The Ramanujan Journal

, 20:409

The Askey scheme as a four-manifold with corners

Open Access

DOI: 10.1007/s11139-009-9208-7

Cite this article as:
Koornwinder, T.H. Ramanujan J (2009) 20: 409. doi:10.1007/s11139-009-9208-7


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.


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

Mathematics Subject Classification (2000)

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© The Author(s) 2009

Authors and Affiliations

  1. 1.Korteweg-de Vries InstituteUniversity of AmsterdamAmsterdamThe Netherlands

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