Fourier Transform of the Orthogonal Polynomials on the Unit Ball and Continuous Hahn Polynomials

Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to Hermite functions, which are eigenfunctions For multivariate case, using transform and Parseval’s identity, very recently, some examples this type have been introduced orthogonality relations discussed. In present paper, method applied for on unit ball. these ball obtained. By a new family functions introduced. results expressed in terms continuous Hahn polynomials.