How to get the residue of this funciton at z=i

[justin_huang]

Homework Statement

f(z)=cot(pi*z)/(z^2+1)

Homework Equations

The Attempt at a Solution

now I want to get the residue at z=i, I know the definition of f(z)'s residue form
but when I try to get the expansion of cot(pi*z) at z=i, I used a lot of method
like use sin*csc this form but due to the reason I cannot get the expansion of csc(A+B)
i CANNOT get the result

Could you tell me the formula of csc(A+B) or other more easier method to figure this problem? thanks

 

[SteamKing]

cot = cotangent = cos / sin. I don't know why you are using csc = cosecant = 1 / sin

 

[justin_huang]

cot = cotangent = cos / sin. I don't know why you are using csc = cosecant = 1 / sin

cause i need to get the multiplication of two polynomial not division

 

[Dick]

cause i need to get the multiplication of two polynomial not division

You don't have to expand cot(pi*z) at z=i. cot(pi*z) is analytic at z=i, it has a perfectly well defined limit there. The singularity is only in the denominator.

 

[justin_huang]

You don't have to expand cot(pi*z) at z=i. cot(pi*z) is analytic at z=i, it has a perfectly well defined limit there. The singularity is only in the denominator.

I got it... thanks so much