Find the poles of f(z)=11+zwf(z)=\frac 1{1+z^w} for w>1w \gt 1

I am trying to use contour integration on the following integrand between 0 and , however I am not sure how to go about finding the poles for it:


Consider the denominator equal to zero:




How would I go about determining the types of poles we would have for f(z) given the many different forms it could take dependent on w?


so w is a natural number greater than 1. So all you need is to solve zw=1, that is to say, all the w-roots of 1.

These are unique and there are exactly w of them, so your function will have poles of order 1 at the w roots of 1. They all lie on the unit circle.

Source : Link , Question Author : Jeremy Jeffrey James , Answer Author : Ant

Leave a Comment