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  "body": "\n## Summary\n\nThe Dawson function is $F(x) = e^{-x^2} \\int_0^x e^{t^2}\\, dt$.\nIt is a scaled form of the imaginary error function: $F(x) = \\frac{\\sqrt{\\pi}}{2} e^{-x^2} \\operatorname{erfi} x$, where $\\operatorname{erfi} x = -i \\operatorname{erf}(ix)$ and $\\operatorname{erf}$ is the [[error function|7Y56QCZSZJ]].\nIt is the imaginary part of the [[Faddeeva function|3GHGFTMFQR]] on the real line, up to the factor $\\frac{2}{\\sqrt{\\pi}}$.\nIt appears in plasma physics, in spectroscopy and in the Hilbert transform of the Gaussian.\n\n## Explanations\n\n### L1 human\n\nThe integral of $e^{t^2}$ grows extremely fast, and the factor $e^{-x^2}$ tames this growth.\nWhat is left is a small odd function: it rises from $0$, reaches a maximum of about $0.54$ near $x \\approx 0.92$, and then decays like $\\frac{1}{2x}$.\nSo the Dawson function is a bounded smooth bump on the positive side with its mirror image on the negative side.\n",
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