  In this paper, we study the gap probability problem of the (symmetric) Jacobi
unitary ensemble of Hermitian random matrices, namely the probability that the
interval $(-a,a)\:(0<a<1)$ is free of eigenvalues. Using the ladder operator
technique for orthogonal polynomials and the associated supplementary
conditions, we derive three quantities instrumental in the gap probability,
denoted by $H_{n}(a)$, $R_{n}(a)$ and $r_{n}(a)$. We find that each one
satisfies a second order differential equation. We show that after a double
scaling, the large second order differential equation in the variable $a$ with
$n$ as parameter satisfied by $H_{n}(a)$, can be reduced to the
Jimbo-Miwa-Okamoto $\sigma$ form of the Painlev\'{e} V equation.
