= Rapid-rotation slow magneto-Coriolis branch
{title2=$\omega_s^2\sim a^2(K^2a^2-Hh^2)/(4\Omega^2k_z^2)$}
For fixed wavevector with $k_z\ne0$, fixed nonzero <Alfvén frequency> $a$, and $|\Omega|\to\infty$, the two roots in $X=\omega^2$ of the <stratified magneto-Coriolis wave> polynomial have $X_f\sim4\Omega^2k_z^2/K^2$ and the displayed slow root. This follows from the sum of roots being $4\Omega^2k_z^2/K^2+O(1)$ and their product being $a^2(K^2a^2-Hh^2)/K^2$. The slow branch is oscillatory for $K^2a^2>Hh^2$ and growing or decaying for the reversed inequality. At equality its frequency vanishes and the original stationary equations must be used.
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