Removable singularity: Difference between revisions
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In [[complex analysis]], a '''removable singularity''' is a type of [[singularity]] of a [[function (mathematics)|function]] of a [[complex number|complex]] variable which may be removed by redefining the function value at that point. | In [[complex analysis]], a '''removable singularity''' is a type of [[singularity]] of a [[function (mathematics)|function]] of a [[complex number|complex]] variable which may be removed by redefining the function value at that point. | ||
Revision as of 16:43, 6 February 2009
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 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.