Solutions to variant of $q$-hypergeometric equation of degree 2 associated with $q$-middle convolution
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908852606205952 |
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| author | Arai, Yumi |
| author_facet | Arai, Yumi |
| contents | We investigate the integral representations of solutions to the variant of $q$-hypergeometric equation of degree 2 obtained through $q$-middle convolution by using transformation formulas for $q$-hypergeometric series. We show the correspondence between these integral solutions and solutions obtained by other methods. We also show the linear relationships among the integral solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions to variant of $q$-hypergeometric equation of degree 2 associated with $q$-middle convolution Arai, Yumi Classical Analysis and ODEs 33D60, 33D15 We investigate the integral representations of solutions to the variant of $q$-hypergeometric equation of degree 2 obtained through $q$-middle convolution by using transformation formulas for $q$-hypergeometric series. We show the correspondence between these integral solutions and solutions obtained by other methods. We also show the linear relationships among the integral solutions. |
| title | Solutions to variant of $q$-hypergeometric equation of degree 2 associated with $q$-middle convolution |
| topic | Classical Analysis and ODEs 33D60, 33D15 |
| url | https://arxiv.org/abs/2403.02662 |