= Weighted stellar pulsation Rayleigh quotient
{title2=$\mathcal R[\xi]$}
For radial adiabatic <stellar oscillations>, the quotient is $\mathcal R[\xi]=\int[\gamma p r^4|\xi\prime|^2+r^3((4-3\gamma)p)\prime|\xi|^2]dr/\int\rho r^4|\xi|^2dr$. Regular-centre and free-surface endpoint conditions remove the boundary term. The infimum is the fundamental squared frequency; any negative trial value proves radial instability. A variable <stellar adiabatic exponent> must remain inside the derivative.
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