Example 32.  The conformal mapping   .
It can be constructed via the Schwarz-Christoffel integral  ,  
also  .  
The image of the upper half-plane    is the region in the -plane bounded by the negative  -axis,  the segment ,  and the ray  .  
Remark. This is Exercise 3 (Extra Example 1) in Section 11.9 and Example 11.29 in  Section 11.10, and is illustrated in Figure 11.77 and Figure 11.87.
Hint: Set    and   ,  and the angles are .

Details 32.

Under Construction

Return to the Complex Analysis Project