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arXiv · 2002.01518

Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials

Donghyun Kim
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Abstract

The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\alpha$, $\beta$ and $q$. They are closely connected to a model from statistical mechanics called the partially asymmetric simple exclusion process (PASEP) and they can be obtained as a specialization of the Askey-Wilson polynomials. We give two different combinatorial formulas for the coefficients of the (transformed) Al-Salam-Chihara polynomials. Our formulas make manifest the fact that the coefficients are polynomials in $\alpha$, $\beta$ and $q$ with positive coefficients.

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Donghyun Kim. 2020-02-04. Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials. https://arxiv.org/abs/2002.01518

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