论文标题
al-Salam-Chihara多项式系数的组合公式
Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials
论文作者
论文摘要
Al-Salam-Chihara多项式是一个变量$ x $的正交多项式的重要家族，具体取决于3个参数$α$，$β$和$ Q $。它们与称为部分不对称的简单排除过程（PASEP）的统计力学密切连接到模型，可以作为Askey-Wilson多项式的专业化获得。我们给出了两个不同的组合公式，以用于（转化的）al-Salam-Chihara多项式的系数。我们的公式使该系数以$α$，$β$和$ Q $为正系数的多项式显示出一个事实。
The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $α$, $β$ 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 $α$, $β$ and $q$ with positive coefficients.
