Math Help Forum - View Single Post

Random Variable · #3 June 4th, 2009, 04:21 PM

You could try the following:

$Res[h,z_{0}] = \lim_{z \to z_{0}} \frac {d}{dz} (z-z_{0})^{2} h(z)$

$= \lim_{z \to z_{0}} \frac {d}{dz} (z-z_{0})^{2} \frac {1}{f(z)}$

then using the product rule

$= \lim_{z \to z_{0}} \Big(2(z-z_{0}) \frac {1}{f(z)} + (z-z_{0})^{2} \frac {-1}{[f(z)]^2} f'(z) \Big)$

And then since the forms of both terms are indeterminate, apply L'Hospital's rule. But multiple applications will be required.