A discrete approach to monotonicity of zeros of orthogonal polynomials

Ismail, Mourad E. H.; Muldoon, Martin E.

doi:10.1090/S0002-9947-1991-1014251-8

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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 | References | Similar Articles | Additional Information

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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