Question

Find the Laurent’s series representation of ?(?) =
1/?(?−1) valid for |?| > 1. What conclusion can you draw based on the number of terms contained in the principal part of it?

Answer 1

Let us simplify .

Since , i.e., , we can expand the above expression in the form of

By canceling term , we get

The number of terms in principal part is nothing but the number of terms in powers of . Here, we can see that an infinite number of negative power terms of z. Hence we conclude that has an essential singularity at .