Abstract
Abstract We characterize the continuous q-ultraspherical polynomials in terms of the special form of the coefficients in the expansion DqPn(x) in the basis {Pn(x)}, Dq being the Askey-Wilson divided difference operator. The polynomials are assumed to be symmetric, and the connection coefficients are multiples of the reciprocal of the square of the L2 norm of the polynomials. A similar characterization is given for the discrete q-ultraspherical polynomials. A new proof of the evaluation of the connection coefficients for big q-Jacobi polynomials is given.
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