We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials, Charlier, Krawtchouk, Meixner and Hahn. We also provide lower bounds on the minimal distance between their consecutive zeros.
We show that the functionis the orthonormal Laguerre polynomial of degree k and d m , d M are some approximations for the extreme zeros. As a corollary we obtain a very explicit, uniform in k and α, sharp upper bound on the Laguerre polynomials.
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