  The velocity distribution of a granular gas is analyzed in terms of the
Sonine polynomials expansion. We derive an analytical expression for the third
Sonine coefficient a_3. In contrast to frequently used assumptions this
coefficient is of the same order of magnitude as the second Sonine coefficient
a_2. For small inelasticity the theoretical result is in good agreement with
numerical simulations. The next-order Sonine coefficients a_4, a_5 and a_6 are
determined numerically. While these coefficients are negligible for small
dissipation, their magnitude grows rapidly with increasing inelasticity for 0<
epsilon < 0.6. We conclude that this behavior of the Sonine coefficients
manifests the break down of the Sonine polynomial expansion caused by the
increasing impact of the overpopulated high-energy tail of the distribution
function.
