A note on the tetrahedral index and the Hahn-Exton q-Bessel function
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908619917754368 |
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| author | Celoria, Daniele |
| author_facet | Celoria, Daniele |
| contents | The purpose of this short note is twofold: First to elucidate some connections between the ``building block'' of Dimofte--Gaiotto--Gukov's $3$D index, known as the tetrahedral index $I_Δ(m,e)$, and Hahn--Exton's $q$-analogue of the Bessel function $J_ν(z;q)$. The correspondence between $I_Δ$ and $J_ν$ will allow us to translate useful relations from one setting to the other. Second, we want to introduce to the $q$-hypergeometric community some possibly new techniques, theory and conjectures arising from applications of physical mathematics to geometric topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the tetrahedral index and the Hahn-Exton q-Bessel function Celoria, Daniele Geometric Topology Classical Analysis and ODEs Number Theory The purpose of this short note is twofold: First to elucidate some connections between the ``building block'' of Dimofte--Gaiotto--Gukov's $3$D index, known as the tetrahedral index $I_Δ(m,e)$, and Hahn--Exton's $q$-analogue of the Bessel function $J_ν(z;q)$. The correspondence between $I_Δ$ and $J_ν$ will allow us to translate useful relations from one setting to the other. Second, we want to introduce to the $q$-hypergeometric community some possibly new techniques, theory and conjectures arising from applications of physical mathematics to geometric topology. |
| title | A note on the tetrahedral index and the Hahn-Exton q-Bessel function |
| topic | Geometric Topology Classical Analysis and ODEs Number Theory |
| url | https://arxiv.org/abs/2510.26079 |