Uniform multi-parameter limit transitions in the Askey tableau

绘制 $q$-Askey 方案。III. $q=1$ 时的 Verde-Star 方案

Charting the $q$-Askey scheme. III. Verde-Star scheme for $q=1$

本文借助 Verde-Star 的三个多项式序列，对 $q=1$ Askey 方案中的正交多项式族、超几何表示及极限关系进行统一分类与图形化参数化。

Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy

A $\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\mathbb{D}$. It is known that the system of polynomials, orthogonal with respect to this weight, and the associated functions satisfy a linear, first order homogeneous matrix equation in the divided-difference operator termed the spectral equation. Attached to the spectral equation is a structure which constitutes a number of relations such as those arising from compatibility with the three-term recurrence relation. Here this structure is elucidate…