Applications of q-difference equation and homogeneous q-shift operator rΦs(Dxy) in q-polynomials

Abstract

In this paper, the generalized homogeneous q-shift operator is constructed. The q-difference equation is then utilized to construct numerous polynomial q-identities, such as the generating function and its extension, Rogers’ formula and its extension, and Mehler’s formula and its extension for the generalized q-hypergeometric polynomials. Also demonstrated is a transformational identity involving generating functions for the generalized q-hypergeometric polynomials.

Keywords

• Generating function
• Mehler’s formula
• Rogers formula
• A transformational identity