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Welcome to the ASTROJPY wiki! \begin{align} \sigma^2_{los} &= \frac{2}{I(R)}\int_R^\infty \left(1-\beta\frac{R^2}{r^2}\right)\nu(r)\sigma^2(r)\frac{r{\rm d}r}{\sqrt{r^2-R^2}}\ \nu(r)\sigma^2(r) &= \int_r^\infty \left(\frac{s}{r}\right)^{2\beta}\nu(s)\frac{GM(s)}{s^2}{\rm d}s \end{align}