Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments
Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions Φ₂, Φ₃, and Ξ₂ for two large arguments, but their technique cannot handle the Humbert function Ψ₁. In this paper, we establish the leading asymptotic behavior of the Humbert function Ψ₁ for two large argumen...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212346 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments. Peng-Cheng Hang and Min-Jie Luo. SIGMA 20 (2024), 074, 13 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions Φ₂, Φ₃, and Ξ₂ for two large arguments, but their technique cannot handle the Humbert function Ψ₁. In this paper, we establish the leading asymptotic behavior of the Humbert function Ψ₁ 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 ₚ ( ⩽ ) for large parameters, which are not contained in the NIST handbook.
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| ISSN: | 1815-0659 |