# Thread: Order of Poles of a Complex Function with Trigonometric Functions

1. ## Order of Poles of a Complex Function with Trigonometric Functions

This really should be simple but it's not quite getting through my thick skull!!

Given that the function 1/z^2 had a pole z_0=0 of order 2, does the function 1/(z^2 Sin[z]), with a particular pole at z_0=0, have order 2 or 3?

2. Originally Posted by Jippo
This really should be simple but it's not quite getting through my thick skull!!

Given that the function 1/z^2 had a pole z_0=0 of order 2, does the function 1/(z^2 Sin[z]), with a particular pole at z_0=0, have order 2 or 3?
As $\sin(z) \sim z$ near $z=0$ the pole is of order 3.

RonL

3. Thanks very much Captain Black!