An expansion of (q, λ)-derivative operator

摘要

We give the concept of Generalized Rogers-Szego polynomials based on the (q, lambda)derivative operator and (q, mu)-derivative operator. Then we use the method of Liu's calculus to obtain the expansion theorem involving Generalized Rogers-Szego polynomials. In addition, we use two kinds of the (q, lambda)-exponential functions and extend some identities of Zhang. At last, we consider the properties when lambda = 1 and mu = 1, and use the method of the generating functions and q-Mehler formula for Al-Salam-Carlitz polynomials to establish some new identities.

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