A formula for the local Heun solution
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917275271954432 |
|---|---|
| author | Šťovíček, Pavel |
| author_facet | Šťovíček, Pavel |
| contents | The local Heun solution is the unique solution to Heun's equation which is analytic in the unit disk centered at $0\in\mathbb{C}$ and taking the value $1$ at the center of the disk. In this paper, as an application of the theory of orthogonal polynomials, we are able to express the coefficients in the corresponding power series as finite multiple sums. In addition, the obtained formula can be used to derive an explicit estimate on the coefficients giving a hint on their asymptotic behavior for large indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A formula for the local Heun solution Šťovíček, Pavel Complex Variables Classical Analysis and ODEs 33E30, 42C05, 47B36, 30D15 The local Heun solution is the unique solution to Heun's equation which is analytic in the unit disk centered at $0\in\mathbb{C}$ and taking the value $1$ at the center of the disk. In this paper, as an application of the theory of orthogonal polynomials, we are able to express the coefficients in the corresponding power series as finite multiple sums. In addition, the obtained formula can be used to derive an explicit estimate on the coefficients giving a hint on their asymptotic behavior for large indices. |
| title | A formula for the local Heun solution |
| topic | Complex Variables Classical Analysis and ODEs 33E30, 42C05, 47B36, 30D15 |
| url | https://arxiv.org/abs/2601.12888 |