  Two-dimensional sl(n) quantum Toda field theory on a sphere is considered.
This theory provides an important example of conformal field theory with higher
spin symmetry. We derive the three-point correlation functions of the
exponential fields if one of the three fields has a special form. In this case
it is possible to write down and solve explicitly the differential equation for
the four-point correlation function if the fourth field is completely
degenerate. We give also expressions for the three-point correlation functions
in the cases, when they can be expressed in terms of known functions. The
semiclassical and minisuperspace approaches in the conformal Toda field theory
are studied and the results coming from these approaches are compared with the
proposed analytical expression for the three-point correlation function. We
show, that in the framework of semiclassical and minisuperspace approaches
general three-point correlation function can be reduced to the
finite-dimensional integral.
