The Generalized Homogeneous q-Shift Operator _r Φ_s (D_xy ) for q-Identities and q-Integrals
DOI:
https://doi.org/10.24996/ijs.2023.64.11.29Keywords:
homogeneous q-shift operator, Hiene's transformation, Jackson's transformation, q-hypergeometric polynomials, generating function, Rogers formula, Srivastava-Agarwal generating function, Askey-Wilson integral, Andrews-Askey q-integralAbstract
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.