## The Generalized Hahn Polynomials

## The Generalized Hahn Polynomials

*M. A. Abdlhusein*

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## Abstract

In this paper, we represent the generalized Hahn polynomials '(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.

## Keywords

Hahn polynomials, Cauchy operator, generating function, extended Mehler's formula, q-integral.