Editing Essential singularity (section)

{{Short description|Location around which a function displays irregular behavior}}
{{For|essential singularities of real valued functions|Classification of discontinuities}}

[[File:Essential singularity.png|right|220px|thumb|Plot of the function {{math|exp(1/''z'')}}, centered on the essential singularity at {{math|1=''z'' = 0}}. The hue represents the [[Arg (mathematics)|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).]]
[[File:Modell des Graphen von 6w=eˆ(1-6z) -Schilling XIV, 6 - 312- (2).jpg|thumb|Model illustrating essential singularity of a complex function {{math|1=6''w'' = exp(1/(6''z''))}}]]

In [[complex analysis]], an '''essential singularity''' of a [[Function (mathematics)|function]] is a "severe" [[singularity (mathematics)|singularity]] near which the function exhibits striking behavior. 

The category ''essential singularity'' is a "left-over" or default group of [[Isolated singularity|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 &ndash; [[removable singularity|removable singularities]] and [[pole (complex analysis)|pole]]s. In practice some{{Who?|date=January 2022}} include non-isolated singularities too; those do not have a [[Residue (complex analysis)|residue]].