Askey-Wilson polynomials for root systems of type
. (English) Zbl 0797.33014
Richards, Donald St. P. (ed.), Hypergeometric functions on domains of positivity, Jack polynomials, and applications. Proceedings of an AMS special session held March 22-23, 1991 in Tampa, FL, USA. Providence, RI: American Mathematical Society. Contemp. Math. 138, 189-204 (1992).
The author describes Macdonald’s orthogonal polynomials associated with root systems, observes that for the root system these are a special case of the Askey-Wilson polynomials, and then finds a generalization of the Macdonald polynomials for that introduces two additional parameters so that when these become the Askey- Wilson polynomials. These generalized Askey-Wilson polynomials are orthogonal with respect to the weight
where , .
|33D70||Basic hypergeometric functions and integrals in several variables|
|33D80||Connections of basic hypergeometric functions with groups, algebras and related topics|
|17B20||Simple, semisimple, reductive Lie (super)algebras|