Reformulation of $q$-Middle Convolution and Applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910164176601088 |
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| author | Arai, Yumi Takemura, Kouichi |
| author_facet | Arai, Yumi Takemura, Kouichi |
| contents | We reformulate the $q$-convolution and the $q$-middle convolution introduced by Sakai and Yamaguchi, and we introduce $q$-analogues of the addition which is related to the gauge-transformation. A merit of the reformulation is the additivity on composition of two $q$-middle convolutions. We obtain sufficient conditions that the Jackson integrals associated with the $q$-convolution converge and satisfy the $q$-difference equation associated with the $q$-convolution. We present several third-order linear $q$-difference equations and solutions of them by using the $q$-middle convolution and the $q$-analogues of the addition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reformulation of $q$-Middle Convolution and Applications Arai, Yumi Takemura, Kouichi Classical Analysis and ODEs 33D15, 39A13 We reformulate the $q$-convolution and the $q$-middle convolution introduced by Sakai and Yamaguchi, and we introduce $q$-analogues of the addition which is related to the gauge-transformation. A merit of the reformulation is the additivity on composition of two $q$-middle convolutions. We obtain sufficient conditions that the Jackson integrals associated with the $q$-convolution converge and satisfy the $q$-difference equation associated with the $q$-convolution. We present several third-order linear $q$-difference equations and solutions of them by using the $q$-middle convolution and the $q$-analogues of the addition. |
| title | Reformulation of $q$-Middle Convolution and Applications |
| topic | Classical Analysis and ODEs 33D15, 39A13 |
| url | https://arxiv.org/abs/2503.11214 |