Re: Residue of a function

Quote:

Originally Posted by

**uhfwheh** I need to find the residue of f(z) = 1/(sin(z)) at z=Pi

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I had a similar exercise for z=Pi/2. I found the expansion of f(z) to be 1/z + z/6 + ...

then calculating the residue for a simple pole (?) i found that lim as z-->Pi/2 of (z - Pi/2)*(1/z + z/6 + ...) = 0

I find I get the same residue for z=Pi, but I think this is wrong

Since this is a simple pole, the residue can be calculated by . So in this case where we have

Re: Residue of a function

Quote:

Originally Posted by

**Prove It** Since this is a simple pole, the residue can be calculated by

. So in this case where

we have

thank you!!!

but wouldn't that also be the case if we want to find the residue at Pi/2? I'm slightly confused

Re: Residue of a function

Quote:

Originally Posted by

**uhfwheh** thank you!!!

but wouldn't that also be the case if we want to find the residue at Pi/2? I'm slightly confused

ah, never mind, you can't since cos(pi/2)=0

Re: Residue of a function

You wouldn't evaluate residue at because your function doesn't have a pole there...