A generalization of Hodges's method of obtaining the gradient expansion is derived and then employed to determine the sixth-order term. The formula for it is as follows: T₆= (3{{^2) }^-413}45360{^{-13}13 ({{^2}) }^2+2575144{ ({{^2}) }^3}+24916{ ({) }^2 ({^4}) }+149918{ ({) }^2 ({{^2}) }^2}-130736{ ({) }^2 ({^2}{^2}) }+34318{ ({{}{^2}) }^2+834172 ({{^2}) ({) }^4}-16004952592{ ({) }^6}d^3r}}. For atomic densities, T₆ is divergent near the nucleus and at large distances.
Dave Murphy (Thu,) studied this question.