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  "body": "\n## Summary\n\nA function of several complex variables is a function $f(z_1, \\dots, z_n)$ whose arguments are $n$ complex numbers, that is, a function on a subset of $\\C^n$.\nThe theory of several complex variables studies such functions, mainly the [[holomorphic|507C34W0ZT]] ones, and the domains and spaces on which they live.\nMany facts of one complex variable carry over, such as power series expansions and the [[Cauchy integral formula on a polydisc|FG5448NZ18]].\nOther facts change deeply when $n \\ge 2$.\nZeros are never isolated, some domains force holomorphic functions to extend to larger domains, and the [[unit ball|PDQ9KW9FAP]] and the [[polydisc|DJBWP7D3M8]] are not biholomorphic.\n\n## Explanations\n\n### L1 human\n\nIn one complex variable a function takes one complex number $z$ and returns a complex number.\nIn several complex variables it takes a list $(z_1, \\dots, z_n)$ of complex numbers.\nA picture: $\\C^n$ is like $\\R^{2n}$, with each coordinate $z_j = x_j + i y_j$ giving two real directions.\nFor example, $f(z_1, z_2) = z_1 z_2 + z_2^2$ is a function of two complex variables.\nIt is a polynomial in each variable, and such functions are the simplest examples of the theory.\n",
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