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Interlacing of the zeros of Jacobi polynomials with different parameters

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Abstract

We prove results for the interlacing of zeros of Jacobi polynomials of the same or adjacent degree as one or both of the parameters are shifted continuously within a certain range. Numerical examples are given to illustrate situations where interlacing fails to occur.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X3, Rondebosch, 7701, Cape Town, South Africa

    Kathy Driver

  2. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa

    Kerstin Jordaan & Norbert Mbuyi

Authors
  1. Kathy Driver
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  2. Kerstin Jordaan
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  3. Norbert Mbuyi
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Corresponding author

Correspondence to Kerstin Jordaan.

Additional information

Dedicated to the memory of Luigi Gatteschi.

Research of Kathy Driver author is supported by the National Research Foundation of South Africa under grant number 2053730.

Research by the last two authors is supported by the National Research Foundation of South Africa under grant number 2054423.

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Driver, K., Jordaan, K. & Mbuyi, N. Interlacing of the zeros of Jacobi polynomials with different parameters. Numer Algor 49, 143–152 (2008). https://doi.org/10.1007/s11075-008-9162-2

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  • DOI: https://doi.org/10.1007/s11075-008-9162-2

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