= Logarithmic-potential two-integral distribution
{title2=$F=AL_z^2e^{-4E/V^2}+Be^{-2E/V^2}$}
The singular <axisymmetric logarithmic gravitational potential> admits this stationary <galactic distribution function> with
$$
A=\frac{4\sqrt2(1-q^2)}{\pi^{5/2}Gq^2V^3},\qquad B=\frac{2q^2-1}{4\pi^{5/2}Gq^2V}.
$$
The zero of <specific orbital energy> is the printed logarithmic convention. Products of <Gaussian integrals> normalize its two spatial density terms. For $1/2\le q^2\le1$ the two terms are separately nonnegative; mildly prolate models require a bound on their sum.
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