Removable singularity

In complex analysis, a removable singularity is a type of singularity of a function of a complex variable which may be removed by redefining the function value at that point.

A function f has a removable singularity at a point a if if there is a neighbourhood of a in which f is holomorphic except at a and the limit $\lim _{z\rightarrow a}f(z)$ exists. In this case, defining the value of f at a to be equal to this limit (which makes f continuous at a) gives a function holomorphic in the whole neighbourhood.

An isolated singularity may be either removable, a pole, or an essential singularity.

References

• Tom M. Apostol (1974). Mathematical Analysis, 2nd ed. Addison-Wesley, 458.