= Neutral Rayleigh-mode dispersion correction
{title2=$c_1=-2k_0k_1I/(J+i\pi M)$}
Let $I=\int\phi_0^2dy$, $J=\operatorname{PV}\int U''\phi_0^2/(U-c_0)^2dy$, and $M=U'''(0)\phi_0(0)^2/U'(0)^2$. The <Wronskian> identity for the first-order <Rayleigh equation for inviscid shear flow>, combined with <neutral-mode critical-layer matching>, gives $2k_0k_1I=-c_1(J+i\pi M)$. For real $k_1$, its imaginary part is $2k_0k_1I\pi M/(J^2+\pi^2M^2)$. The <Cauchy principal value> is necessary when the outer forcing has a simple real pole.
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