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  "body": "\n## Definition\n\nAn entire function is a function $f : \\mathbb{C} \\to \\mathbb{C}$ that is [[holomorphic|0DG0Z72CQD]] on all of $\\mathbb{C}$.\n\n## Remarks\n\nPolynomials, the [[complex exponential|054VXHMCA3]] and the complex [[sine and cosine|0A7YDKRNR6]] are entire.\nSums, products and compositions of entire functions are entire.\nAn entire function is equal to one power series $\\sum_{n \\ge 0} a_n z^n$ that converges for every $z \\in \\mathbb{C}$.\nBy [[Liouville's theorem|0EHKVRF4J6]], each bounded entire function is constant.\n\n## Explanations\n\n### L1 human\n\nAn entire function is a function that is holomorphic at every complex number, with no exceptions.\nFor example, $z^3 - 2z + 5$ and $e^z$ are entire, but $1/z$ is not, because it is not defined at $0$.\n",
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