Back Істотна асаблівы пункт Byelorussian Singularitat essencial Catalan Esenca specialaĵo Esperanto Singularidad esencial Spanish تکینگی اساسی Persian Singularité essentielle French Lényeges szingularitás Hungarian 真性特異点 Japanese Елеулі ерекше нүкте Kazakh 본질적 특이점 Korean

Essential singularity

For essential singularities of real valued functions, see Classification of discontinuities.
Plot of the function exp(1/z), centered on the essential singularity at z = 0. The hue represents the complex argument, the luminance represents the absolute value. This plot shows how approaching the essential singularity from different directions yields different behaviors (as opposed to a pole, which, approached from any direction, would be uniformly white).
Model illustrating essential singularity of a complex function 6w = exp(1/(6z))

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

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[who?] include non-isolated singularities too; those do not have a residue.

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