THE GENERALIZED HAHN POLYNOMIALS

In this paper, we represent the generalized Hahn polynomials phi((a))(n) (x, y) by the Cauchy operator for deriving its identities: generating function, Mehler's formula, Rogers formula (with some of its applications), Rogers-type formula, extended generating function, extended Mehler's formula, extended Rogers formula and another extended identities. Also, the Rogers-type formula for the bivariate (generalized) (classical) Rogers-Szego polynomials will be given by two methods. Then we give the q-integral representation for the generalized Hahn polynomials, bivariate Rogers-Szego polynomials, and the generalized Rogers-Szego polynomials.