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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212346 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments. Peng-Cheng Hang and Min-Jie Luo. SIGMA 20 (2024), 074, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708898057682944 |
|---|---|
| author | Hang, Peng-Cheng Luo, Min-Jie |
| author_facet | Hang, Peng-Cheng Luo, Min-Jie |
| citation_txt | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments. Peng-Cheng Hang and Min-Jie Luo. SIGMA 20 (2024), 074, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-19T07:57:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212346 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T07:57:12Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hang, Peng-Cheng Luo, Min-Jie 2026-02-05T09:54:43Z 2024 Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments. Peng-Cheng Hang and Min-Jie Luo. SIGMA 20 (2024), 074, 13 pages 1815-0659 2020 Mathematics Subject Classification: 33C20; 33C65; 33C70; 41A60 arXiv:2403.14942 https://nasplib.isofts.kiev.ua/handle/123456789/212346 https://doi.org/10.3842/SIGMA.2024.074 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. The authors thank the referees for their valuable comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments Article published earlier |
| spellingShingle | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments Hang, Peng-Cheng Luo, Min-Jie |
| title | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments |
| title_full | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments |
| title_fullStr | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments |
| title_full_unstemmed | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments |
| title_short | Asymptotics of the Humbert Function Ψ₁ for Two Large Arguments |
| title_sort | asymptotics of the humbert function ψ₁ for two large arguments |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212346 |
| work_keys_str_mv | AT hangpengcheng asymptoticsofthehumbertfunctionψ1fortwolargearguments AT luominjie asymptoticsofthehumbertfunctionψ1fortwolargearguments |