Some operator identities and q-series transformation formulas Original Research Article

In this paper, we show how to use the q-exponential operator techniques to derive a transformation formula for the q-Hahn polynomials from the q-Chu–Vandermonde identity. With the same method we also show that the two terms 3φ2 transformation formula of Sears can be recovered from Rogers’ iteration of Heineʹs transformation formula, and the celebrated Sears 4φ3 transformation formula can be derived from his 3φ2 transformation formula with the same method. We also provide new proofs of the three terms Sears 3φ2 transformation formula and an identity of Andrews by our method. We re-derive the q-analogue of Barnes’ second lemma from the q-analogue of Barnes’ first lemma in one step. In addition we generalize two Ramanujanʹs formulas for beta integrals as two more general integrals . Finally, we establish two general transformation formulas for bilateral series.