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:
f(z)=11+zw,w∈Z:w>1
Consider the denominator equal to zero:
1+zw=0
⇒zw=−1
⇒z=−11w≡w√z
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?
Answer
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.
Attribution
Source : Link , Question Author : Jeremy Jeffrey James , Answer Author : Ant
