A generalization of Zwegers' multivariable $μ$-function
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913737967927296 |
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| author | Shibukawa, G. Tsuchimi, S. |
| author_facet | Shibukawa, G. Tsuchimi, S. |
| contents | We introduce a one parameter deformation of Zwegers' multivariable $μ$-function by applying iterations of the $q$-Borel summation method, which is also a multivariate analogue of the generalized $μ$-function introduced by the authors. For this deformed multivariable $μ$-function, we give some formulas, for example, forward shift formula, translation and $\mathfrak{S}_{N+1}$-symmetry. Further we mention modular formulas for the Zwegers' original multivariable $μ$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalization of Zwegers' multivariable $μ$-function Shibukawa, G. Tsuchimi, S. Classical Analysis and ODEs 33D15, 39A13, 30D05, 11F50, 33D70 We introduce a one parameter deformation of Zwegers' multivariable $μ$-function by applying iterations of the $q$-Borel summation method, which is also a multivariate analogue of the generalized $μ$-function introduced by the authors. For this deformed multivariable $μ$-function, we give some formulas, for example, forward shift formula, translation and $\mathfrak{S}_{N+1}$-symmetry. Further we mention modular formulas for the Zwegers' original multivariable $μ$-function. |
| title | A generalization of Zwegers' multivariable $μ$-function |
| topic | Classical Analysis and ODEs 33D15, 39A13, 30D05, 11F50, 33D70 |
| url | https://arxiv.org/abs/2503.11955 |