Stieltjes transform for a distribution $F(x)$ is defined as
$m(z)=\int \frac{dF(x)}{x−z}$ where z is complex with positive imaginary parts and $F(x)$ is a distribution function.
Basically, I am stuck with evaluating Stieltjes transforms for given PDFs.
I referred to "Random matrix theory and wireless communications By Antonia M. Tulino, Sergio Verdú" and on page 37 http://bit.ly/qnf39U, they give an example
$S(z)=\frac{1}{2π}\int_{-2}^2 \frac{\sqrt{4−x^2}}{(x−z)}\;dx = \frac{1}{2}\left[−z\pm \sqrt{z^2−4}\right].$ I can't see how they came to this result. Any leads?