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.Comment: 14 pages; Section 3 revise
