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User:Tohline/Math/EQ RadialPulsation02

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~0 = \frac{d^2x}{d\xi^2} + \biggl[ 4 - (n+1) Q \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi}  
+ (n+1) \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_g } \biggr)  \frac{\xi^2}{\theta} 
- \alpha Q\biggr]  \frac{x}{\xi^2}

where:    ~Q(\xi) \equiv - \frac{d\ln\theta}{d\ln\xi} \, ,    ~\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c} \, ,     and,     ~\alpha \equiv \biggl(3 - \frac{4}{\gamma_\mathrm{g}}\biggr)

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