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arXiv · 2412.06844

Interlacing of zeros from different sequences of Meixner-Pollaczek, Pseudo-Jacobi and Continuous Hahn polynomials

Aletta Jooste·Kerstin Jordaan
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Abstract

In this paper we consider interlacing of the zeros of polynomials from different sequences $\{p_n\}$ and $\{g_n\}$. In our main result we consider a mixed recurrence equation necessary for existence of a linear term $(x-A)$ so that the $(n+1)$ zeros of $(x-A)g_n(x)$ interlace with the $n$ zeros of $p_n$. We apply our result to Meixner-Pollaczek, Pseudo-Jacobi and Continuous Hahn polynomials to obtain new interlacing results for the zeros of polynomials of the same degree from different polynomial sequences.

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Aletta Jooste, Kerstin Jordaan. 2024-12-07. Interlacing of zeros from different sequences of Meixner-Pollaczek, Pseudo-Jacobi and Continuous Hahn polynomials. https://arxiv.org/abs/2412.06844

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