= Height-evaluation gravitational softening
{title2=$\Phi_\epsilon(\mathbf R)=-G\int\Sigma(\mathbf R')(|\mathbf R-\mathbf R'|^2+\epsilon^2)^{-1/2}d^2R'$}
Evaluating the potential of a <razor-thin disk> at height $\epsilon$ gives a softened horizontal force. Its Fourier multiplier is $e^{-k\epsilon}$ times the <razor-thin disk Poisson kernel>. This suppresses short <wavelengths> while retaining the long-wave potential. A real finite-thickness profile generally has a different full reduction factor.
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