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**-

**a**), 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.