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Math Help - Uniform Convergence

  1. #1
    Junior Member
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    Uniform Convergence

    I need some help in proving the following lemma

    Lemma . if  f_j are holomorphic functions on  U and  f_j \rightarrow uniformly on compact subsets of  U , then any derivatives
     (\frac{\partial}{\partial z_1})^l (\frac{\partial}{\partial z_2})^k f_j
    converges to
     (\frac{\partial}{\partial z_1})^l (\frac{\partial}{\partial z_2})^k f
    Uniformly on compacts sets.

    Proof:
    i tried to fix  P \in U and choose  r > 0 such that  \overline{D}^2(P,r) \subseteq U. i have some problem expressing  f_j on D^2(P,r) as a Cauchy integral of  f_j on  \partial D^2(P,r) and differentiating it under integral sign.
    I need some help please
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  2. #2
    Junior Member
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    Re: Uniform Convergence

    i need some help guys...please help me!
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  3. #3
    Super Member girdav's Avatar
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    Re: Uniform Convergence

    What are z_1 and z_2?
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