Hey guys
Im having a panic as i should be revising, but instead im stuck on a question from my coursework, can anyone help
Find and classify the singularities of
(pi*cot(pi*x))/x^2
thanks
cot=cos/sin
For any , there is a singularity, because thereafter,
Now I believe there is a triple pole for 0, and simple pole (not too sure) for any integer in
you can check it by finding the Laurent series near these points.
For any , there is a singularity, because thereafter,
Now I believe there is a triple pole for 0, and simple pole (not too sure) for any integer in
you can check it by finding the Laurent series near these points.
The smallest value of such that is so is a pole of order 3.
The smallest value of such that is so is a simple pole (the more PC expression is pole of order 1).
Last edited by mr fantastic; Jan 5th 2009 at 12:14 AM.
Reason: Typos fixed from rushed cut and paste