Conformal mapping of a strip onto a circular numerable polygon of strip type

We consider a simply connected domain of strip type with the symmetry of transfer. The boundary of the domain consists of circular arcs (circular numerable polygon). We write the Schwarz derivative of the mapping of a strip onto a circular numerable polygon in terms of elliptic functions. We obtain a generalization of the Schwarz–Christoffel formula for mapping of a strip onto a numerable polygon with the boundary consisting of straight line segments. One special case of a numerable polygon with additional symmetry with respect to a vertical line is considered.