If a complex function
has an isolated singularity
at a point a
and the Laurent series
expansion about a
involves no negative powers of (z
), then the singularity is referred to as "removable". Such a singularity is literally removable
in the sense that simply assigning an appropriate value to the function at the singularity
would make it analytic
at that point. For example, the function which is equal to 1 at the origin and zero everywhere else has a removable singularity at the origin. Obviously, assigning zero to this function at the origin makes it analytic
there; in general, the correct value to assign is the limit
of the function as it approaches the singularity.
A removable singularity can also be defined as a singularity about which the function is bounded.