begin{equation*}label{eq:pareto mle2}
A_0 = frac{1}{(alpha+t_x)^{r+s+x}}{}_2F_1left(r+s+x,x+1;r+s+x+1;frac{alpha-beta}{alpha + t_x} right ) "\" <br>
 - frac{1}{(alpha+T)^{r+s+x}}{}_2F_1left(r+s+x,x+1;r+s+x+1;frac{alpha-beta}{alpha + T} right ),
end{equation*}