Large-degree asymptotic expansions for the Jacobi and related functions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915399295041536 |
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| author | Nemes, Gergő |
| author_facet | Nemes, Gergő |
| contents | Simple asymptotic expansions for the Jacobi functions $P_ν^{(α, β)}(z)$ and $Q_ν^{(α, β)}(z)$ for large degree $ν$, with fixed parameters $α$ and $β$, are surprisingly rare in the literature, with only a few special cases covered. This paper addresses this notable gap by deriving simple (inverse) factorial expansions for these functions, complemented by explicit and computable error bounds. Additionally, we provide analogous results for the associated functions $\mathsf{Q}_ν^{(α, β)}(x)$ and $\mathrm{Q}_ν^{(α, β)}(x)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large-degree asymptotic expansions for the Jacobi and related functions Nemes, Gergő Classical Analysis and ODEs 41A60, 33C05, 33C45 Simple asymptotic expansions for the Jacobi functions $P_ν^{(α, β)}(z)$ and $Q_ν^{(α, β)}(z)$ for large degree $ν$, with fixed parameters $α$ and $β$, are surprisingly rare in the literature, with only a few special cases covered. This paper addresses this notable gap by deriving simple (inverse) factorial expansions for these functions, complemented by explicit and computable error bounds. Additionally, we provide analogous results for the associated functions $\mathsf{Q}_ν^{(α, β)}(x)$ and $\mathrm{Q}_ν^{(α, β)}(x)$. |
| title | Large-degree asymptotic expansions for the Jacobi and related functions |
| topic | Classical Analysis and ODEs 41A60, 33C05, 33C45 |
| url | https://arxiv.org/abs/2411.10942 |