q²-Kampé de Fériet series and sums of continuous dual q^±2-Hahn polynomials Available to Purchase

Two types of bilinear sums involving continuous dual q²- and q⁻²-Hahn polynomials with a particular choice of parameters are identified with bilinear sums of balanced basic hypergeometric ₂ϕ₂-series. A symmetry relation with respect to the eigenvalues of the polynomials is established for the sum τ(q^2r, z) depending on two further complex parameters r and z. An explicit expression as a linear combination of four q²-Kampé de Fériet series is obtained for a bilateral bilinear sum of continuous dual q^±2-Hahn polynomials. For generic parameters, application of the symmetry relation allows to describe the sum τ(q^2r, z) in terms of eight q²-Kampé de Fériet series. Special cases include partial derivatives of the latter. Five term recurrence relations for τ(q^2r, z) can be derived with respect to each of its parameters. Considerable simplifications are observed at z = −1 or z = q^±1, where the sum τ(q^2r, z) is essentially given by very well poised balanced ₈W₇-series with base q⁴ or q.