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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 removable if there is a function $g$ that is [[holomorphic|0DG0Z72CQD]] on the disc $|z - c| \u003c r$ with $g(z) = f(z)$ for each $z$ with $0 \u003c |z - c| \u003c r$.\n\n## Remarks\n\nThe standard example is $f(z) = \\frac{\\sin z}{z}$ at $0$. With $g(0) = 1$, the function $g$ is the sum of $1 - \\frac{z^2}{3!} + \\frac{z^4}{5!} - \\cdots$, which is holomorphic.\nThe singularity is removable if and only if the [[principal part|0NDV5R6Z6X]] of $f$ at $c$ is $0$.\n[[Riemann's theorem|0BSQDZWF34]] says that the singularity is removable if $f$ is bounded near $c$.\n\n## Explanations\n\n### L1 human\n\nA removable singularity is a hole in the domain of the function that you can fill with one value.\nAfter you fill it, the function is holomorphic at the point too.\n",
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  "name": "Removable singularity",
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