Bound on the extreme zeros of orthogonal polynomials

Ismail, Mourand E. H.; Li, Xin

doi:10.1090/S0002-9939-1992-1079891-5

Bound on the extreme zeros of orthogonal polynomials
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by Mourand E. H. Ismail and Xin Li

Proc. Amer. Math. Soc. 115 (1992), 131-140

DOI: https://doi.org/10.1090/S0002-9939-1992-1079891-5

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Abstract:

Using chain sequences we formulate a procedure to find upper (lower) bounds for the largest (smallest) zero of orthogonal polynomials in terms of their recurrence coefficients. We also apply our method to derive bounds for extreme zeros of the Laguerre, associated Laguerre, Meixner, and Meixner-Pollaczek polynomials. In addition, we consider bounds for the extreme zeros of Jacobi polynomials of degree $n$ and parameters ${a_n}$ and ${b_n}$.

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