Carlitz's q‐Operators for the Generalized Homogeneous Hahn Polynomials

ABSTRACT In this paper, motivated by Carlitz's ‐operators and Liu's generalized homogeneous Hahn polynomials, we show how to construct Carlitz's ‐operators of the generalized homogeneous Hahn polynomials. We derive several generating functions for the generalized homogeneous Hahn polynomials by applying the method of exponential operator decomposition. In addition, we deduce Rogers type bilinear, trilinear, and mixed‐type generating functions as well as the Srivastava–Agarwal‐type generating functions for the generalized homogeneous Hahn polynomials, which provide extensions of the results of Carlitz, Abdlhusein, and Saad and Abdlhusein.