On a formula of the $q$-series $_{2k+4}ϕ_{2k+3}$ and its applications Article Swipe
Related Concepts
Series (stratigraphy)
Mathematics
Pure mathematics
Combinatorics
Geology
Paleontology
George E. Andrews
,
Mohamed El Bachraoui
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.01875
· OA: W4407184984
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.01875
· OA: W4407184984
In this paper we apply a formula of the very-well poised $_{2k+4}ϕ_{2k+3}$ 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.
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