  We rewrite Arthur's asymptotic formula for weighted orbital integrals on real
groups with the aid of a residue calculus and extend the resulting formula to
the Schwartz space. Then we extract the available information about the
coefficients in the decomposition of the Fourier transforms of Arthur's
invariant distributions I_M(\gamma) in terms of standard solutions of the
pertinent holonomic system of differential equations. This allows us to
determine some of those coefficients explicitly. Finally, we prove descent
formulas for those differential equations, for their standard solutions and for
the aforementioned coefficients, which reduce each of them to the case that
\gamma is elliptic in M.
