparison between both results.
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