Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook