  We consider the rational Heun operator defined as the most general
second-order $q$-difference operator which sends any rational function of type
$[(n-1)/n]$ to a rational function of type $[n/(n+1)]$. We shall take the poles
to be located on the Askey-Wilson grid. It is shown that this operator is
related to the one-dimensional degeneration of the Ruijsenaars-van Diejen
Hamiltonians. The Wilson biorthogonal functions of type ${_{10}}\Phi_9$ are
found to be solutions of a generalized eigenvalue problem involving rational
Heun operators of the special "classical" kind.
