Conformal mapping of the halfplane onto a strip with variable width

summary:By using Schwarz-Christoffel theorem the author deduces the conformal mapping of a halfplane onto an infinitely long strip whose one boundary id a straight line while the other one is a polygonal line consisting of two half lines parallel to the first boundary and connected by a segment whose slope angle is a fractional multiple of $\pi$. This mapping is expressed by means of elementary functions distinguishing the cases when $\pi$ is divided by odd or even integer; some important properties of this mapping are shown