A generalization of the Christoffel–Schwartz formula

As a generalization of the well-known Christoffel–Schwartz formula, a formula is obtained for mapping the interior of the unit disk onto a domain whose boundary consists of $n$ arcs of curves, each of which, under the choice of some branch of the transformation $\zeta=w^m$, $m>0$, passes through a rectilinear segment of the $\zeta$-plane. It is shown that the class $B_m$ of Bazilevich functions coincides with the class $\overline L_m$ of functions representable by means of the obtained formula of the special type.