The Askey scheme as a four-manifold with corners

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.

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

Cited by in corpus (6)

• Towards a full solution of the large N double-scaled SYK model
• Orthogonal polynomials, a short introduction
• Charting the $q$-Askey scheme
• An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension
• On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
• Charting the $q$-Askey scheme. III. Verde-Star scheme for $q=1$