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Small problem, can anyone help?

  1. May 5, 2004 #1
    Just got this complex analysis problem that's bugging me. If b in U is an isolated essentially singular point for f(z) in U, what type of singularity can
    g(z) = 1/f(z) have? Is it just an essentially singular pt for g(z) as well, it's not a pole or removable singularity is it? Can anyone help me with this?
  2. jcsd
  3. May 6, 2004 #2


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    I believe you're right. Since U is an essential singularity, f(z) need not approach infinity, as z approaches U. So, if f(z) = w at U, then g(z) will not, in general, go to infinity or to zero. Of course, it's not clear that g(z) must even have a singular point at U, but it looks like it will.
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