The Operator r0s and the Polynomials Kn

Abstract

Based on basic hypergeometric series, a new generalized q-operator r0s has been constructed and obtained some operator identities. Also, a new polynomial Kn(a1.....,ar,b1....,bs, c; a;q) is introduced. The generating function and its extension, Mehler’s formula and its extension and the Rogers formula for the polynomials Kn(a1.....,ar,b1....,bs, c; a;q) have been achieved by using the operator r0s . In fact, this work can be considered as a generalization of Liu work’s by imposing some special values of the parameters in our results. Therefore the q^-1  Rogers-Szegö polynomials hn(a, b/q) can be deduced directly.