Article

The Ramanujan Journal

, 20:409

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

The Askey scheme as a four-manifold with corners

  • Tom H. KoornwinderAffiliated withKorteweg-de Vries Institute, University of Amsterdam Email author 

Abstract

Racah and Wilson polynomials with dilated and translated argument are reparametrized such that the polynomials are continuous in the parameters as long as these are nonnegative, and such that restriction of one or more of the new parameters to zero yields orthogonal polynomials lower in the Askey scheme. Geometrically this will be described as a manifold with corners.

Keywords

Askey scheme Hypergeometric orthogonal polynomials Limit relations Three-term recurrence relations Manifold with corners

Mathematics Subject Classification (2000)

33C45