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essential singularity
In complex analysis, an essential singularity of a function is a "severe" singularity near which the function exhibits odd behavior.
The category ''essential singularity'' is a "left-over" or default group of 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.
==Formal description==
Consider an open subset ''U'' of the complex plane C. Let ''a'' be an element of ''U'', and ''f'' : ''U'' \ → C a holomorphic function. The point ''a'' is called an ''essential singularity'' of the function ''f'' if the singularity is neither a pole nor a removable singularity.
For example, the function ''f''(''z'') = ''e''1/''z'' has an essential singularity at ''z'' = 0.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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