  We compute the correlation functions of irregular Gaiotto states appearing in
the colliding limit of the Liouville theory by using "regularizing" conformal
transformations mapping the irregular (coherent) states to regular vertex
operators in the Liouville theory. The $N$-point correlation functions of the
irregular vertex operators of arbitrary ranks are expressed in terms of
$N$-point correlators of primary fields times the factor that involves
regularized higher-rank Schwarzians of the above conformal transformation. In
particular, in the case of three-point functions the general answer is
expressed in terms of DOZZ (Dorn-Otto-Zamolodchikov-Zamolodchikov) structure
constants times exponents of regularized higher-derivative Schwarzians. The
explicit examples of the regularization are given for the ranks one and two.
