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  "body": "\n## Definition\n\nLet $c$ be an [[isolated singularity|0TYB3HM9KE]] of $f$.\nThe singularity $c$ is essential if it is neither a [[removable singularity|0P18JC72RE]] nor a [[pole|0WPQYW8MTE]] of $f$.\n\n## Remarks\n\nThe singularity $c$ is essential if and only if the [[principal part|0NDV5R6Z6X]] of $f$ at $c$ has infinitely many nonzero terms.\nEquivalently, $f(z)$ has no limit in $\\mathbb{C}$ as $z \\to c$, and $|f(z)|$ does not tend to $\\infty$.\nThe standard example is [[exp(1/z) at 0|0NB31CC4SN]]. The function $\\sin(1/z)$ also has an essential singularity at $0$.\nNear an essential singularity, $f$ comes close to each complex value, by the [[Casorati–Weierstrass theorem|02HHNPC8ED]].\n\n## Explanations\n\n### L1 human\n\nAn essential singularity is a bad point that is neither a removable hole nor a point where the function simply goes to infinity.\nNear such a point, the function behaves wildly: along different paths it can go to $0$, to infinity, or to any other value.\n",
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