2018 Fiscal Year Final Research Report
New aspects of special functions
| Project/Area Number |
26400122
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Chuo University |
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Principal Investigator |
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| Research Collaborator |
Isojima Shin
Igarashi Hikaru
Kojima Kentaro
Sato Tsukasa
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | ホインの微分方程式 / パンルヴェ方程式 / 超離散方程式 / ｑ差分 / q-Heun equation / Ruijsenaars system / 可積分系 / 特殊関数 |
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| Outline of Final Research Achievements |
Special functions are the important function as well as the elememtary functions. We obtained several results on Heun's differential equation, Painleve equations and their q-deformations.
We investigated the asymptotics of the solutions to the ultradiscrete Painleve II equation. We introduced q-Heun equation and its variants by degerenations of the Ruijsenaars-van Diejen system. We also obtained the results on the relationship with the q-Painleve equations and on the characterization of the variants of q-Heun equation in terms of the difference analogue of the regular singularity and the apparent singularity.
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| Free Research Field |
特殊関数
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| Academic Significance and Societal Importance of the Research Achievements |
超離散パンルヴェ第二方程式における成果は、ｑ離散パンルヴェ方程式やパンルヴェ方程式の解に対する研究への応用につながると考えている。また、q-ホイン方程式の研究は、Luc Vinet, Alexei Zhedanov らの別の動機からの研究にも関係しており、今後の発展につながる可能性がある。
潜在的には、新たな特殊関数として物理学などへの応用が期待される。
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