The Generalized Homogeneous q-Shift Operator _r Φ_s (D_xy ) for q-Identities and q-Integrals - Abdul-Ghani, Samaher A.; Saad, Husam L. (Iraqi Journal of Science, 2023)
In this paper, we illustrate how to use the generalized homogeneous -shift operator in generalizing various well-known q-identities, such as Hiene’s transformation, the q-Gauss sum, and Jackson’s transfor- mation. For the polynomials , we provide another formula for the generating function, the Rogers formula, and the bilinear generating function of the Srivastava-Agarwal type. In addition, we also generalize the extension of both the Askey-Wilson integral and the Andrews-Askey integral.