Someone me with this Laurent Expansion

[Jonnnnn]

Homework Statement

the Laurent expansion of f(z)=e^1/sin(z) at the isolated singularity z=π

Homework Equations

The Attempt at a Solution

I tried rewriting 1/sin(z) into exponential form, but it seems have no help for the expansion. Would someone give me some inspirations?

 

[RUber]

Can you remove the singularity?

 

[Jonnnnn]

Can you remove the singularity?

Actually, the singularity here is an essential singularity, which is not removable I think.

 

[RUber]

I found a similar problem explained at http://math.stackexchange.com/questions/120282/residue-of-z2-e1-sin-z-at-z-pi/120450#120450
I think there maybe some pieces of that expansion that you could use.

 

[Jonnnnn]

I found a similar problem explained at http://math.stackexchange.com/questions/120282/residue-of-z2-e1-sin-z-at-z-pi/120450#120450
I think there maybe some pieces of that expansion that you could use.

Thank you very much RUber! That's exactly what I'm dealing with.