  We study the Toda field theory with finite Lie algebras using an extension of
the Goulian-Li technique. In this way, we show that, after integrating over the
zero mode in the correlation functions of the exponential fields, the resulting
correlation function resembles that of a free theory. Furthermore, it is shown
that for some ratios of the charges of the exponential fields the four-point
correlation functions which contain a degenerate field satisfy the Riemann
ordinary differential equation. Using this fact and the crossing symmetry, we
derive a set of functional equations for the structure constants of the A_2
Toda field theory.
