Asymptotics of the Humbert Function $Ψ_1$ for Two Large Arguments
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913462752378880 |
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| author | Hang, Peng-Cheng Luo, Min-Jie |
| author_facet | Hang, Peng-Cheng Luo, Min-Jie |
| contents | Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions $Φ_2$, $Φ_3$ and $Ξ_2$ for two large arguments, but their technique cannot handle the Humbert function $Ψ_1$. In this paper, we establish the leading asymptotic behavior of the Humbert function $Ψ_1$ for two large arguments. Our proof is based on a connection formula of the Gauss hypergeometric function and Nagel's approach (2004). This approach is also applied to deduce asymptotic expansions of the generalized hypergeometric function $_pF_q$ $(p\leqslant q)$ for large parameters, which are not contained in NIST handbook. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics of the Humbert Function $Ψ_1$ for Two Large Arguments Hang, Peng-Cheng Luo, Min-Jie Classical Analysis and ODEs 33C20, 33C65, 33C70, 41A60 Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions $Φ_2$, $Φ_3$ and $Ξ_2$ for two large arguments, but their technique cannot handle the Humbert function $Ψ_1$. In this paper, we establish the leading asymptotic behavior of the Humbert function $Ψ_1$ for two large arguments. Our proof is based on a connection formula of the Gauss hypergeometric function and Nagel's approach (2004). This approach is also applied to deduce asymptotic expansions of the generalized hypergeometric function $_pF_q$ $(p\leqslant q)$ for large parameters, which are not contained in NIST handbook. |
| title | Asymptotics of the Humbert Function $Ψ_1$ for Two Large Arguments |
| topic | Classical Analysis and ODEs 33C20, 33C65, 33C70, 41A60 |
| url | https://arxiv.org/abs/2403.14942 |