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  "body": "\n## Definition\n\nThe *Dawson function* is the function $F \\colon \\R \\to \\R$ given by\n$$F(x) = e^{-x^2} \\int_0^x e^{t^2}\\, dt,$$\nwhere $e$ denotes the [[exponential function|0J0FCWV32D]] and the integral is a [[definite integral|04TMP0XGMJ]].\n\n## Remarks\n\nExample: $F(0) = 0$, and $F$ is odd because $e^{t^2}$ is even.\nThe product rule gives the differential equation $F'(x) = 1 - 2x F(x)$, with $F(0) = 0$.\n\nNon-example: $x \\mapsto e^{x^2} \\int_0^x e^{-t^2}\\, dt$ is not the Dawson function; the signs of the exponents are swapped, and this function grows without bound.\n\nWith the imaginary error function $\\operatorname{erfi} x = \\frac{2}{\\sqrt{\\pi}} \\int_0^x e^{t^2}\\, dt$ one has $F(x) = \\frac{\\sqrt{\\pi}}{2} e^{-x^2} \\operatorname{erfi} x$.\nFor large $x$, $F(x) \\sim \\frac{1}{2x}$.\nSome texts call this $D_+(x)$ and also use $D_-(x) = e^{x^2} \\int_0^x e^{-t^2}\\, dt$, which is the non-example above.\n",
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