Question

Which is the concrete formula for the conformal mapping (normalized at infinity), acting from $\mathbb C \backslash D^*$ onto

$\mathbb C\backslash[-1, 1]$?

Here $\mathbb C$ denotes the set of all complex numbers and $D^*$ denotes the closed unit disk of the complex plane.

Also, I would be interested in references containing many examples of such of conformal mappings, by replacing the interval $[-1, 1]$ with other various subsets of the complex plane.

Thanks a lot.

Answer 1

Finally I found that the conformal mapping is given by the formula f(z)=(1/2)(z + 1/z). Thanks any whay.