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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.09931 |
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Table of Contents:
- In this paper we consider connection formulae for orthogonal polynomials in the context of Christoffel transformations for the case where a weight function, not necessarily even, is multiplied by an even function $c_{2k}(x),k\in N_0$, to determine new lower bounds for the largest zero and upper bounds for the smallest zero of a Meixner-Pollaczek polynomial. When $p_n$ is orthogonal with respect to a weight $w(x)$ and $g_{n-m}$ is orthogonal with respect to the weight $c_{2k}(x)w(x)$, we show that $k\in\{0,1,\dots,m\}$ is a necessary and sufficient condition for existence of a connection formula involving a polynomial $G_{m-1}$ of degree $(m-1)$, such that the $(n-1)$ zeros of $G_{m-1}g_{n-m}$ and the $n$ zeros of $p_n$ interlace. We analyse the new inner bounds for the extreme zeros of Meixner-Pollaczek polynomials to determine which bounds are the sharpest. We also briefly discuss bounds for the zeros of Pseudo-Jacobi polynomials.