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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.
References:
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[5] Филъчаков П. Ф.: Приближенные методы конформных отображений. Киев 1964, стр. 235. Zbl 1117.65300
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[7] Говорков В. А.: Электрические и магнитные поля. Москва 1960, стр. 243. Zbl 1004.90500
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