Zeros of linear combinations of Laguerre polynomials from different sequences |
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| Authors: | Kathy Driver Kerstin Jordaan |
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| Institution: | a Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X3, Rondebosch 7701, Cape Town, South Africa
b Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa |
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| Abstract: | We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely  and  . 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  ,  , 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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| Keywords: | 33C45 42C05 |
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