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{title2=$F_D(z)=e^{-z^2}\int_0^z e^{u^2}\,du$}
{wiki}

= Dawson integral
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{synonym}

The Dawson function obeys $F_D'+2zF_D=1$ by <differentiation>. Its large-real-argument <asymptotic expansion> begins $F_D(z)=1/(2z)+1/(4z^3)+O(z^{-5})$. This inverse-power behavior contrasts with the separate exponentially growing factors in its definition.

Dawson function

Gaussian drift primitives

Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 336 / 2 / iii / Solution

{wiki=Dawson_function}

The Dawson function, denoted as \$ D(x) \$, is a special function that arises in various fields of mathematics and physics. It is defined as follows: \\\[ D(x) = e^\{-x^2\} \\int_0^x e^\{t^2\} \\, dt \\\] This function is named after the mathematician Dawson, who first studied it in the 19th century.


codex/dawson-integral

Dawson function ( $F_{D} (z) = e^{- z^{2}} \int_{0}^{z} e^{u^{2}} d u$ )

Gaussian drift primitives ( $E_{0} (z), E_{1} (z)$ )

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Dawson function (FD​(z)=e−z2∫0z​eu2du)

Gaussian drift primitives (E0​(z), E1​(z))