Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra

Understand

The algebraic underpinning of the tridiagonalization procedure is investigated.

• The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadratic Jacobi algebra.
• It is shown that under tridiagonalization, the quadratic Jacobi algebra becomes the quadratic Racah-Wilson algebra associated to the generic Racah/Wilson polynomials.
• A degenerate case leading to the Hahn algebra is also discussed.