Univalent conformal mappings by generalized Christoffel–Schwartz integral onto polygonal domains with countable set of vertices

We obtain a formula for the conformal mapping of the upper half-plane onto a polygonal domain. This structural formula generalizes the Schwartz–Christoffel equation and is written with the use of partial solution to the Hilbert boundary-value problem with a countable set of points of discontinuity of the coefficients and with turbulence at infinity of logarithmic type. We also prove closedness and existence of univalent mappings among given ones.