On extreme zeros of classical orthogonal polynomials

Let x1x1 and xkxk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree kk. We shall establish sharp inequalities of the form x1Bxk>B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with a high precision.