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Nature of singularity

  1. Aug 6, 2015 #1
    what is the nature of singularity of the function f(x)=exp(-1/z) where z is a complex number?
    now i arrive at two different results by progressing in two different ways.
    1) if we expand the series f(z)=1-1/z+1/2!(z^2)-... then i can say that z=0 is an essential singularity.
    2) now again if i take the limit of the function from either sides of zero, i see it exists finitely, therefore not a singular point at all.
  2. jcsd
  3. Aug 6, 2015 #2
    It is an essential singularity.

    Can you expand on this? Don't forget that ##z## is a complex number, so just taking the two sided limits in ##\mathbb{R}## is not good enough.
  4. Aug 6, 2015 #3


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    For Real z < 0, the limit as z ->0 is infinite.
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