Complex Analysis problem

  • #1

Homework Statement

Let f and g be two holomorphic functions in a connected open set D of the plane which have no zeros in D; if there is a sequence an of points such that lim an = a and an does not equal a for all n, and if

f'(an)/f(an)=g'(an)/g(an)

show that there is a constant c such that f=cg in D.

Homework Equations

If f is identically zero at a point in a connected open set, then f is identically zero on the whole set.


The Attempt at a Solution

I have shown that (f/g)'(a) = 0, but I don't see how that would imply that the derivative is identically zero at that point.
 
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Answers and Replies

  • #2
HallsofIvy
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I don't know what you mean by "identically 0 at a point"! "Identically" zero means zero at every point of some set. Are you sure you have quoted your "relevant equation" correctly?
 
  • #3
I don't know what you mean by "identically 0 at a point"! "Identically" zero means zero at every point of some set. Are you sure you have quoted your "relevant equation" correctly?

Ah, sorry. What I mean is that the derivatives of f of every order are 0 at that point, so that f is equal to the zero function at that point. I may be abusing the term.
 

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