Characterizations of Continuous and Discrete <i>q</i>-Ultraspherical Polynomials
Characterizations of Continuous and Discrete <i>q</i>-Ultraspherical Polynomials
Abstract We characterize the continuous q -ultraspherical polynomials in terms of the special form of the coefficients in the expansion D qPn ( x ) in the basis { P n ( x )}, D q being the Askey-Wilson divided difference operator. The polynomials are assumed to be symmetric, and …