Zeros of linear combinations of Laguerre polynomials from different sequences

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Zeros of linear combinations of Laguerre polynomials from different sequences

Driver, Kathy (Cathryn Helena Stanford); Jordaan, Kerstin Heidrun
URI: http://hdl.handle.net/2263/11304
Date: 2009

Abstract:

We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely Rn = Lαn + aL α’n and Sn = Lαn + bLα’n-1. Proofs and numerical counterexamples are given in situations where the zeros of Rn, and Sn, respectively, interlace (or do not in general) with the zeros of Lαk, Lαk, 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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