Essential singularity

In complex analysis, an essential singularity of a function is a "severe" singularity near which the function exhibits odd behavior.

For essential singularities of real valued functions, see Classification of discontinuities.

The category essential singularity is a "left-over" or default group of isolated singularities that are especially unmanageable: by definition they fit into neither of the other two categories of singularity that may be dealt with in some manner – removable singularities and poles. In practice some include non-isolated singularities too; those do not have a residue.

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