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

[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.

[发布日期] 2019-12-01

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