| Project/Area Number |
22KF0323
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| Project/Area Number (Other) |
21F21020 (2021-2022)
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Multi-year Fund (2023)
Single-year Grants (2021-2022) |
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| Section | 外国 |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
ネメシュ ゲルグ (2023) 東京都立大学, 理学研究科, 特任准教授 (20994495)
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| Host Researcher |
首藤 啓 (2021) 東京都立大学, 理学研究科, 教授 (60206258)
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| Foreign Research Fellow |
ネメシュ ゲルグ 東京都立大学, 理学研究科, 特任准教授 (20994495)
NEMES GERGO 東京都立大学, 理学(系)研究科(研究院), 外国人特別研究員
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| Project Period (FY) |
2023-03-08 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2023: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2022: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2021: ¥300,000 (Direct Cost: ¥300,000)
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| Keywords | asymptotics / resurgence / exact WKB analysis / Borel summability / asymptotic analysis / special functions / Stokes phenomenon |
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| Outline of Research at the Start |
The topic of the research belongs to the field of asymptotic analysis of mathematics. In mathematics, differential calculus is used to describe the local behaviour of functions, whereas asymptotic analysis tries to capture and study their long-term behaviour. The functions we study originate from quantum mechanical problems.
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| Outline of Annual Research Achievements |
We have established the Borel summability of formal solutions for a broad class of higher-order linear ODEs with a large parameter. The problem of Borel summability for formal solutions of such equations has posed a longstanding challenge in the field of exact asymptotics. A manuscript summarising these results is currently under review. Furthermore, we investigated the resurgence properties of the incomplete gamma function in the transition region by analysing the asymptotics of the late coefficients in its asymptotic expansion. The findings have been published in the journal SIGMA. Prior to this paper, there has been no investigation in the existing literature regarding the resurgence properties of asymptotic expansions in transition regions.
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