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

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Homework Help Overview

The problem involves finding the residue of the function f'/f at the point 0, given that f has a zero of multiplicity k at that point. The subject area relates to complex analysis and the properties of residues in relation to analytic functions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the definition of the residue at zero and its implications for the problem. There is an attempt to express the function f in terms of its zero at 0, leading to questions about the analytic nature of f at that point.

Discussion Status

The discussion is ongoing, with participants seeking clarification on definitions and exploring the implications of the zero of multiplicity k. Some guidance has been offered regarding the importance of understanding the definition of the residue before proceeding.

Contextual Notes

There is a focus on the analytic properties of the function f at 0, and the implications of its zero of multiplicity k are under consideration. Participants are navigating the definitions and concepts necessary to approach the problem effectively.

luke1001
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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!
 
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What is the definition of the residue at 0?
 
matt grime said:
What is the definition of the residue at 0?

hmm, do you mean f is analytic at 0?
 
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.
 

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