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Isolated singularity

In complex analysis, a branch of mathematics, an isolated singularity is a singularity of a function f at a point z such that there exists an open disk centered at z within which f is analytic at every point except z.

Every singularity of a meromorphic function is isolated, but isolation of singularities is not alone sufficient to guarantee a function is meromorphic. Many important tools of complex analysis such as Laurent series and the residue theorem require that all relevant singularities of the function be isolated.

Examples