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Complex Series converfence proof

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose we already know series [tex]u(z) = \displaystyle\sum_{n=0}^\infty u_n(z)[/tex]is uniformly convergent in the entire complex plain and we can perform term by term integration and differentation each term [tex]u_n(z)[/tex] in the analyitic function. use cauchy-riemann equations to show that the sum of u(z) is analytic in the entire complex plain.


    2. Relevant equations
    [tex]$\displaystyle \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y},\quad
    \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x},$[/tex]


    3. The attempt at a solution
    My only guess at a solution would be to use the CR equations for each term in the sequence. ??
     
  2. jcsd
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