Identifying Pole Order to the Test for Pole Procedure

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SUMMARY

The discussion centers on identifying the pole order for a function in the context of a test for pole procedure. It is established that the pole at z=7 is of order 3, correcting a previous assumption of order 7, which was identified as a typographical error. The definition of a pole of order n at z=z0 is clarified, stating that (z-z0)nf(z) must have a non-zero limit as z approaches z0, which aligns with the findings presented.

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Homework Statement



Test for pole procedure.
As attached powerpoint.
Pse advise.

Homework Equations





The Attempt at a Solution

 

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Basically, what you have is right- although you should "suspect" that the pole at z= 7 is of order 3, not 7. I suspect that was a typo! A function, f(z) has "a pole of order n at z= z0" if and only if (z- z0)nf(z) has a non-zero limit as z goes to z0 and that is exactly what you have shown.
 

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