How would you find and classify all the singularities of the function f(z) = cot (z)/z^4? Clearly the function is undefined at 0, so has a singularity at 0, but there surely must be more to this?
Follow Math Help Forum on Facebook and Google+
Now you have to find the order of the pole, if it's indeed one (it seems to be) that is to find n such that has a limit as z goes to 0.
what ?
= 0 ? so the singularity at z = 0 is a simple pole? is that correct to say? I'm uncertain as to why it is zcot(z) and not just cot(z)/z^4?
Originally Posted by Roxanne123456789 = 0 ? so the singularity at z = 0 is a simple pole? is that correct to say? I'm uncertain as to why it is zcot(z) and not just cot(z)/z^4? No. The previous poster is giving you a hint as to what the smallest integer value of is such that exists and is finite.
Also, your problem said to "find and classify all the singularities". Since this function has a singularity wherever sin(z) is 0.
View Tag Cloud