Inner Bounds for the Extreme Zeros of the Hahn, Continuous Hahn and Continuous Dual Hahn Polynomials
نویسنده
چکیده
We apply Zeilberger’s algorithm to generate relations of finite-type necessary to obtain inner bounds for the extreme zeros of orthogonal polynomial sequences with 3F2 hypergeometric representations. Using this method, we improve previously obtained upper bounds for the smallest and lower bounds for the largest zeros of the Hahn polynomials and we identify inner bounds for the extreme zeros of the Continuous Hahn and Continuous Dual Hahn polynomials. Numerical examples are provided to illustrate the quality of the new bounds.
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