Association schemes and quadratic transformations for orthogonal polynomials
- Cite this article as:
- Chihara, L. & Stanton, D. Graphs and Combinatorics (1986) 2: 101. doi:10.1007/BF01788084
Special cases of the Askey-Wilson polynomials are the eigenmatrices of the classical association schemes. Three constructions on the schemes — multiple polynomial structures, bipartite halves, and antipodal quotients — give quadratic transformations for the polynomials. It is shown that these transformations essentially follow from a quadratic transformation for the Askey-Wilson polynomials. Explicit formulas for the eigenmatrices of three related association schemes are given.