Removable Singularity: Is it the Same as a Simple Pole?

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SUMMARY

A simple pole, defined as a pole of order 1, is not equivalent to a removable singularity. The integral of 1/z over the unit circle serves as a definitive example illustrating that a simple pole cannot be removed. This distinction is crucial in complex analysis, as it affects the behavior of functions near singular points.

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MMS
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Hi guys,

Is it right to say that a simple pole (pole of order 1) is a removable singularity (and vice versa)?
 
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MMS said:
Hi guys,

Is it right to say that a simple pole (pole of order 1) is a removable singularity (and vice versa)?
No. A pole of order 1 is not removable. Think about the integral of 1/z on the unit circle.
 
I realized it as soon as I posted this thread and forgot to delete it.

Anyway, thank you!
 

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