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  "body": "\n## Definition\n\nLet $c$ be an [[isolated singularity|0TYB3HM9KE]] of $f$, so that $f$ is holomorphic on $0 \u003c |z - c| \u003c r$ for some $r \u003e 0$.\nThe singularity $c$ is a pole of $f$ if $|f(z)| \\to \\infty$ as $z \\to c$. This means that for each $K \u003e 0$ there is $\\delta \u003e 0$ such that $|f(z)| \u003e K$ for each $z$ with $0 \u003c |z - c| \u003c \\delta$.\n\n## Remarks\n\nThe point $c$ is a pole of $f$ if and only if $f(z) = \\frac{g(z)}{(z - c)^m}$ near $c$, for an integer $m \\ge 1$ and a function $g$ that is holomorphic near $c$ with $g(c) \\neq 0$. The integer $m$ is the [[order of the pole|0YK27TJ4WF]].\nEquivalently, $1/f$ extends to a holomorphic function near $c$ with a [[zero|0CEGEASY49]] at $c$.\nFor example, $\\frac{1}{z^2 (z - 1)}$ has a pole of order $2$ at $0$ and a pole of order $1$, a simple pole, at $1$.\n\n## Explanations\n\n### L1 human\n\nA pole is a point where the function goes to infinity, in the way $1/z$ or $1/z^3$ does at $0$.\nNear a pole, $1/f$ is a holomorphic function with a zero there.\n",
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