Applications of the Operator _r Φ_s in q-identities

Abstract

In this paper, we set up the general operator , and then we find some of its operator identities that will be used to generalize some well-known -identities, such as Cauchy identity, Heine’s transformation formula and the -Pfaff-Saalschütz summation formula. By giving special values to the parameters in the obtained identities, some new results are achieved and/or others are recovered.