LIMIT TRANSITIONS FOR BC TYPE MULTIVARIABLE ORTHOGONAL POLYNOMIALS

Limit transitions will be derived between the five parameter family of Askey-Wilson polynomials, the four parameter family of big q-Jacobi p olynomials and the three parameter family of little q-Jacobi polynomia ls in n variables associated with root system BC. These limit transiti ons generalize the known hierarchy structure between these families in the one variable case. Furthermore it will be proved that these three families are q-analogues of the three parameter family of BC type Jac obi polynomials in n variables. The limit transitions will be derived by taking limits of q-difference operators which have these polynomial s as eigenfunctions.