On Some Limit Cases of Askey–Wilson Polynomials

AbstractWe show that limit transitions from Askey–Wilson polynomials toq-Racah, little and bigq-Jacobi polynomials can be made rigorous on the level of their orthogonality measures in a suitable weak sense. This allows us to derive the orthogonality relations and norm evaluations for theq-Racah polynomials, little and bigq-Jacobi polynomials by taking limits in the orthogonality relations and norm evaluations for the Askey–Wilson polynomials