2025/02/03 by Andrews, George E., Bachraoui, Mohamed El
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2502.01875
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 \frac1(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.