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Zeros of linear combinations of Laguerre polynomials from different sequences

✍ Scribed by Kathy Driver; Kerstin Jordaan

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 294 KB
Volume: 233
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.02.091

No coin nor oath required. For personal study only.

✦ Synopsis

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely

Proofs and numerical counterexamples 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 α k , L α k , k = n or n -1. The results we prove hold for continuous, as well as integral, shifts of the parameter α.

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