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

[MMS]

Hi guys,

Is it right to say that a simple pole (pole of order 1) is a removable singularity (and vice versa)?

 

[lavinia]

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.

 

[MMS]

I realized it as soon as I posted this thread and forgot to delete it.

Anyway, thank you!