let $\displaystyle D\subset \mathbb{C}$ be open, let $\displaystyle f\to\mathbb{C}$ be holomorphic, and let $\displaystyle z_0 \epsilon \mathbb{C}`D$ be a zero of order one of $\displaystyle f$. Show that

res$\displaystyle (\frac{1}{f};z_0)=\frac{1}{f'(z_0)}$

let $\displaystyle D\subset \mathbb{C}$ be open, let $\displaystyle f\to\mathbb{C}$ be holomorphic, and let $\displaystyle z_0 \epsilon \mathbb{C}`D$ be a simple pole for$\displaystyle f$. Show that

$\displaystyle res(gf;z_0)=g(z_0)res(f;z_0)$

for every holomorphic function $\displaystyle g\cup z_0 \to \mathbb{C}$

any tips?

found it online

http://books.google.ca/books?id=WZX4...sult#PPA175,M1

don't know if that link works since it's rather convoluted, Complex analysis by serge lang page 175

in case anyone else wanted to know this