Complete asymptotic expansions of the Humbert function $Ψ_1$ for two large arguments
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913893078532096 |
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| author | Hang, Peng-Cheng Hu, Liangjian Luo, Min-Jie |
| author_facet | Hang, Peng-Cheng Hu, Liangjian Luo, Min-Jie |
| contents | In our recent work [SIGMA \textbf{20} (2024), 074, 13 pages], the leading behaviour of the Humbert function $Ψ_1[a,b;c,c';x,y]$ when $x\to\infty$ and $y\to +\infty$ has been derived in a direct and simple manner. In this paper, we obtain the complete asymptotics of $Ψ_1$ in the general case $x,y\to\infty$ along a new path. Indeed, our proof is based on a sharp estimate on ${}_2F_2[a,b-n;c,d-n;z]$, which is valid uniformly for $n\in\mathbb{Z}_{\geqslant 0}$ and large $z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21985 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete asymptotic expansions of the Humbert function $Ψ_1$ for two large arguments Hang, Peng-Cheng Hu, Liangjian Luo, Min-Jie Classical Analysis and ODEs 33C70, 41A60, 30E15 In our recent work [SIGMA \textbf{20} (2024), 074, 13 pages], the leading behaviour of the Humbert function $Ψ_1[a,b;c,c';x,y]$ when $x\to\infty$ and $y\to +\infty$ has been derived in a direct and simple manner. In this paper, we obtain the complete asymptotics of $Ψ_1$ in the general case $x,y\to\infty$ along a new path. Indeed, our proof is based on a sharp estimate on ${}_2F_2[a,b-n;c,d-n;z]$, which is valid uniformly for $n\in\mathbb{Z}_{\geqslant 0}$ and large $z$. |
| title | Complete asymptotic expansions of the Humbert function $Ψ_1$ for two large arguments |
| topic | Classical Analysis and ODEs 33C70, 41A60, 30E15 |
| url | https://arxiv.org/abs/2410.21985 |