# Help! Laurent series

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• November 4th 2007, 10:50 AM
janfg67
Help! Laurent series
Hi everyone... I need help with a Laurent series. The problem is finding the finite Laurent series for (1 + z^2) / (z-2) for |z-2| > 2. I'm having trouble getting the algebraic manipulation of some form of: 1/(1 + g(z-2) ) or 1/(1 - g(z-2)). The finite part is also throwing me off. Thanks for any help you can give!
• November 5th 2007, 08:29 AM
ThePerfectHacker
Quote:

Originally Posted by janfg67
Hi everyone... I need help with a Laurent series. The problem is finding the finite Laurent series for (1 + z^2) / (z-2) for |z-2| > 2. I'm having trouble getting the algebraic manipulation of some form of: 1/(1 + g(z-2) ) or 1/(1 - g(z-2)). The finite part is also throwing me off. Thanks for any help you can give!

$\frac{z^2 + 1}{z-2} = \frac{(z^2 - 4)+5}{z-2} = \frac{(z-2)(z+2)}{z-2} + \frac{5}{z-2}$
So,
$(z+2) + 5(z-2)^{-1} = 5(z-2)^{-1} + 4 +(z-2)$