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**chisigma** If f(z) has only 'simple poles' $\displaystyle \alpha_{1}, \alpha_{2}, ..., \alpha_{n}$ , then is...

$\displaystyle \displaystyle f(z)= \sum_{n=1}^{n} \frac{r_{n}}{z-\alpha_{n}}$ (1)

... where...

$\displaystyle \displaystyle r_{n}= \lim_{z \rightarrow \alpha_{n}} f(z)\ (z-\alpha_{n})$ (2)

Now it is evident that the limits (2) are 'ideterminate forms' of the type $\displaystyle \frac{0}{0}$ so that they can be solved using l'Hopital's rule...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$