I didn't have any problem with compilation of code snippet. After completing it to small document it works fine.
However, your first equation is to long that can be fit into text width, so I suggest to break it into two lines by using multlined
math environment from mathtools
package. Also for definition of \abs{...}
. I would rather use macro \DeclarePairedDelimiter
from the same package than define own command. It is also better to replace with Bigl(
, Bigr)
or \left[
, right]
. they are more meaningful than your defined command \vast
:
\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\begin{document}
\begin{align*}
f_{y_1,y_2} (y_1,y_2)
& = \begin{multlined}[t]
f_{X_1,X_2}\left(y_1, \frac{1-y_1}{2} -
\sqrt{\frac{y_2}{2} - \frac{y_1^2}{2} - \frac{(1-y_1)^2}{4}}\,\right) \abs{J_1} + \\
f_{X_1,X_2}\left(y_1, \frac{1-y_1}{2} +
\sqrt{\frac{y_2}{2} - \frac{y_1^2}{2} - \frac{(1-y_1)^2}{4}}\,\right) \abs{J_2}
\end{multlined}\\
f_{y_1,y_2} (y_1,y_2)
& = \frac{\Gamma(\alpha_1 +\alpha_2)}{\Gamma(\alpha_1) \Gamma(\alpha_2)}
\left[\Bigl(\frac{(1-y_1)}{2} - \sqrt{R}\Bigr)^{\alpha_2 -1} +
\Bigl( \frac{1-y_1}{2}+ \sqrt{R}\Bigr)^{\alpha_2 -1} \right]\\
\end{align*}
\end{document}
result is:

\vast
command?