English

The Askey scheme as a four-manifold with corners

Classical Analysis and ODEs 2009-12-04 v2

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

Cite

@article{arxiv.0909.2822,
  title  = {The Askey scheme as a four-manifold with corners},
  author = {Tom H. Koornwinder},
  journal= {arXiv preprint arXiv:0909.2822},
  year   = {2009}
}

Comments

29 pages, 8 figures, figures improved, references and remarks added, accepted by Ramanujan Journal

R2 v1 2026-06-21T13:46:43.297Z