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  "body": "\n## Definition\n\nLet $c \\in \\mathbb{C}$ and let $r, R$ be such that $0 \\le r \u003c R \\le \\infty$.\nThe annulus with center $c$, inner radius $r$ and outer radius $R$ is the subset\n$$A(c; r, R) = \\{ z \\in \\mathbb{C} : r \u003c |z - c| \u003c R \\}$$\nof the [[complex plane|0CTE7A31XQ]]. Here $|z - c|$ is the [[modulus|0KW2X0TFBX]] of $z - c$.\n\n## Remarks\n\nEach annulus is a [[domain|097KNJFJ7V]].\nFor $r = 0$, the annulus is the punctured disc $0 \u003c |z - c| \u003c R$. For $r = 0$ and $R = \\infty$, it is $\\mathbb{C} \\setminus \\{c\\}$.\nFor $R \u003c \\infty$, its area is $\\pi (R^2 - r^2)$.\nHolomorphic functions on an annulus have [[Laurent expansions|06WHRARZKY]].\n\n## Explanations\n\n### L1 human\n\nAn annulus is the ring between two circles with the same center, without the two circles.\nFor example, $1 \u003c |z| \u003c 2$ is the set of the points whose distance to $0$ is between $1$ and $2$.\n",
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