Sharp parameter intervals for interlacing of zeros of equal degree Laguerre polynomials

JOURNAL OF APPROXIMATION THEORY

卷:248

Article

Driver, Kathy¹  Muldoon, Martin E.² 

[1] Univ Cape Town, Dept Math & Appl Math, ZA-7708 Cape Town, South Africa

[2] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada

关键词: Laguerre polynomials;    Zeros;    Interlacing;    Bessel functions;    Sturm Comparison Theorem;   

DOI  :  10.1016/j.jat.2019.105303

来源: Elsevier

【 摘 要 】

We prove that, for each alpha > -1, the t-interval (0, 2] is sharp for interlacing to hold for every n is an element of N between the zeros of the equal degree Laguerre polynomials L-n((alpha)) (x) and L-n((alpha +t)) (x). We use a recent result proved by Palmai (2013) that, for mu, nu > -1, the positive zeros of the Bessel functions J(nu)(x) and J(mu)(x) are interlacing if and only if vertical bar - nu vertical bar <= 2. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free