How do I find the residue of 1/(z^2 sinz) ? It seems to me that it has a 3rd order singularity at z=0, but I cant find the residue. Thanks for any help rendered.
Alternatively, you could find and use the first few terms of the Laurent series of (from which it immediately follows that the residue is equal to 1/6).
I tried using the formula but I got this equation eventually (attached along this reply). I could not eliminate the sinz at the denominatior, causing my ans to tend to inf as z tends to 0. Have I used the formula wrongly or is there another formula to get the residue?
Note that has a pole of order 1 at z = 0 since is finite (and is equal to 1). Furthermore, .
To get the value of b, substitute into and re-arrange:
Expand and equate coefficients:
Coefficient of z: a = 0.
Coefficient of : .