Title

Interlacing of zeros of orthogonal polynomials under modification of the measure

Authors

Authors

D. K. Dimitrov; M. E. H. Ismail;F. R. Rafaeli

Comments

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Abbreviated Journal Title

J. Approx. Theory

Keywords

Orthogonal polynomials; Classical orthogonal polynomials; q-orthogonal; polynomials; Zeros; Interlacing; Monotonicity; LINEAR-COMBINATIONS; DIFFERENT SEQUENCES; JACOBI-POLYNOMIALS; Mathematics

Abstract

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure d mu(x), supported on the interval (a, b) and the other with respect to the measure vertical bar x - c vertical bar(tau)vertical bar x - d vertical bar(gamma) d mu(x), where c and d are outside (a, b). We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < tau, gamma <= 1 or gamma = 0 and 0 < tau <= 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. (c) 2013 Elsevier Inc. All rights reserved.

Journal Title

Journal of Approximation Theory

Volume

175

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

64

Last Page

76

WOS Identifier

WOS:000325121000004

ISSN

0021-9045

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