Example 31.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
also  .
The image of the upper half-plane    is the portion of the first quadrant    that lies below the region where  ,
the right angle channel in the first quadrant, which is bounded by the coordinate axes and the rays  .
Remark. This is Example 11.28 in Section 11.9 and Exercise 9 (Extra Example 3) in Section 11.1, and is illustrated in Figure 11.74 and Figure 11.107.  
Hint: Set ,  ,  ,  ,  and  ,  ,  ,  ,  
and the angles are .

Details 31.

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