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.
