The basic and extended identities for certain q-polynomials

الملخص EN

In this paper, we introduce the generating function, Mahler's formula, Roger’s formula, the linearization formula and the inverse relation of the linearization formula of the polynomials, which is defined by L.

Carlitz [3].

Also we introduce an extension of the generating function and extension of the Roger’s formula, the extended generating function of involves a 2 □ 1 sum and the extended Rogers formula involves a 3 □ 2 sum. All identities will be derived depending on the roles of the exponential operator E (Ɵ) after representing the polynomials Gn (xiq) by this operator.