Abstract
A four-parameter family of multivariable big q-Jacobi polynomials and a three-parameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality is proved with the help of a second-order q-difference operator which is diagonalized by the multivariable polynomials. A link is made between the orthogonality measures and R. Askey's q-extensions of Selberg's multidimensional beta-integrals.
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