 Dawson function

The Dawson function obeys $F_D^{\prime }+2z{F}_D=1$ 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.

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.