Elliptic Racah polynomials

Abstract

Upon solving a finite discrete reduction of the difference Heun equation, we arrive at an elliptic generalization of the Racah polynomials. We exhibit the three-term recurrence relation and the orthogonality relations for these elliptic Racah polynomials. The well-known $q$-Racah polynomials of Askey and Wilson are recovered as a trigonometric limit.

18 pages

References in corpus (2)

• The rational Heun operator and Wilson biorthogonal functions
• Sklyanin-like algebras for ($q$-)linear grids and ($q$-)para-Krawtchouk polynomials

Cited by in corpus (2)

• $q$-Racah probability distribution
• Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry