- #1
daoshay
- 14
- 0
Homework Statement
Classify the isolated singularities and find the residues
[tex]
\frac {\sin(\frac {1}{z})}{1-z}
[/tex]
Homework 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?
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.