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January 17th, 2010, 11:34 AM   #1
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bounded domain, meromorphic functions

Let be a bounded domain, and let and be meromorphic functions on that extend to be analytic on . Suppose that on . Show by example that and can have different numbers of zeros on . What can be said about and ? Prove your assertion.

I do not see what example I can use here. I think what we can say is that they have the same number of zeros minus poles. I just don't see an example here. Thanks.
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