A ] 1 2 N ov 2 00 2 On zeros of polynomials and allied functions satisfying second order differential equations

We shall give bounds on the spacing of zeros of certain functions belonging to the LaguerrePólya class and satisfying a second order linear differential equation. As a corollary we establish new sharp inequalities on the extreme zeros of the Hermite, Laguerre and Jacobi polynomials, which are uniform in all the parameters.

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