Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials |
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| Authors: | Kathy Driver Kerstin Jordaan |
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| Affiliation: | (1) Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X3, Rondebosch, 7701, Cape Town, South Africa;(2) Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa |
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| Abstract: | We study the interlacing property of zeros of Laguerre polynomials of adjacent degree, where the free parameters differ by an integer, and of the same degree, where the free parameter is shifted continuously. Similar interlacing results are proven for the positive zeros of Gegenbauer polynomials. Research by Kathy Driver is supported by the National Research Foundation of South Africa under grant number 2053730. Research by Kerstin Jordaan is partially supported by the National Research Foundation of South Africa under grant number 2054423. |
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| Keywords: | 33C05 30C15 |
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