When a complex function f
has an isolated singularity
at a point a
which is neither a pole
nor a removable singularity
, it is said to have an essential singularity
. This is equivalent to saying that the Laurent series
ly many terms involving negative power
s of (z
), so that f
fails to be differentiable
for all n
An example of a function with an essential singularity is e1/z, which has an essential singularity at the origin.
Essential singularities are occasionally referred to as "irregular singularities".