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  "body": "\n## Summary\n\nA polydisc in $\\C^n$ is a product of $n$ open discs of the complex plane, one in each coordinate.\nIt is the basic domain of [[several complex variables|BH57D2FBNR]], playing the role that the disc plays in one variable.\nThe [[Cauchy integral formula on a polydisc|FG5448NZ18]] follows from the one-variable formula applied in each coordinate, and it leads to power series expansions.\nIts [[distinguished boundary|A6HN207Y2T]] is a torus, much smaller than its topological boundary.\n\n## Explanations\n\n### L1 human\n\nA polydisc is what one gets by letting each coordinate $z_j$ range over its own disc, independently of the others.\nIn $\\C^2$, the unit polydisc is the set of pairs $(z_1, z_2)$ with $\\abs{z_1} \u003c 1$ and $\\abs{z_2} \u003c 1$.\nIt is a complex analogue of a box, or of a square in the plane.\nThe point $(0.9, 0.9)$ lies in the unit polydisc of $\\C^2$, but not in the [[unit ball|PDQ9KW9FAP]], since $0.81 + 0.81 \u003e 1$.\n",
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