We show that some nonnegative quadratic forms containing orthogonal polynomials, such as e.g. the Christoffel Darboux kernel for x= y in the classical case, provide a lot of information about behavior of the polynomials on the real axis. We illustrate the method for the case of Hermite polynomials and use it to derive new explicit bounds for binary Krawtchouk polynomials.
Academic Press
We derive new conditions for the nonexistence of integral zeros of binary Krawtchouk polynomials. Upper bounds for the number of integral roots of Krawtchouk polynomials are presented.
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