# Order of Poles of a Complex Function with Trigonometric Functions

• Jul 30th 2006, 09:09 AM
Jippo
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?
• Jul 30th 2006, 09:37 AM
CaptainBlack
Quote:

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
• Jul 31st 2006, 12:40 AM
Jippo
Thanks very much Captain Black!