Example 11.26.  Use the Schwarz-Christoffel formula to verify that    maps the upper half plane    onto the semi infinite strip    shown in Figure 11.72.

Figure 11.72  The region with and .

Explore Solution 11.26.

Enter the formula and integrate it to construct  f(z).

Remark.   No matter how tempting the integrand    may seem, the logarithm does not have the proper branch cut for this problem, and we must use the familiar integrand  .  Switching the order of terms in the square root will solve this problem.

Now solve for the coefficients  A  and  B.

Use Mathematica to graph conformal mapping  w = f(z).

We see that  w = Arcsin(z)  maps the upper half plane    onto the semi infinite strip  .

(c) 2006 John H. Mathews, Russell W. Howell