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Bound on the extreme zeros of orthogonal polynomials


Authors: Mourand E. H. Ismail and Xin Li
Journal: Proc. Amer. Math. Soc. 115 (1992), 131-140
MSC: Primary 33C45; Secondary 26C10, 33C15
DOI: https://doi.org/10.1090/S0002-9939-1992-1079891-5
MathSciNet review: 1079891
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1079891-5
Keywords: Bounds, chain sequences, Chihara-Wall-Wetzel theorem, Laguerre polynomials, largest zero, Meixner polynomials, Meixner-Pollaczek polynomials, recurrence relations, smallest zero
Article copyright: © Copyright 1992 American Mathematical Society

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