(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the residue of sinz/z^4

2. Relevant equations

The residue for a pole of order m at 0 is given my:

lim z->0 [1/(m-1)!d^{m-1}/dz^{m-1}[(z^{m}f(z)]]

3. The attempt at a solution

Clearly the pole has order 3:

So we get:

Re(0) = limz->0[1/2d^{2}/dz^{2}[sinz/z]]

I get that the only term in the limit that doesn't go to zero is:

Re(0) = limz->0[-1/2sinz/z] = -1/2

But I should get -1/3!

Apparantly something goes wrong somewhere as I should get a tree from differentiation. Can anyone see where that is? :S

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# Homework Help: Find residue of sinz/z^4

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