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Help for essential singularity problem

  1. May 5, 2004 #1
    Hello, can anyone help me out here?
    If you have a function f(z) in U, and b in U, such that b is an isolated essentially singular point for f(z) in U, what type of singularity can
    g(z) = 1/f(z) have?
     
  2. jcsd
  3. May 5, 2004 #2

    HallsofIvy

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    Try thinking about it the other way around. Suppose f(z) is analytic at q but f(q)= 0. What kind of singularity can 1/f(z) have at q?

    Suppose f(z) has a pole at q. What kind of singularity can 1/f(z) have at q?
     
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