In this paper we apply a formula of the very-well poised \(_{2k+4}\phi _{2k+3}\) to write a k-tuple sum of q-series as a linear combination of terms wherein each term is a product of expressions of the form \(\frac{1}{(qy, qy^{-1};q)_\infty }\) . As an application, we shall express a variety of sums and double sums of q-series as linear combinations of infinite products. Our formulas are motivated by their connection to overpartition pairs.
