  The recently proposed expression for the general three point function of
exponential fields in quantum Liouville theory on the sphere is considered. By
exploiting locality or crossing symmetry in the case of those four-point
functions, which may be expressed in terms of hypergeometric functions, a set
of functional equations is found for the general three point function. It is
shown that the expression proposed by the Zamolodchikovs solves these
functional equations and that under certain assumptions the solution is unique.
