Finding the Residue of f'/f at 0 with a Zero of Multiplicity k

[luke1001]

Homework Statement

Let f has a zero of multiplicity k at 0.

Find the residue of f'/f at 0

The Attempt at a Solution

I'm kind of get stuck on this one. I got only this far: Since f has a zero of multiplicity k at 0, then f(z) = (z^k)g(z) :(

Thanks a lot for helping!

 

[matt grime]

What is the definition of the residue at 0?

 

[luke1001]

What is the definition of the residue at 0?

hmm, do you mean f is analytic at 0?

 

[matt grime]

You're attempting to find the residue at zero. It would seem like a good starting point to write down the definition(s) of the residue at zero - if you don't know what to find you will never find it.