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Complex Analysis- Singularities

  • #1
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Homework Statement


Let f be analytic at the complex plane excapt for z= -1 and z=3 which are simple poles of f.

Let [tex] \Sigma_{-\infty}^{-1} a_{n}(z-2)^{n} [/tex] be the Laurent series of f.
In part A I've found that the series converges at 1<|z-2|<3 .
B is: Find the coeefficients [tex] a_{n} [/tex] of the given Laurent series.
Hint: Look at [tex] g(z) = (z+1)(z-3)f(z) [/tex]


Homework Equations


The Attempt at a Solution


We know that g(z) has no poles or singularities whatsoever. So Laurent series of g is actually a Taylor series... But how can we find from this data the given coeefficients?

Thanks in advance
 

Answers and Replies

  • #2
vela
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Are you sure that's a correct Laurent series for f(z)? Doesn't it have an essential singularity at z=2?
 
  • #3
108
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I'm sure indeed...I had no typos in this one... But the an's can be also zero or something...
 

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