Coulomb integrals in Liouville theory and Liouville gravity

We study four-point correlation function in Liouville field theory. If one of the fields is degenerate, such a function is described in terms of Coulomb integrals. We find some non-trivial relations on these integrals, which can be used to obtain new exact results in conformal field theory. In particular, we calculate four-point correlation function in minimal quantum gravity. The result agrees with the results obtained recently by different methods [1, 2].