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Will anybody please tell me what is the statement of the "Uniqueness theorem" in Complex analysis??

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- Thread starter matheater
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- #1

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Will anybody please tell me what is the statement of the "Uniqueness theorem" in Complex analysis??

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nicksauce

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I have the sum:

Let f:C-->C be analytic s.t f(1/n)=1/n^2,n=1,2,3........

Then(out of 4 ans i am giving the correct one)f(z)=z^2 for all z in C

The solution is done as follows:

Let g(z)=z^2 for all z in C.Then f(z)=g(z) for all z in {1/n :n=1,2,3.}.since {1/n :n=1,2,3.} is an infinite set having a limit point "0",so by "uniqueness theorem" f(z)=g(z) for all z in C.

Here i want to have the statement of this Uniqueness theorem...

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