On a formula of the $q$-series $_{2k+4}ϕ_{2k+3}$ and its applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909474550185984 |
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| author | Andrews, George E. Bachraoui, Mohamed El |
| author_facet | Andrews, George E. Bachraoui, Mohamed El |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01875 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a formula of the $q$-series $_{2k+4}ϕ_{2k+3}$ and its applications Andrews, George E. Bachraoui, Mohamed El Combinatorics Number Theory 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. |
| title | On a formula of the $q$-series $_{2k+4}ϕ_{2k+3}$ and its applications |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2502.01875 |