I am having some problems with residue problems in complex analysis, they seem to be fairly simple problems, so my understanding of the method to solve them must be wrong.(adsbygoogle = window.adsbygoogle || []).push({});

1. Calculate the residue at z=0 of the function:

[tex]f(z) = \frac{sinh(z)}{z^4(1-z^2)}[/tex]

I first Taylor expand sinh(z) to an adequate number of terms:

[tex] sinh(z) = z + \frac{z^3}{3!} + \frac{z^5}{5!} + \frac{z^7}{7!} +...[/tex]

now I divide the function through by z^4, I ignore the (1-z^2 component because at z=0 this is equal to 1. (This may be my bad assumption, but I don't see an alternative way to do the problem)

[tex] f(z) = z^{-3} + \frac{1}{6z} + \frac{z}{5!} + \frac{z^3}{7!} +...[/tex]

I pull out the 1/z component only and get an answer that the residue is 1/6, but the book gives me an answer 7/6, what am I forgetting?

~Lyuokdea

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# Homework Help: Calculating Residues

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