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

Classify the isolated singularities and find the residues

[tex]

\frac {\sin(\frac {1}{z})}{1-z}

[/tex]

2. Relevant equations

I know the Taylor series expansion for 1/(1-z) when |z|<1

and I think I know the Taylor series for sin(1/z). The reciprocal of each term of the Taylor series of sin(z), right?

3. The attempt at a solution

znot = 0 is an essential singularity and znot = 1 is a simple pole.

I've tried using the limit approach to find the singularity at znot = 1, but I keep getting -sin(1) as an answer. I am thinking I should change sin(1/z) into (e^iz - e^-iz) / 2i,but I'm not sure if that is the right direction. If someone could just nudge me in the right direction, I'd be pumped.

P.S. I gave up on latex for now, it was driving me nuts...I'm learning from looking at other people's code. It kept throwing in a sin function into an expression I never coded a sin in. I have some learning to do.

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# Residues of an essential singularity and a simple pole

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