论文标题
关于构成ASKEY的一部分的多项式家庭的家庭 - 威尔逊计划及其概率应用
On the families of polynomials forming a part of the Askey--Wilson scheme and their probabilistic applications
论文作者
论文摘要
我们回顾了六个正交多项式家族的特性，这些族构成了该集合的主要大部分，称为ASKEY - WWILSON的多项式方案。我们提供了它们之间的连接系数以及所谓的线性化公式以及其他有用的有限有限和无限扩展和身份。本文的一个重要部分是呈现概率模型的介绍，其中大多数这些多项式都出现。最近15年来，这些结果散布在文献中。我们将它们放在一起，以使这些家庭的整体前景了解，并了解其至关重要的ro。试图概括高斯分布并找到其有限的支持概括。该论文基于最近的文献中的65个项目。
We review the properties of six families of orthogonal polynomials that form the main bulk of the collection called the Askey--Wilson scheme of polynomials. We give connection coefficients between them as well as the so-called linearization formulae and other useful important finite and infinite expansions and identities. An important part of the paper is the presentation of probabilistic models where most of these families of polynomials appear. These results were scattered within the literature in recent 15 years. We put them together to enable an overall outlook on these families and understand their crucial rôle in the attempts to generalize Gaussian distributions and find their bounded support generalizations. The paper is based on 65 items in the predominantly recent literature.
