# Removable Singularity

### (Theory) ###### Theory ## What is Removable singularity?

In complex analysis, a removable singularity of a holomorphic function is a point at which the function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point. For instance, the (unnormalized) sinc function has a singularity at z = 0. This singularity can be removed by defining , which is the limit of as z tends to 0. The resulting function is holomorphic. In this case the problem was caused by being given an indeterminate form. Taking a power series expansion for around the singular point shows that Formally, if is an open subset of the complex plane , a point of , and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on . We say is holomorphically extendable over if such a exists.

### Technology Types

analytic functionbernhard riemanndifferential equationequationfunctionmathematical relationmathematical statementmathematical theoremmeromorphic functionordinary differential equationpropositionstatementtheoremtheory

### Synonyms

Removable singular pointRiemann's theorem on removable singularities

### Translations

Ophefbare singulariteit (nl)Riemannscher Hebbarkeitssatz (de)Singularidade removível (pt)Устранимая особая точка (ru)Усувна особлива точка (uk)可去奇点 (zh)可除特異点 (ja)

## Tech Info

Source: [object Object]
— Date merged: 11/6/2021, 1:32:49 PM
— Date scraped: 5/20/2021, 6:49:28 PM