An expansion of %$(q, \lambda )%$-derivative operator

Abstract We give the concept of Generalized Rogers–Szegö 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–Szegö polynomials. In addition, we use...
Ausführliche Beschreibung

Abstract We give the concept of Generalized Rogers–Szegö 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–Szegö 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. Ausführliche Beschreibung