Example 33.  The conformal mapping   .
It can be constructed via the Schwarz-Christoffel integral  ,  
also  .  
The image of the upper half-plane    is the upper half-plane together with the semi-infinite strip -1<u<1, v<0.
Remark. This is Exercise 4 (Extra Example 2) in Section 11.9 and Example 11.34 in Section 11.11, and is illustrated in Figure 11.78. and Figure 11.98.
Hint: Set    and  , where  ,  ,    and   ,  ,  ,  and the angles are  .

Details 33.

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