NEW BOUNDS FOR HAHN AND KRAWTCHOUK POLYNOMIALS

New identities for the sum of squares for the Hahn and Krawtchouk poly nomials orthogonal on the set {0,..., N} are derived which generalize the trigonometric identity for the Chebyshev polynomials, of the first and second kind. These results are applied to obtain conditions (on t he degree of the polynomials) such that the polynomials are bounded (o n the interval [0, N]) by their values at the points 0 and N. As speci al cases we obtain a discrete analogue of the trigonometric identity a nd bounds for the discrete Chebyshev polynomials of the first and seco nd kind.