A
complex function f is said to have an
isolated singularity at a
point z if it fails to be
analytic at
z, but there exists
a
neighbourhood of
z on which
f is
analytic everywhere but
z. (In other words,
f is analytic on some punctured disk centred at
z, but not at
z.) For example, the function 1 / (z
2+4) has isolated singularities at 2
i and -2
i.
Isolated singularities are further classified as removable singularities, poles or essential singularities.