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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A discrete approach to monotonicity of zeros of orthogonal polynomials

Authors: Mourad E. H. Ismail and Martin E. Muldoon
Journal: Trans. Amer. Math. Soc. 323 (1991), 65-78
MSC: Primary 33C50; Secondary 15A42
MathSciNet review: 1014251
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Abstract: We study the monotonicity with respect to a parameter of zeros of orthogonal polynomials. Our method uses the tridiagonal (Jacobi) matrices arising from the three-term recurrence relation for the polynomials. We obtain new results on monotonicity of zeros of associated Laguerre, Al-Salam-Carlitz, Meixner and Pollaczek polynomials. We also derive inequalities for the zeros of the Al-Salam-Carlitz and Meixner polynomials.

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Keywords: Orthogonal polynomials, zeros, monotonicity, recurrence relations, Jacobi matrices
Article copyright: © Copyright 1991 American Mathematical Society