A set of sums for continuous dual q-2-Hahn polynomials

An infinite set {τ(l)(y;r,z)}r,lisanelementofN0 of linear sums of continuous dual q-2-Hahn polynomials with prefactors depending on a complex parameter z is studied. The sums τ(l)(y;r,z) have an interpretation in context with tensor product representations of the quantum affine algebra Uq'(sl(2)) involving both a positive and a negative discrete series representation. For each l>0, the sum τ(l)(y;r,z) can be expressed in terms of the sum τ(0)(y;r,z), continuous dual q2-Hahn polynomials, and their associated polynomials. The sum τ(0)(y;r,z) is obtained as a combination of eight basic hypergeometric series. Moreover, an integral representation is provided for the sums τ(l)(y;r,z) with the complex parameter restricted by |zq|<1. This gives rise to a bilinear summation formula for the continuous dual q-2-Hahn polynomials.