  We show that the equilibrium positions of the Ruijsenaars-Schneider-van
Diejen systems with the trigonometric potential are given by the zeros of the
Askey-Wilson polynomials with five parameters. The corresponding single
particle quantum version, which is a typical example of "discrete" quantum
mechanical systems with a q-shift type kinetic term, is shape invariant and the
eigenfunctions are the Askey-Wilson polynomials. This is an extension of our
previous study [1,2], which established the "discrete analogue" of the
well-known fact; The equilibrium positions of the Calogero systems are
described by the Hermite and Laguerre polynomials, whereas the corresponding
single particle quantum versions are shape invariant and the eigenfunctions are
the Hermite and Laguerre polynomials.
