Asymptotic distribution of zeros of polynomials satisfying difference equations

Authors:
I. V. Krasovsky
Affiliations:
Technische Universität Berlin, Fachbereich Mathematik MA 7-2, Strasse des 17. Juni 136, D-10623 Berlin, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 2
Cited 2

Asymptotics of extreme zeros of the Meixner-Pollaczek polynomials

ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
Asymptotic formulas for the zeros of the Meixner polynomials

Journal of Approximation Theory

On extreme zeros of classical orthogonal polynomials

Journal of Computational and Applied Mathematics
Spectral Collocation Methods for Differential-Algebraic Equations with Arbitrary Index

Journal of Scientific Computing

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Abstract

We propose a way to find the asymptotic distribution of zeros of orthogonal polynomials pn(x) satisfying a difference equation of the form B(x)pn(x + δ) - C(x,n)pn(x) + D(x)pn(x - δ) = 0. We calculate the asymptotic distribution of zeros and asymptotics of extreme zeros of the Meixner and Meixner-Pollaczek polynomials. The distribution of zeros of Meixner polynomials shows some delicate features. We indicate the relation of our technique to the approach based on the Nevai-Dehesa-Ullman distribution.