Thread: Finding and classifying singularities

I thought I had a grasp on this topic, but then they threw in this question:

Find and classify the singularities of
π cot(πz )
Z^2

With the use of cot I'm confused which techniques to use because I know what to use if it's sin(z) or cos(z) but not cos(z)/sin(z)

Any help insight or tricks would be greatly appreciated.

Hello,

Originally Posted by shadowdom

I thought I had a grasp on this topic, but then they threw in this question:

Find and classify the singularities of
π cot(πz )
Z^2

With the use of cot I'm confused which techniques to use because I know what to use if it's sin(z) or cos(z) but not cos(z)/sin(z)

Any help insight or tricks would be greatly appreciated.

But you don't have to worry oO

If you're not used to the cot function, you can substitute by cos/sin.
Singularities appear at points where the function is not defined, and whether it's cot or cos/sin, they're the same.


0 is obviously a singularity (not necessarily a pole because of sin(pi z))


So here, there are also singularities for any (the set of integers)

Cheers that does help, but how would I continue to classify each point?