Notes On Carlitz's q-Operators
Notes On Carlitz's q-Operators
In this paper, Carlitz's $q$-operator and the auxiliary ones are applied to prove $q$-Christoffel-Darboux formulas and some Carlitz type generating functions. In addition, the technique of exponential operator decomposition to deduce $q$-Mehler's formulas for Rogers-Szego and Hahn polynomials are shown.