Advances in the Continuous Dual Hahn Polynomials

In this paper, we investigate some advanced properties of the continuous dual Hahn polynomials which are orthogonal in a single variable. In particular, we derive various families of bilinear and bilateral generating functions from them. We also obtain recurrence relations for these polynomials with the help of three-term contiguous relations of classical hypergeometric series. Furthermore, we give some integral representations.