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  "body": "\n## Summary\n\nThe error function is $\\operatorname{erf} x = \\frac{2}{\\sqrt{\\pi}} \\int_0^x e^{-t^2}\\, dt$.\nIt is the integral of the Gaussian bell curve, scaled so that $\\operatorname{erf} x \\to 1$ as $x \\to \\infty$.\nIt gives the [[cumulative distribution function|0H8H7ZTHW2]] of the [[normal distribution|05AQE0QR0D]], and it appears in solutions of the [[heat equation|VP2HN86VAG]].\nIt has no expression in terms of elementary functions.\n\n## Explanations\n\n### L1 human\n\nThe bell curve $e^{-t^2}$ is the shape of the normal distribution.\nThe error function measures the area under this curve between $0$ and $x$, scaled so that the total area on the positive side is $1$.\nIt starts at $0$, rises quickly, and levels off near $1$ after $x \\approx 2$.\nFor example, $\\operatorname{erf}(1/\\sqrt{2}) \\approx 0.683$: a normal random value lies within one standard deviation of the mean with probability about $68\\%$.\n",
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