Title

Interlacing Of Zeros Of Orthogonal Polynomials Under Modification Of The Measure

Keywords

Classical orthogonal polynomials; Interlacing; Monotonicity; Orthogonal polynomials; Q-orthogonal polynomials; Zeros

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 dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (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 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 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. © 2013 Elsevier Inc.

Publication Date

11-1-2013

Publication Title

Journal of Approximation Theory

Volume

175

Number of Pages

64-76

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jat.2013.07.007

Socpus ID

84884360345 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84884360345

This document is currently not available here.

Share

COinS