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  "body": "\n## Summary\n\nThe order of a [[meromorphic function|0ZZ7ZYDR8W]] at a point $a$ is the integer $n$ such that it behaves like $c (z - a)^n$ near $a$, with $c \\neq 0$.\nSee the [[definition|K2S5TAW2BF]].\nAt a zero it is the [[order of the zero|0QX19C7K1C]].\nAt a pole it is minus the [[order of the pole|073MWACF1K]].\nThis single integer turns products of meromorphic functions into sums, like a logarithm.\n\n## Explanations\n\n### L1 human\n\nNear $0$, the function $z^3$ vanishes like the third power of $z$, and $1/z^2$ blows up like the second power of $1/z$.\nThe order records both at once with a sign: $3$ for $z^3$ and $-2$ for $1/z^2$.\nAt ordinary points, where the function is neither $0$ nor infinite, the order is $0$.\nWhen you multiply two functions, their orders add, just as exponents add when you multiply powers.\n",
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