A q-series expansion formula and the Askey-Wilson polynomials

Previously, we proved a q-series expansion formula which allows us to recover many important classical results for q-series. Based on this formula, we derive a new q-formula in this paper, which clearly includes infinitely many q-identities. This new formula is used to give a new proof of the orthogonality relation for the Askey-Wilson polynomials. A curious q-transformation formula is proved, and many applications of this transformation to Hecke type series are given. Some Lambert series identities are also derived.