I am very confused about how to actually compute a Laurent series. Given an analytic function, we can write down its poles. Then, if I understand correctly, we have to write a Laurent series for each pole. What I'm confused about is the actual mechanics of writing one down. I know that for f(z) with pole at f(z0) that we can write(adsbygoogle = window.adsbygoogle || []).push({});

f(z) = (a_p)/(z-z0)^p + ...+ a_1/(z-z0) + a0 + a1(z-z0) + ...

what I don't understand is how to get the a[tex]^{n}[/tex] coefficients. I know we have the formula a[tex]_{n}[/tex] = (1/2*[tex]\pi[/tex]*i) * [tex]\oint[/tex][tex]\frac{f(z)}{(z-z0)^{n+1}}[/tex] dz, but all the examples I have just pop out the series (no one is doing any integrals). I must be missing something obvious!!

If I can put it into the form f(z) = 1/(1+z) then I can use a geometric series to write this out...

but what if it's something like 1/z?

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# Confused about computing Laurent series

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