Singularities Complex Analysis

[Darth Frodo]

Homework Statement

Determine the location and type of singularity of f(z) = 1/sin^2(z)

Homework Equations

The Attempt at a Solution

I'm not really sure how to calculate this. At this point, we don't have explicit formulae for the coefficients of a Laurent series so I really don't know what to do. Taylor series?

Any help would be much appreciated. Thanks.

 

[Dick]

Homework Statement

Determine the location and type of singularity of f(z) = 1/sin^2(z)

Homework Equations

The Attempt at a Solution

I'm not really sure how to calculate this. At this point, we don't have explicit formulae for the coefficients of a Laurent series so I really don't know what to do. Taylor series?

Any help would be much appreciated. Thanks.

You could just use the definition. A function 1/f(z) has a singularity at z=a if f(a)=0. If (z-a)^n/f(z-a) has a finite limit as z->a then then the singularity is order n. Where does sin^(z)=0 and what power n do you need?