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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.
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