Chapter 14.11, Problem 12MP

Let $f(z)$ be the branch of $\sqrt{z^2-1}$ which is positive for large positive real values of z. Expand the square root in powers of $1/z$ to obtain the Laurent series of $f(z)$ about $\infty .$ Thus by Problem 8.1 find the residue of $f(z)$ at $\infty .$ Check your result by using equation (8.2).