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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 byH  n    (  a  )    ,R  n    (  a  )    , andr  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 byH  n    (  a  )can be reduced to the Jimbo–Miwa–Okamoto σ form of the Painlevé V equation.

Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling