Zeros of linear combinations of Laguerre polynomials from different sequences

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Driver, Kathy¹  Jordaan, Kerstin² 

[1] Univ Cape Town, Dept Math & Appl Math, ZA-7701 Cape Town, South Africa

[2] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

关键词: Laguerre polynomials;    Zeros;    Interlacing properties;    Linear combinations;   

DOI  :  10.1016/j.cam.2009.02.091

来源: Elsevier

【 摘 要 】

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely R(n) = L(n)(alpha) + aL(n)(alpha') and S(n) = L(n)(alpha) + bL(n-1)(alpha'). Proofs and numerical counter examples are given in situations where the zeros of R(n), and S(n), respectively, interlace (or do not in general) with the zeros of L(k)(alpha), L(k)(alpha'), k = n or n - 1. The results we prove hold for continuous, as well as integral, shifts of the parameter alpha. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free