The structure relation for Askey–Wilson polynomials

作者:

Highlights:

摘要

An explicit structure relation for Askey–Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey–Wilson inner product and which sends polynomials of degree n to polynomials of degree n+1. By specialization of parameters and by taking limits, similar structure relations, as well as lowering and raising relations, can be obtained for other families in the q-Askey scheme and the Askey scheme. This is explicitly discussed for Jacobi polynomials, continuous q-Jacobi polynomials, continuous q-ultraspherical polynomials, and for big q-Jacobi polynomials. An already known structure relation for this last family can be obtained from the new structure relation by using the three-term recurrence relation and the second order q-difference formula. The results are also put in the framework of a more general theory. Their relationship with earlier work by Zhedanov and Bangerezako is discussed. There is also a connection with the string equation in discrete matrix models and with the Sklyanin algebra.

论文关键词:33D45,33C45,Structure relation,Askey–Wilson polynomials,Classical orthogonal polynomials,Askey scheme,Lowering and raising relations

论文评审过程:Available online 28 November 2006.

论文官网地址:https://doi.org/10.1016/j.cam.2006.10.015

Back to Top