= Instability threshold of a gravitating particle lattice
For $q=GmF(hk)/(h^3\Omega^2)$, the squared dimensionless growth rates are $s^2/\Omega^2=(q-1\pm\sqrt{9q^2-26q+1})/2$. Exponential growth begins for $q>(13-4\sqrt{10})/9$. Since the <gravitating lattice Fourier kernel> is largest at $hk=\pi$, the full infinite lattice is exponentially unstable when $Gm/(h^3\Omega^2)>(13-4\sqrt{10})/[9F(\pi)]$. Marginal repeated imaginary roots and zero-frequency secular modes require separate treatment.
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