= Lowered Maxwellian velocity distribution
{title2=$f(v)=A[e^{-v^2/(2\sigma^2)}-e^{-v_e^2/(2\sigma^2)}]\mathbf1_{v<v_e}$}
A <lowered Maxwellian velocity distribution> subtracts the value of a <Maxwell-Boltzmann velocity distribution> at the <escape velocity> and sets the result to zero beyond escape. This gives a nonnegative <phase-space distribution function> vanishing continuously at the boundary. If $A=n_0/(2\pi\sigma^2)^{3/2}$ and $x_e=v_e/(\sqrt2\sigma)$, its actual <number density> is $n=n_0[\operatorname{erf}x_e-2x_ee^{-x_e^2}/\sqrt\pi-4x_e^3e^{-x_e^2}/(3\sqrt\pi)]$. Thus $n_0$ is a normalization parameter, not generally the integrated density. Integrating only speeds below $V<v_e$ gives the same bracket with the first two terms at $X=V/(\sqrt2\sigma)$ and the last term $-4X^3e^{-x_e^2}/(3\sqrt\pi)$.
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