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arXiv · 2202.10167

On another characterization of Askey-Wilson polynomials

D. Mbouna·A. Suzuki
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Abstract

In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} \phi(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $\phi$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson operator and $\mathcal{S}_q$ the averaging operator, are the multiple of Askey-Wilson polynomials, or specific or limiting cases of them.

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D. Mbouna, A. Suzuki. 2022-02-21. On another characterization of Askey-Wilson polynomials. https://arxiv.org/abs/2202.10167

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