On a formula of the q-series 2k+4ϕ2k+3 and its applications

In this paper we apply a formula of the very-well poised 2k+4ϕ2k+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 1(qy,qy-1;q)∞. 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.