On zeros of polynomials associated with Heun class equations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912669022289920 |
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| author | Mori, Mizuki Takemura, Kouichi |
| author_facet | Mori, Mizuki Takemura, Kouichi |
| contents | Schäfke and Schmidt established that the asymptotics of the coefficients of the local solution to some linear differential equation is related to global structures of solutions. The Heun class equations have the accessory parameters, and we investigate the polynomials whose variable is the accessory parameter which appears as the coefficients of the local solution. By calculating the zeros of the polynomials numerically, we obtain the data of the spectral related to the Heun class equations numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On zeros of polynomials associated with Heun class equations Mori, Mizuki Takemura, Kouichi Classical Analysis and ODEs Mathematical Physics 33E10, 34M03 Schäfke and Schmidt established that the asymptotics of the coefficients of the local solution to some linear differential equation is related to global structures of solutions. The Heun class equations have the accessory parameters, and we investigate the polynomials whose variable is the accessory parameter which appears as the coefficients of the local solution. By calculating the zeros of the polynomials numerically, we obtain the data of the spectral related to the Heun class equations numerically. |
| title | On zeros of polynomials associated with Heun class equations |
| topic | Classical Analysis and ODEs Mathematical Physics 33E10, 34M03 |
| url | https://arxiv.org/abs/2503.10355 |